Search

This paper investigates the influence of non-homogeneous elastic foundations on the free vibration characteristics of functionally graded graphene platelets reinforced composite plates submerged in fluid medium. A novel aspect of this study lies in exploring various distributions of the foundation, positioned either centrally within the plates or along their edges. The stiffness of the foundation is computed using Selvadurai's method, which accounts for subgrade soil properties and foundation depth. Material properties of the plates are examined by employing the rule of mixtures alongside the Halpin–Tsai micromechanical model. Hydrostatic pressure and free surface waves are not considered, given the assumption of an ideal and incompressible fluid. The theoretical framework is grounded in a novel inverse trigonometric shear deformation plate theory, where the transverse shear stress distribution is established using a newly developed inverse trigonometric function. The equations of motion are efficiently resolved through Galerkin's method. The efficacy of this approach lies in its utilization of integration to address the distribution issue of the foundation, obviating the need for deploying intricate algorithms. The proposed theory demonstrates enhanced accuracy in predicting natural frequencies compared to other published shear deformation plate theories. Moreover, this paper delves into the effect of material properties and the fluid environment on the natural frequencies of the structures. Particularly significant is our thorough investigation of the impact of variations in the locations, material properties, and sizes of the foundation on the free vibration of these plates, all of which bear great importance in structural design. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation on optimum layer thickness and fiber orientations of laminated composite plates against buckling under complex loading conditions by using a new optimization procedure that effectively utilizes computational efforts. In this proposed procedure, a finite element model of the laminated composite plates is developed for the buckling analysis and the interior point optimization procedure is used to maximize the buckling coefficient, aiming to determine the optimum values of fiber orientation angles and thickness. In optimization scenarios, the laminated composite plates are subjected to single and complex loading conditions, including compression, shear, bending and a combination of two or more of these loading types. The computational performance of the proposed optimization procedure is evaluated to investigate and present the effect of various factors including the number of layers, length-to-thickness ratios, aspect ratios, and boundary conditions on the optimum buckling analysis. [ABSTRACT FROM AUTHOR]

This paper presents the delamination impact over the dynamic response of the variable angle tow (VAT) composite plates. The VAT plates with various fiber angles are constrained to different boundary conditions for parametric investigation, while delamination is made to present over two different locations with varying sizes. A comparative stochastic vibration study is performed to evaluate the contribution of composite properties to delaminated and intact plates. The randomness in the material properties is modeled with the efficient Latin hypercube sampling method. The polynomial neural network-based surrogate model, considered an efficient substitute for computationally expensive Monte Carlo simulation, is employed in the present work to examine the stochastic behavior of VAT plates. The contribution of the composite properties on the uncertain vibration characteristics is evaluated. It is observed from the investigations that the sensitivity of the composite properties varies significantly with the delamination. Lastly, a failure probability estimation is carried out with a developed polynomial neural network-based surrogate model to provide safe design estimation for various cases. [ABSTRACT FROM AUTHOR]

In this paper, a meshfree Jacobi point interpolation (MJPI) approach for the free vibration and stationary stochastic response analyses of heated composite laminated plate with varying thickness and curvilinear fiber is developed. The theoretical formulations for heated composite laminated plate with varying thickness and curvilinear fiber are established by using Hamilton's principle in framework of first order shear deformation theory. The effect of thermal stress generated by the temperature variation is considered based on the thermo-elastic theory. The displacement components of the plate are approximated by using the MJPI shape function. The boundary conditions considered in this study are achieved by using the artificial spring technique. The accuracy and reliability of the proposed MJPI shape function are confirmed by comparing with numerical results from the published literature and finite element software ABAQUS. Several comparisons show that the differences between the numerical results from current method, reference and ABAQUS software are less than 1%. Finally, the effects of different parameters such as temperature difference, fiber direction coefficient, thickness gradient and thickness power index on the free vibration and stationary stochastic response of the composite laminated plate are investigated. [ABSTRACT FROM AUTHOR]

The low power density and high frequency loss of the core limits the miniaturization of high-frequency transformers (HFT) with an increase of the switching frequency. In this paper, a composite core with laminated nanocrystalline films and ferrite sheets is proposed based on the high saturation magnetic flux density of nanocrystalline and the low loss of ferrite. The two materials are laminated at a certain thickness ratio to form a composite unit. Then multiple layers of units are stacked to form the composite core. A homogenization model is established to calculate the equivalent permeability. Then the magnetic field strength of the composite core can be obtained, which can be used to calculate the magnetic flux density in different materials. An optimization model is built with the objective of optimizing the core loss and power density by adjusting the thickness ratio. Based on the non-dominated sorting genetic algorithm II (NSGA-II), it obtains the optimal thickness ratio. Simulation results show that the composite core increases the magnetic flux density from 0.3 T to 0.55 T over a ferrite core. A 100 V/200 V, 1 kW, 20 kHz composite core HFT prototype is developed. The power density is increased by 23.5% when compared to a ferrite HFT. The core loss is reduced by 37% when compared to nanocrystalline HFT, and the efficiency is increased from 94% to 96.5%. [ABSTRACT FROM AUTHOR]

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate's thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin's method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear forced vibration responses of axially moving functionally graded carbon nanotube reinforced composite (FG-CNTRC) rectangular thin plates are investigated. In the frame of classical plate theory and von Kármán geometric nonlinear theory, the nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are established by Hamilton's principle and discretized through the Galerkin method. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in the literature. The frequency response curves (FRCs) of axially moving FG-CNTRC plates subjected to transverse harmonic concentrate excitation are calculated by using the incremental harmonic balance (IHB) method. The stability and bifurcation characteristics of period solutions obtained through the IHB method are analyzed by Floquet theory. The isolated detached resonance curves (DRCs) are observed inside the main continuous FRCs of axially moving FG-CNTRC plates. Saddle-node bifurcation, Hopf bifurcation, quasi-periodic motion and the internal resonance caused by the modal coupling effect are analyzed. The numerical results illustrate the effects of the CNT distribution, volume fraction, axially moving velocity, aspect ratio and width-to-thickness ratio on the nonlinear dynamic responses of axially moving FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

