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In this paper, wave propagation in functionally graded (FG) porous plates resting on Winkler-Pasternak foundation is studied using a quasi-3D shear deformation theory. The proposed theory has a new displacement field that includes indeterminate integral terms and contains fewer unknown variables taking into account the effect of transverse shear and thickness stretching. The parameters of the elastic foundation are introduced in the present formulation following the mathematical model of Pasternak. In addition, the effect of porosity is studied. The material of the FG plate is inhomogeneous and the material properties are assumed to vary continuously in the thickness direction according to a power law of the volume fraction. The equations governing wave propagation in the plates resting on an elastic foundation are derived using Hamilton's principle. Then, the dispersion relationship between frequency and wave number is solved analytically. A comprehensive numerical result is accomplished to evaluate the effects of the volume fraction index, the porosity, thickness ratio (h/a), and the wave number on the wave propagation in functionally graded porous plates are discussed in detail. [ABSTRACT FROM AUTHOR]

The key aim of this research is to develop an analytical model for the forced vibration of graphene-reinforced composite (GRC) cylindrical shell with viscous damping and thermal environment effects under several boundary conditions. The prescribed mechanical and thermal characteristics of the GRC layer are evaluated utilizing a micromechanical extended Halpin–Tsai technique. Further, the governing equations are determined to be grounded on the shear deformation theory (SDT) with the von Kármán-form in terms of the geometric nonlinearity. The basic nonlinear partial differential governing equation is transformed into a nonlinear ordinary differential equation with the Galerkin-based method. The resulting ordinary governing differential equations are systematically solved based on the multiple scales scheme in order to obtain the nonlinear forced vibration frequency response of the laminated GRC cylindrical shell in the presence of damping impact and subjected to multiple boundary conditions. The validation of the obtained expressions is achieved by comparing them with the available literature data where the comparison revealed a clear consistency between them. Moreover, a parametric investigation is provided to illustrate the impacts of the distribution of graphene layers, elastic foundation coefficients, damping ratios, temperature effects and dimensionless radial excitation amplitude on the forced nonlinear amplitude-frequency ratio responses for a functionally-graded graphene-reinforced composite (FG-GRC)-layered cylindrical shells. The analytical outcomes indicate that the different distribution types of graphene, elastic foundation coefficients, damping ratios, temperature, and radial excitation parameters have a noteworthy impact on the frequency–amplitude behaviors of an FG-GRC-layered cylindrical shell. In addition, the new insights gained from this research might contribute to a deeper understanding of the nonlinear forced vibration responses in subsequent analysis and design techniques for giving appropriate benchmark findings. [ABSTRACT FROM AUTHOR]

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass. [ABSTRACT FROM AUTHOR]

This paper presents a novel shear deformation theory for analyzing porous microbeams' bending, buckling, and free vibration resting on a foundation. The proposed shear function incorporating three kinetic variables satisfies zero-traction boundary conditions on the top and bottom surfaces of the beams and does not require a shear correction factor. The modified couple stress theory accounts for the size-dependent effects, and the governing equations are derived from Lagrange's equation using the proposed shear function. Legendre–Ritz functions are developed to analyze the porous microbeams' buckling, free vibration, and bending behaviors. The effects of material length scale parameter, porosity, span-to-height ratio, boundary condition, and foundation parameter on the mechanical responses of beams are investigated. Numerical results demonstrate the accuracy and efficiency of the proposed theory and can serve as benchmarks for future analysis of porous microbeams on elastic foundations. [ABSTRACT FROM AUTHOR]

This is a unique study in which a damped porous microplate's nonlinear vibration and response are analyzed semi-analytically using MSGT and HSDT under localized loading. The substrate is modeled using the Winkler-Pasternak elastic foundation. Partial differential equations are obtained using Hamilton's principle and solved by Galerkin's method. IHB and Newmark's methods are used to trace the nonlinear vibration and response. The results show that uniform porosity leads to lower stiffness compared to symmetric porosity distribution. Pasternak foundation parameter has a larger impact on stiffness compared to Winkler parameter. The effect of geometric nonlinearity is weakened while using MSGT. [ABSTRACT FROM AUTHOR]