The advantages of carbon nanotubes (CNTs) in fortifying the glass fiber reinforced polymeric (GFRP) composites are discussed in this paper. Bolted steel straps are utilized at the edges of composite plate to establish clamped conditions in the test setup. To minimize uncertainties caused by bolt attachments, a genetic algorithm-based model updating approach has been implemented by introducing artificial linear springs at the margins to achieve a better balance between theory and reality. The accuracy of the plate's results (natural frequencies and mode shapes) is verified, and the mechanical properties of randomly dispersed CNTs are incorporated in the formulations of folded plates. Remarkably, the motion equations are brought forward by the first order shear deformation theory (FSDT). Thereafter, two-directional generalized differential quadrature (2D-GDQ) technique is employed to determine natural frequencies from available motion, continuity, and boundary equations. The results of the folded plate are validated first by an experimental modal testing and finally some effective parameters such as folding angle, CNT weight ratio, boundary condition and flange-shape length are examined. [ABSTRACT FROM AUTHOR]

By using an effective theoretical model, efficiency and accuracy of design for laminated plates can be significantly improved. However, the existing five-variable higher-order models will encounter difficulty to accurately produce interlaminar stresses, which will influence evaluation on interlaminar performance of laminated plates. Thus, this paper attempts to propose an efficient higher-order model with five variables, where the Legendre polynomial is introduced into in-plane displacement field at each layer. By enhancing compatible condition of displacements and equilibrium condition of stresses, the unknowns depending on the layer number have been eliminated. Differing from other existing five-variable higher-order models, the proposed model can describe the zig-zag effect of in-plane displacements, and fulfill continuity of transverse shear stresses at interfaces. The governing equations are further derived through the principle of virtual displacement, and analytical solutions for only simply-supported plates have been presented. To assess the capability of the proposed method, three-dimensional elasticity solutions have been employed for comparison, and other five-variable higher-order models from the literature have been also chosen for assessment. Numerical results show that the proposed model possesses the same computational efficiency as the selected five-variable models, but can predict more accurate results. In addition, the proposed model is employed to analyze bending behaviors of sandwich and composite plates, and accurate results can be also acquired. Therefore, the present model is proposed to design laminated plates. [ABSTRACT FROM AUTHOR]

The nonlinear static and vibration response of micro composite sandwich plate with honeycomb core have been investigated in this paper. The displacement–strain of skins via higher-order shear deformation theory (HSDT) is obtained. In frame work Halpin–Tsai model the composites plate with two layers of Graphene platelet reinforcement (GPLRC) with uniform distribution pattern and a hexagonal honeycomb core is considered. The governing equations of sandwich plate are derived by implementing Hamilton's principle and solved Perturbation method. For investigating the accuracy, this paper is validated with other previous researches and a good correlation is observed between the results. Finally, the important findings of this research indicate that the ratio of core thickness, inclined angle, and thickness to inclined length have significant effects on nonlinear frequencies–amplitude and deflection response. Based on the results of this article designers can development of different parts of aircraft. [ABSTRACT FROM AUTHOR]

The paper investigates the normal interaction between the steel striker, carbon fiber and aramid fiber reinforced plastic plates at a speed ranging from 166.6 to 184.2 m/s. A series of physical and numerical experiments with impact load is conducted to design a mathematical model and numerical algorithm for the composite plate. The behavior and fracture of composites are described by the elastic-brittle model accounting for their different compressive and tensile strengths. The numerical simulation utilizes the finite element method in the EFES software developed by the authors. [ABSTRACT FROM AUTHOR]

Extracting time-varying dynamic characteristics of an aerospace structure under thermal-vibration environment is difficult and complicated since the material properties of the structure fluctuate although the external load is constant. Initially, a composite plate model applied for time-varying system is updated based on finite strip method. Afterward, a thermal-vibration experimental system for realizing high-precision data measurement is designed, and the preliminary experiment certified the validity of experimental method. Finally, the time-varying dynamic characteristics of a typical thermal protective system plate is researched. Results show that the natural frequencies take a downward tendency with respect to heating time, and will undergo a dramatic decrease when the structure reaches the critical bulking temperature, while the damping characteristic shows an adverse trend. In addition, for certifying the applicability and accuracy of the updated model, comparisons between present model and recursive subspace method are conducted. The purpose of this paper is to provide some references on evaluating stability for aerospace structures under severe flight environment. [ABSTRACT FROM AUTHOR]

A static package design of a functionally graded porous plate in microscale which is coated by two polymeric piezoelectric carbon nanotubes reinforced composite (CNTRC) face sheets is provided in this study. The microstructure rests on the Pasternak foundation and is subjected to thermal load. Furthermore, face sheets are subjected to the electric field. With the aid of a quasi-3D hyperbolic shear deformation theory, governing equations of the microplate are derived and then its critical buckling loads are calculated. The properties of all layers alter continuously along with thickness direction due to the CNTs and pores distributions. The size effects are captured by the means of modified couple stress theory (MCST). By conducting the current study, the results emerged in detail to assess the effects of different parameters on buckling of structure. For instance, it is revealed that the highest and lowest critical buckling load and consequently stiffness, is due to the V–A and A–V CNTs dispersion type, respectively. Furthermore, it is revealed that by porosity coefficient enhancement, critical buckling load and consequently, stiffness are reduced dramatically. Current paper outcomes can be used in different fields of sciences such as optimum design of engineering structures or various high-tech industries as aerospace factories. [ABSTRACT FROM AUTHOR]

This paper focuses on optimizing the submerged arc welding encapsulation for domestic steel mills producing bridge stainless steel composite plates. It utilizes a combination of numerical simulation and experimental methods to investigate the changes in temperature field and stress field at the weld joint of the Q370qE/31603 stainless steel composite plate using submerged arc welding. The submerged arc welding of Q370qE/31603 stainless steel composite plate is modeled by the ABAQUS software. The submerged arc welding heat source model is represented by double ellipsoidal heat source model and written in Fortran language. The correctness of the stress field was verified by a layer-by-layer electrolytic polishing method based on the X-ray diffraction method to measure the residual stress at different locations after welding. The simulation and experimental results show that the finite element model is very effective for predicting the temperature and stress of submerged arc welding. By changing the parameters of the submerged arc welding process, the effects of different welding process parameters on the temperature field during the welding process, and the distribution state and pattern of post-weld residual stress were studied. Additionally, the research on the thermo-mechanical coupling for the submerged arc welding process of stainless steel composite plate has been carried out; it was found that there is a strong interaction between temperature and stress fields. The hot rolling tests of the stainless steel composite plates were conducted after welding encapsulation to verify the effectiveness of the submerged arc welding encapsulation model. [ABSTRACT FROM AUTHOR]

In this paper, a low-power fully acoustic non-destructive testing (NDT) of glass fiber-reinforced composite plate has been presented. Input acoustic power in microwatt range was used for local defect resonance (LDR)-based delamination activation. Besides experimental results, numerical simulations were carried out via commercial ABAQUS platform. An oblique incident wave interaction with 3D composite plate was created, and the sound radiation pattern over the plate was studied with an air layer over the plate. In experiment, the sound was generated by a piezospeaker, while a MEMS microphone was used for reception over the plate. Moreover, a laser Doppler vibrometer was utilized for the LDR frequency and corresponding mode shape validation. Frequency spectrum, mode shape at LDR frequency, best wave impinging angle, efficiency, and sound directivity patterns were studied, with angles θ, ϕ = 10°, 30° being found to correspond to the best direction for sonic excitation. Moreover, fully acoustic system was found to be more efficient than partial acoustic system, i.e., that with contact excitation. The proposed method can be used for inspection of large structures taking advantage of the long-distance non-contact excitation. [ABSTRACT FROM AUTHOR]

This paper studies the ultimate strength and progressive damage behavior of imperfect composite laminated plates under end-shortening strain using the semi-analytical finite strip method (FSM). Plates with various thicknesses and boundary conditions are perused. First-order shear deformation theory with the assumption of large deflections is considered. To analyze the failure in the laminates, the Hashin and Rotem failure criterion is used, and once the failure occurs, the material properties decrease instantaneously. Three different scenarios have been considered to apply material properties degradation in the failed ply: the complete ply degradation scenario, the strip degradation scenario (SDS), and the strip region degradation scenario. In the first scenario, the properties of the entire ply are degraded instantaneously after predicting the failure. In contrast, in the SDS, the reduction of material properties occurs only in the strip where the failure has occurred. In the third scenario, in order to increase the accuracy of damage analysis, each strip is divided into three regions, and material properties are degraded in the strip's region where the failure has happened. A convergence study is performed with regard to both the number of terms of displacement fields along the strip and the number of strips used across the laminates. To validate the damage responses, the results obtained by the proposed method have been compared with the finite element method (FEM) and available results in the literature. The introduced approach overcomes the limitations of previous methods, such as Ritz, in applying different boundary conditions and is much more suitable than the FEM in terms of simplicity of implementation and computational time. [ABSTRACT FROM AUTHOR]

With the special physical characteristics, graphene is considered as an excellent candidate for various engineering applications. Due to the electromechanical coupling properties and significant variations in material characteristics at the interfaces of adjacent layers, existing higher-order models reported in the literature may lack the necessary capability to achieve precise prediction of natural frequencies for piezoelectric graphene-reinforced composite plates. This paper will develop advanced plate theory for the vibration analysis of graphene-reinforced composite plates with a macro fiber composite piezoelectric layer. The number of displacement variables in the developed theory is independent of the layer number. In contrast to earlier higher-order theories, the proposed plate theory incorporates a modified interlaminar shear stress field that accounts for the electromechanical properties. Furthermore, the modified transverse shear stress field can be adsorbed in the equations of motion by means of Hamilton's principle, which can effectively improve the ability to predict natural frequencies of piezoelectric laminated plates. Using the exact solutions and the results obtained from other theories, the performance of the developed theory is evaluated. Compared with the existing higher-order models, the proposed theory is more accurate in predicting natural frequencies. Additionally, a parametric study is conducted for the influences of several significant parameters of graphene and the piezoelectric plate on the vibration responses of the smart composite plates with graphene reinforcements. [ABSTRACT FROM AUTHOR]

In this paper, a rectangular bistable composite laminated plate is studied through dynamic modeling, numerical simulation and experiment. A theoretical model is elucidated, elaborating the dynamic snap-through and nonlinear dynamics of the rectangular bistable composite laminated plate. The potential energy curve, the restoring force curve and the stiffness curve are graphically presented, exhibiting differences from those of square bistable plates. The two potential wells and the negative stiffness region are asymmetric. The dynamic snap-through elucidated by curvature and displacement is graphically presented in phase diagrams and time history diagrams. Due to the asymmetry of the double potential wells, the dynamic snap-through may be unidirectional rather than repeated, and the nonlinear dynamic responses around the two potential wells are asymmetric, which depends on initial positions. In frequency sweep, the frequency-amplitude response curves are characterized by the softening nonlinear stiffness effect and the hysteresis, where there are multiple peaks displaying the first several modes of the rectangular bistable plate around one stable state. The nonlinear dynamic responses are characterized by the periodic and chaotic vibrations, the 1/2 subharmonic resonance, the unidirectional dynamic snap-through and the repeated dynamic snap-through. When the excitation frequency is equal to the first mode frequency for the lower stable state or the third mode frequency for the upper stable state, the dynamic snap-through is found to occur. Linear mode frequencies can show the mechanism of the snap-through to a certain extent. At mode frequencies, sufficient energy is gathered to actuate the snap-through. Unlike square bistable plates, rectangular bistable plates may only be characterized by the unidirectional snap-through under the specific energy input, which depends on initial positions. For rectangular bistable plates, two opportune excitation frequencies that have to be selected can lead to the repeated snap-through. This research is beneficial to the development of aerospace structures, bistable energy harvesters and vehicle vibration isolation devices. Compared to the old work, this work is more in line with the actual situation, where a high aspect ratio morphing wing can adjust its airfoil according to different tasks based on rectangular bistable plates which are more suitable for potential applications in the future. [ABSTRACT FROM AUTHOR]

The analysis of a composite plate by refined plate theories is presented in this paper. The displacement fields of monolayer plate are expressed by means of Carrera unified formulation (CUF), and Taylor-like series expansion is employed along the thickness direction. The governing differential equation of monolayer plate is derived by Hamilton's principle, and the related element stiffness matrix, mass matrix, and load vector are obtained. The element matrix of composite plate is obtained by superimposing single-layer plate elements, and the global matrix is obtained in the finite element framework. Due to the shear locking phenomenon of thin plate, the higher-order model is revised by tensor component mixed interpolation (MITC). The accuracy and reliability of the present model are demonstrated by comparing with classical plate model (classical plate theory and first-order shear deformation theory) and a solid model generated in the commercial software ANSYS. Meanwhile, the geometric parameter optimization of composite plate is studied based on the constructed higher-order model by the multi-objective genetic algorithm. [ABSTRACT FROM AUTHOR]

The objective of this paper is to numerically characterize the interaction effects between the plasticity of composite patch repaired aluminum plates and the damage to the adhesive bonding the plate and the composite. An experimental study was conducted to validate the numerical approach used. In the experimental approach, fatigue tests were carried out on notched specimens for both aluminum alloys: 2024 T3 and 7075 T6. In the numerical part, the aluminum plate with the composite patch and the adhesive was modeled. It was assumed an elastoplastic behavior of the aluminum alloy and the adhesive. It was integrated the damage zone law into the calculation code to predict the damage in the adhesive. The numerical study allowed to correlate the damaged area in the adhesive and the plastic area in the repaired aluminum. Based on the results obtained, 2024-T3 alloy has better fatigue life and reduced crack propagation rate compared to 7075-T6 alloy. [ABSTRACT FROM AUTHOR]

The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical. [ABSTRACT FROM AUTHOR]

In this paper, free vibration of rotating functionally graded (FG) porous eccentric semi-annular (ESA) and eccentric annular (EA) plates reinforced with graphene nanoplatelets (GPLs) in a thermal environment is solved with the help of transformed differential quadrature method (TDQM). Symmetrical and asymmetrical distributions are considered for both the porosity and the graphene nanoplatelets; the estimation of the Young's modulus is conducted by the model of Halpin–Tsai. A higher-order shear deformation theory is considered as the basis for the employment of the Hamilton's principle for the derivation of both the initial equations of the plates-up to the dynamic equilibrium point and the oscillation phenomena afterward. The method of TDQ utilizes a conformal mapping in order to obtain the DQ weighting coefficients and then discretizes the partial differential equations of the motion, as well as the boundary conditions; this discretization takes place in the physical domain directly. The results indicate that the employed numerical approach is advantageous in high solution accuracy in addition to fast convergence rate. Furthermore, the variation of the natural frequencies of the FG plates with different boundary conditions is investigated by taking into account the influences of several parameters: the geometry, such as eccentricity, thickness ratio, radius ratio; the material, such as the type of porosity and GPLs, the porosity parameter and the weight fraction of GPLs, and other parameters, such as temperature difference and rotating speed. [ABSTRACT FROM AUTHOR]

This paper deals with the natural frequency and stability of axially moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular thin plates. Based on Reddy's first-order shear deformation theory, the partial differential equations of motion for axially moving FG-CNTRC plates in thermal environment are derived by Hamilton's principle and discretized by the Galerkin method. The in-plane displacement and inertia of the plate are retained in the dynamic model. By solving the complex eigenvalues of the gyroscope system, the variations of natural frequencies of the axially moving FG-CNTRC plates with axial moving velocity are obtained, and the stability of the plates is analyzed. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in literature. The divergence and flutter type of instability, critical divergence velocity, and critical flutter velocity are studied. The numerical results reveal the effects of CNT distribution, volume fraction, aspect ratio, width-to-thickness ratio, and temperature rise on the natural frequencies of the plates. Additionally, the effects of geometry parameters on the critical divergence velocity and critical flutter velocity of axially moving FG-CNTRC plates are studied by plotting the instability regions. [ABSTRACT FROM AUTHOR]

Without regarding interlayer continuity of transverse shear stresses in the displacement expressions, traditional higher-order plate theories have difficulty in predicting continuous shear stress fields accurately for multilayered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with independent CNT distributions in each layer. In this paper, a new higher-order continuous shear stress multilayered plate model is developed for high-accuracy analysis of FG-CNTRC plates. In the theoretical formulation, higher-order interpolation functions and piecewise descriptions are adopted for transverse shear stress fields. By fulfilling the interlayer continuity of shear stresses and displacements, the displacement expressions for FG-CNTRC plates are formulated. The accuracy of the proposed model is determined by two kinds of parameters: the order of assumed transverse shear stress fields and the number of subdivisions. Compared with traditional higher-order theories, the proposed model can accurately predict continuous transverse shear stresses for FG-CNTRC plates with different CNT configurations by constitutive relations directly. Additionally, a four-node rectangular plate element associated with the proposed model is formulated. Results show that the proposed model agrees well with the exact solutions and results from ANSYS. With the same amount of calculation, the proposed higher-order model has higher accuracy than the model with more subdivisions, especially for asymmetric plates with discontinuous CNT ply angle. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for simulating the crack propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The numerical method is based on 2-D natural element method (NEM) which can overcome the inherent demerits of FEM and conventional meshfree methods. The 3-D displacement field of cracked orthotropic plate is formulated using the (1, 1, 0)* hierarchical model and approximated by 2-D NEM. The thickness-wise mixed-mode stress intensity factors (SIFs) are computed using the modified interaction integral I(1,2) and the 2-D complex-valued crack-tip singular fields. The crack propagation angle is determined by the modified maximum circumferential stress (MCS) criterion, and the crack trajectories are predicted by an incremental crack propagation simulation scheme. The present numerical method is verified from the comparison of predicted crack trajectories with the published reference solutions. Moreover, using the developed numerical method, the crack trajectory characteristics of FG-CNTRC plates are parametrically investigated with respect to the major parameters. From the parametric investigation, it is found that the crack trajectories of FG-CNTRC are significantly influenced by the material orientation angle and the stiffness ratio. But, the effects of the initial crack angle and the volume fraction and volume fraction pattern of CNTs are not remarkable. [ABSTRACT FROM AUTHOR]

Based on Gurtin–Murdoch's theory, a new mechanistic laminated nanoplate model composed of nanocomposites under various boundary conditions is proposed, where the top and bottom surfaces of the laminated nanoplate are regarded as two-dimensional films which have independent surface elastic parameters. The influence of surface Lamé constants and residual stress on static bending and vibration properties for the laminated nanoplate is studied. In order to get approximate solutions of bending deflections and first-order frequencies for the laminated nanoplate with complex boundary conditions, the variational method is employed in this paper. The effectiveness of the presented variational method is verified by comparison with available results. Numerical results indicate that the effective bending stiffness of the laminated nanoplate considering surface effects is obviously different from the classical result. Moreover, the influences of surface effects on bending deflections and first-order frequencies are related to the surface elastic parameters and boundary conditions. The presented method and results provide a theoretical benchmark for other numerical and experimental methods to study nano laminates. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the deep learning technique of the artificial neural network method is used to determine the free vibration parameters of the rectangular bistable composite plates. For this purpose, first, the static and free vibration behaviours of a cross-ply bistable composite plate are studied using analytical, finite element and experimental methods. By comparing them, it is turned out that there is a considerable difference among obtained natural frequencies so that the analytical method is only able to determine the fourth natural frequency and cannot estimate the first three natural frequencies. To solve this problem, the deep neural network is employed to model the modal parameters of the bistable laminate as an explicit mathematical relationship that can be generalized to the other bistable composite plates. This mathematical relation makes it possible to obtain the natural frequencies in each of the stable configurations based on the geometric dimensions of the plate. In the following that, the inverse problem method is considered and the mode management capability is investigated. A fast swarm intelligence algorithm called firefly algorithm is used to optimize the optimization function of the mode management problem. Mode management using the evolutionary algorithm provides the appropriate physical dimensions of the plate according to the scenarios for natural frequencies arrangement. The results are validated by comparing them with those obtained by the finite element method and experiment test, which results show that this method estimates the modal parameters with high accuracy. The method used in this paper can also be applied to determine the modal parameters of other morphing structures. [ABSTRACT FROM AUTHOR]

In this paper, a new bending model for composite laminated shells is proposed based on the refined zigzag theory. This new model is superior to the previous shell models based on the first-order shear deformation theory (FSDT) by introducing in-plane linear zigzag functions along the thickness direction, such that the shear correction coefficients can be omitted. In the present formulation, the bending equilibrium equations and boundary conditions of composite laminated shells are established by the virtual work principle. Without losing generality, Navier series solutions are used to describe the static properties of the composite laminated shells. In order to evaluate the effectiveness and performance of this new model, numerical examples are carried out to discuss the effect of the lamination schemes and geometric parameters on the static properties. In addition, the results are compared with the three-dimensional (3D) elastic theory and FSDT as well as the highly accurate theories in the literature to examine the accuracy. It is observed that the present model not only has the high accuracy of the high-order or other highly accurate models, but also has the intrinsic linear terms of the first-order models, such that it is very suitable for the future deducing finite element method to analyze the large-scale laminates with high computational efficiency. Therefore, the present new model can be a good candidate for engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, the bending deformation, free vibration and forced vibration of one-dimensional hexagonal quasicrystal layered plates with imperfect interfaces are investigated. The generalized linear spring layer model is adopted to simulate the interface bonding defects caused by the slip or debonding of quasicrystal materials due to actual production or interlayer aging. The imperfect interface transfer matrix is established for one-dimensional hexagonal quasicrystal layered plates and the analytical solutions of phonon displacements, phonon stresses, phason displacements and phason stresses for static bending, the natural frequency for free vibration, and the displacements of phonon and phason fields for forced vibration under a harmonic excitation are then derived by the pseudo-Stroh formalism. Numerical examples are provided to analyze the influence of the stacking sequence and the imperfect interface parameter of two sandwich plates composed of crystal and quasicrystal materials on the bending deformation and vibrational response of layered quasicrystal composite plates. Furthermore, the presented three-dimensional plate model is applied to quasicrystal-coated aluminium-based composites in engineering practice. [ABSTRACT FROM AUTHOR]

In this paper, interlaminar stresses in a symmetrical laminated composite plate with a circular hole under uniform heat flux were examined. The analytical solution was achieved based on the boundary-layer theory by Lekhnitskii's solution. The stress relations related out-of-plane stress components were obtained by variational principle states, the minimum principle of complementary energy, zero-order equilibrium relations and boundary conditions for each layer. The unknown factors in the stress relations were obtained by the equilibrium equation in integral form. This solution prepared a calculation method via adaptability for examining the 3D thermal stresses in perforated laminated with curved boundaries. The results were obtained for [ 45 / - 45 ] s, [0/90]s, [ 30 / - 30 ] s lay-ups made of graphite/epoxy and glass/epoxy materials. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic stability analysis of moderately thick viscoelastic plates is performed employing the Boltzmann integral law with constant bulk modulus. The remarkable and new point of the proposed method is that the frequency of a Mindlin viscoelastic plate subjected to simultaneous constant and harmonic in-plane compressive loads is explicitly predictable based on free vibration analysis of an elastic plate. Moreover, the damped part of frequency is easily calculated. Also, the critical excitation for which the system becomes unstable is determined. This method is completely new and significantly reduces the computational cost. The obtained results are compared with other existing results to show the efficiency and accuracy of the proposed method. This method is used to investigate the effects of viscoelastic properties and in-plane compressions on the steady-state responses of Mindlin viscoelastic plates under time-dependent compressive loads. [ABSTRACT FROM AUTHOR]

To find out impact induced defects in a large aerospace structure is quite time consuming due to the large scanning area to be considered. Accurate localization of impacts could narrow the scanning area and improve testing efficiency. In this paper, the multi-frequency characteristic of impact induced guided waves is analyzed. The time of arrival features at various frequencies are extracted from time domain signal by continuous wavelet transform, cross-correlation and Hilbert transform. Two methods, namely image fusion and artificial neural network, are proposed to accomplish the fusion of multi-frequency features. The results show that the mean localization error for the two fusion methods are 4.39 mm and 3.61 mm respectively, the median error for the two methods are 3.56 mm and 3.13 mm. [ABSTRACT FROM AUTHOR]

In Wangermez et al. (Comput Methods Appl Mech Eng 365:113032, 2020) a second-order coupling strategy of a macroscopic description of a structure and an heterogeneous lower scale description of some local details was proposed. As such, the proposed coupling technique is quite elaborate and not suited for an implementation in a legacy code. The purpose of this paper is to facilitate its implementation by means of a dedicated non-intrusive technique. This leads to several implementation propositions, including the use of MPC conditions, which are available in most of the finite element solver. Its interest is that it does not require any modification of the numerical models and can be implemented with any finite element simulation software. The proposed method has been implemented in the finite element Software Z-set™ used by Safran and is illustrated on an example of a 3D woven composite plate in which a severe weaving defect is introduced. [ABSTRACT FROM AUTHOR]

In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling, or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle. [ABSTRACT FROM AUTHOR]

In this paper, a boundary node method is presented to study wave propagation in laminated composite plates. The Zig-Zag theory of Cho and Parmerter is used for deriving the governing equations of laminated plates. To the best of the authors' knowledge, this study is the first one employing the theory in non-stationary dynamic plate problems addressing wave propagation issues. For this theory, there is no information about the Green's functions and thus the presented method can be considered as an alternative to the boundary integral method. With the use of exponential basis functions (EBFs), the response of the structure is first found in the frequency domain and finally the time-domain response is obtained using inverse Fourier transformation. The EBFs are found so that they satisfy the governing equations in the frequency domain. For the first time, in this paper, we shall present explicit relations for the EBFs in the frequency domain for Cho and Parmerter's Zig-Zag theory. The coefficients of the EBFs are found through the collocation of the boundary conditions. The dynamic analysis of some composite laminated plates is presented, and the results are compared to those obtained from the dynamic analysis of two-/three-dimensional finite element method (FEM). We shall discuss the capabilities and limitations of the theory and the solution method. The capability of the method, in the analysis of problems excited by high-frequency loads, is shown in the solution of wave propagation problems for which the FEM needs excessive number of elements and thus it is practically impossible to be applied. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration analysis of combined composite laminated conical–cylindrical shells with varying thickness using the Haar wavelet method (HWM). The displacement field of the combined shell is set based on the first-order shear deformation theory (FSDT), the displacement components, and rotation of individual shells including boundary conditions that are expanded by the Haar wavelet and Fourier series in the meridional and the circumferential direction. By solving the vibration characteristic equation discretized by the Haar wavelet, the vibrational results of combined shells are obtained. Then, the results of the proposed method are compared with those of published literature and finite element analysis (FEA). The results show that HWM has high convergence and high accuracy for the free vibration analysis of the combined composite laminated conical–cylindrical shells with varying thickness. Also, the effects of the parameters such as thickness variation parameters, material properties, geometrical dimensions, and different boundary conditions, on the vibrational behavior of the combined shells are investigated. Finally, new numerical results are provided to illustrate the free vibration behavior of the combined composite laminated conical–cylindrical shells with varying thickness. [ABSTRACT FROM AUTHOR]

In this paper, a progressive damage analysis of two-dimensional C/SiC composites and superalloy mechanically fastened joint with countersunk bolt is implemented to simulate the uniaxial tensile loading process by using a user-defined subroutine UMAT embedded into the general package Abaqus. On basis of the developed damage model, a parametric study is carried out to illustrate the effects of countersunk parameters on tensile performance for the hybrid bolted joint. It is found that there are negligible changes in the stiffness of the bolted joint, as the countersunk height varies from 1.5 to 2.5 mm for the considered bolt-head diameter cases. However, the failure load of the ceramic matrix composite and superalloy hybrid joint exhibits significant changes under different combinations of countersunk parameters. Increasing the countersunk height of the bolt intensifies the initial stress concentration and results in the redistribution of stress around the hole-edge area of the composite material plate. For the bolt-head diameter and countersunk height equal to 9.4 and 1.5 mm, respectively, the joint structure ensures the maximum load-bearing capacity for the studied joint with a countersunk bolt. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of several meta-heuristic algorithms, including Particle Swarm Optimisation (PSO), different variants of Differential Evolution (DE), Biogeography-Based Optimisation (BBO), Cultural Algorithm (CA), Optics-Inspired Optimisation (OIO), and League Championship Algorithm (LCA), for optimum layup of laminated composite plates. The study provides detailed Pseudo codes for different algorithms. The buckling capacity maximisation of a 64-layer laminated composite plate under various load scenarios has been considered as the benchmark problem, in which the design variables are the stacking sequences of layers. A Deep Statistical Comparison (DSC) method is employed to rank the performance of different algorithms. The DSC uses a nonparametric two-sample Kolmogorov-Smirnov test to conduct the performance comparisons between the algorithms. The overall performance rankings obtained from the DSC suggest that the LCA, OIO, and PSO algorithms perform remarkably better in comparison to other algorithms. The comparisons provide some interesting conclusions on the performance of different algorithms. [ABSTRACT FROM AUTHOR]

How to improve the bonding ability and quality performance of heterogeneous plates has always been one of the difficult problems in the field of high-performance heterogeneous composite sheet forming and manufacturing. In this paper, a new manufacturing method of heterogeneous clad plate, hard plate rolling clad plate, is proposed. The hot rolling process of Al/Mg/Al composite slab with or without hard plate was studied. The results show that the shear stress in the rolling direction (RD) can be transformed into the compressive stress in the normal direction (ND), and then the welding pressure between different composite layers can be increased. This method can suppress the bending and edge crack defects and significantly improve the shape quality and forming ability. At the same time, through the study of the interface structure of the composite plate, it can be known that the metallurgical bonding can be achieved with a small reduction after adding the hard plate. Two clear layers of Al3Mg2 and Al17Mg12 intermetallic compounds appear at the Al/Mg interface. The thickness of the diffusion layer is significantly larger than that of the traditional hot-rolled clad plate, and the thickness of the diffusion layer can reach 38 μm when the reduction is 60%. The yield strength is 172.3 MPa and the elongation is 21.5%. To sum up, the hot rolling of hard-plate provides a new idea for the forming and manufacturing of high performance heterogeneous composite plate. [ABSTRACT FROM AUTHOR]

Applications of skew plates in the practical civil engineering are well-established. A look into the papers about the failure of laminated composite structural elements revealed that composite skew plates have not been studied for failure in detail. The first-ply failure load and frequency reduction due to such a failure are reported considering practical parametric variations of composite skew plates. Different well-established failure criteria, including the most recent Puck failure criterion, are used to investigate the first-ply failure response by the finite-element method. The results obtained are postprocessed to formulate specific recommendations regarding the relative behavior of different skew plate combinations in terms of the first-ply failure. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent properties. Nonlinear thermal dependence distribution following a power law is adapted. Various types of multilayered composite plates with position and temperature-dependent material properties are considered. Mathematical formulations and explicit relationships are presented in the frame of finite element methods. The structure is subjected to linear and uniform temperature variations. The temperature and the displacement are expanded in power series with unknown terms, and the numerical solution is obtained by the finite element method. The homotopy method is used for nonlinear thermal buckling, and a continuation procedure is elaborated for nonlinear thermal–displacement responses. The nonlinear thermal critical buckling load is first computed and the postbuckling equilibrium path of FGM and laminated plates under thermal loading is investigated. Temperature-dependent properties and geometry effects as well as boundary conditions on the nonlinear thermal buckling and postbuckling behaviors are analyzed. [ABSTRACT FROM AUTHOR]

The finite element method is used to develop a computational algorithm for solving a limited class of problems on the bending of composite plates reinforced with systems of unidirectional high-strength fibers. It is assumed that a neutral plane exists in the region of the plate and behaves similarly to a flexible nondeformable membrane. The displacements of the plate in the longitudinal direction are linear in thickness. In the case of fiber composites with different elastic moduli in tension and compression, the neutral plane, generally speaking, does not coincide with the median plane. The problem of minimizing the elastic energy functional in accordance with the Lagrange variational principle yields a fourth-order elliptic differential equation for the deflection. The bending stiffnesses of the plate included in the coefficients of the equation are calculated with account for the fact that the elastic characteristics of the reinforcing fibers under tension and compression are significantly different. The numerical solution of the equation is obtained via the finite element method with the help of a Bell triangular element. The paper presents computational results for the bending of rectangular laminated plates in which the fibers are laid in different directions. [ABSTRACT FROM AUTHOR]

The rock plate (RP) method can be used to identify the size and location of potentially dangerous bed separation space (BSS) in coal mines. The RP method is performed in three steps: (1) The rock strata above the coal seam is simplified as a composite plate calculation model; (2) The deflection of rock strata is expressed as a double trigonometric series and obtained using the energy method; (3) The internal-forces and deformation of the RP are solved to determine the size and location of the BSS based on elasticity and a BSS identification process. This requires that the BSS be unbroken, and the BSS upper rock stratum be an aquifer. In this study, the Yuanzigou coal mine was taken as a study case and the RP method was used to determine the size and location of BSS water (BSS-W) above the coal goaf of working face 1,012,001. BSS usually occurs at the contact surface between hard and soft rock strata; at this mine, BSS-W exists between the Yijun conglomerate and the Anding mudstone formations. The results predicted that when the working face advanced 350 m, the third BSS will break, allowing BSS-W to flood into the goaf. These results were verified by borehole video observation. Therefore, two control methods were used: inclined drainage holes drilled from the roadway and spaced holes drilled from the surface in areas with abundant water. This paper thus provides a way to locate the BSS-W and prevent an inrush hazard. [ABSTRACT FROM AUTHOR]

The location optimization of sensors is a essential problem in structural health monitoring systems. Taking the cost of sensors into account, it is uneconomical to install sensors on every part of a structure and moreover in aeronautical industry, the weight is a crucial factor. In this paper, a optimal placement optimization of sensor locations for structural health monitoring systems is studied. Several techniques of optimization of sensors are approached and applied in a shell structure. The structure, a laminate of carbon fiber, was modeled by the finite element method (FEM) and then subject to free vibration. Genetic algorithms (GAs) are then employed to locate the best sensor distribution to cover a specific number of low frequency modes. Numerical results have demonstrated the overall efficiency of sensor delivery methods. Specific problems occurred, especially regarding the method of effective independence, being less efficient and discrepant in relation to the other methods employed. In summary, the results obtained in this paper provide an optimal position for sensors in real SHM systems and experiments. [ABSTRACT FROM AUTHOR]

The NM500/Q345/NM500 composite plates were subjected to different hot rolling and heat treatment processes in this paper. The influence of hot rolling and heat treatment on the microstructure, element distribution and defect composition of the bonding interface of the as-rolled clad plates was studied by using optical microscope, scanning electron microscope, electron backscattered diffraction and transmission electron microscope. Meanwhile, the mechanical properties of wear-resistant steel were analyzed by microhardness and tensile tests. It was revealed that the increase in rolling reduction promoted the metallurgical bonding between NM500 and Q345 steels. The composite texture components of {112} ~ {113} < 110 > , {332} < 113 > , {223} < 110 > , {554} < 225 > and < 110 > ∥RD were formed in the tissue when the reduction rate was 70%. γ/α phase transformation reinforced the texture components and thus increased {332} < 113 > and {554} < 225 > after quenching treatment. Typical lath martensites were present in the structure, and there were high-density dislocations and substructures between the laths. Tempering treatment at 200 °C facilitated the deposition of some needle-like or rod-like ε precipitates in the martensite. The best tensile strength (1432.28 MPa) and elongation (22.68%) in the composite plate could be achieved by post-rolling treatment of quenching at 900 °C and tempering at 200 °C. [ABSTRACT FROM AUTHOR]

The paper presents the results from a study of the interaction of Lamb waves with inhomogeneities in composite plates. It was found that waves of this type are diffracted by inhomogeneities, such as hole and localized mass load of the surface. A method for detecting and localizing inhomogeneities by comparing the distribution of the wave field amplitudes over the plate surface before and after the appearance of inhomogeneities is proposed and tested experimentally. The article was prepared based on materials in a report at the Third All-Russian Acoustics Conference (September 21–25, 2020, St. Petersburg). [ABSTRACT FROM AUTHOR]

This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts. The key equations are formulated built on the two-dimensional model, and the discretization is carried out in terms of only three translational displacement components as the basic unknowns. The high-order spectral elements are applied in the proposed technique to accurately simulate the arc boundaries of cutouts. Characterized by the important semi-analytical feature of the SBFEM, responses of the transverse free vibration are accurately explored. The derivation of governing equations strictly follows the 3D theory of elasticity without introducing any assumptions. The general solution of the SBFEM key equation is in the form of the matrix exponent, which is calculated by the PIM. As a type of highly precise approach, the PIM is introduced to create the global stiffness matrix from the analytical exponential matrix, which can make sure the eigensolutions with enough accuracy. Aided by the methodology of the kinetic energy formula, the global mass matrix of the perforated plate structure is constructed. According to the thin plates, the degree of freedom transform is employed to lower the dimensions of eigenvalue equation and thus improve the computational efficiency. Numerical examples of flexible square and circular plates with various cutouts reveal that excellent agreement is achieved between the natural frequencies predicted by the developed method and those from other methods and exact solutions. Furthermore, the effect of boundary conditions, skew angles, thickness-to-length ratios and sizes of cutouts on distributions of vibration frequencies is discussed. [ABSTRACT FROM AUTHOR]

It has been a vital issue to ensure both the accuracy and efficiency of computational models for analyzing the ballistic impact response of fiber-reinforced composite plates (FRCP). In this paper, a machine learning (ML) model is established in an effort to bridge the ballistic impact protective performance and the characteristics of microstructure for unidirectional FRCP (UD-FRCP), where the microstructure of the UD-FRCP is characterized by the two-point correlation function. The results showed that the ML model, after trained by 175 cases, could reasonably predict the ballistic impact energy absorption of the UD-FRCP with a maximum error of 13%, indicating that the model can ensure both computational accuracy and efficiency. Besides, the model's critical parameter sensitivities are investigated, and three typical ML algorithms are analyzed, showing that the gradient boosting regression algorithm has the highest accuracy among these algorithms for the ballistic impact problem of UD-FRCP. The study proposes an effective solution for the traditional difficulty of the ballistic impact simulation of composites with both high efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a new three-node triangular plate element is proposed to analyze laminated composite plates based on the higher-order shear deformation theory (HSDT). Originating from the MITC3+ shell finite elements, the displacement fields of the HSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. The transverse shear strain fields are separately approximated according to the MITC3+ shear-locking removal technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. Applying the divergence theorem, the surface integration of the in-plane stiffness matrices is transformed into the line integration on the boundary of the smoothing domains. The performance of the so-called ES-MITC3+ plate elements is validated through several numerical examples. The numerical results of the static, frequency and buckling analyses when this new element is used converge to the exact solutions and agree well with those given in other references. [ABSTRACT FROM AUTHOR]

This paper studies the free vibration behavior of hybrid laminated plates using a layer-wise formulation. The laminated structures are made of graphite fiber-reinforced composite (GFRC) and multilayer functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plies. The internal single-walled carbon nanotubes (SWCNTs) are distributed in layer-wise form along the ply thickness direction either uniformly or functionally graded according to four separate patterns. Both the linear and nonlinear of the CNTs distributions form are considered. Theatrical formulations are based on the first-order shear deformation theory (FSDT), and finite element method is employed to obtain the nondimensional natural frequency. The elastic modulus of both GFRC and CNTRC plies composed the hybrid laminated plate is obtained by a micromechanics model. Initially, the provided results are validated by comparing it with the literature; thereafter, a parametric study is carried out the influences of laminates configuration, number of CNTRC plies layers, CNT volume fraction, CNT distribution patterns, linear and nonlinear distribution of CNTs, plate width-to-thickness ratio, plate aspect ratio, boundary conditions, stacking sequences, and number of plies on the free vibration behavior of hybrid laminated plates. Some final remarks considering the laminated plate configuration and the distribution form of the CNT fillers are presented in order to provide a useful observation on the design criteria of the laminated composite plate structures. [ABSTRACT FROM AUTHOR]