Highlights This paper presents an analytical approach for buckling and postbuckling analysis for functionally graded graphene‐reinforced composite (FG‐GRC) toroidal shell segments with the trapezoidal or round corrugated core under the axial tension and compression. The considered shells are placed in a thermal environment and surrounded by an elastic foundation. Based on the von Kármán‐Donnell shell theory with geometrical nonlinearities, Stein and McElman approximation, and a homogenization technique for corrugated shells, the basic equations of shells are established. The previous homogenization technique is improved by adding the thermal forces in the internal force expressions. The shell‐foundation interaction is expressed using the model of the Pasternak assumption. The Ritz energy method is used to obtain the pre‐buckling and postbuckling behaviors of the shells, from which the critical buckling tensions and compressions can be investigated. The influences of FG‐GRC face sheets, corrugated core, and foundation on the buckling behavior of sandwich shells can be shown in the numerical analysis. Postbuckling of toroidal shell segments with the corrugated core is analyzed. A homogenization technique is improved for the thermal forces in the core. The shells are made of functionally graded graphene‐reinforced composite. The nonlinear Kármán‐Donnell shell theory and Ritz energy method are applied. Special effects of input parameters on the buckling behavior are investigated. [ABSTRACT FROM AUTHOR]

This article uses the semi-analytical approach to study the combined nonlinear vibration and nonlinear response of a damped porous microplate under nonuniform periodic parametric excitation to understand the complete nonlinear dynamic behavior of the plate. The plate is supported by a Winkler-Pasternak elastic foundation and modeled using modified strain gradient and third-order shear deformation theories to simulate the small-scale effects and shear deformation, respectively. Using Hamilton's principle, the governing partial differential equations of motion are derived and solved using Galerkin's method to convert them into ordinary differential equations (ODEs). These ODEs are solved using a combined incremental harmonic balance (IHB) and arc-length continuation approaches to get the nonlinear vibration (frequency–amplitude curves). The same ODEs are solved using the Newmark-β technique to obtain the nonlinear response (time–amplitude curves). The effect of elastic foundation parameters and aspect ratio on mode shape is presented. The effect of parameters such as the porosity coefficient, type of porosity, Winkler-Pasternak elastic foundation parameters, different size-dependent theories, plate thickness, size of plate, damping coefficient, different loading profiles, and loading concentrations on the nonlinear vibration and nonlinear response is examined. Also, the dependence of initial displacements on the frequency–amplitude curves with respect to the excitation frequency is demonstrated with the help of time-amplitude curves. [ABSTRACT FROM AUTHOR]

The main goal of this study is to use higher-order isogeometric analysis (IGA) to study the dynamic response of sandwich shells with an auxetic honeycomb core and two different functionally graded materials (FGM) skin layers (namely honeycomb-FGS shells) subjected to dynamic loading. Touratier's non-polynomial higher-order shear deformation theory (HSDT) is used due to its simplicity and performance. The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the dynamic response of honeycomb-FGS shells is carried out in detail. [ABSTRACT FROM AUTHOR]

AbstractThis study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone. [ABSTRACT FROM AUTHOR]

AbstractThis article presents a size dependent mathematical model and an analytical solution methodology to accurately simulate and analyze the size dependent buckling behavior of piezoelectrically layered sandwich nanobeams with perforated core embedded in an elastic medium with flexoelectricity. The electric enthalpy energy function is expressed in terms of the electric and the flexoelectric effects. Regular squared cutouts perforation pattern is adopted for the perforated core. Closed forms for the equivalent geometrical parameters of perforated core are developed. The shear deformation effect is incroporated using the Timoshenko beam theory (TBT). To capture the nonlocality and the microstructure length scale effects, the nonlocal strain gradient elasticity theory is modified and adopted to include the electromechanical nonclassical effects. The Hamiltonian principle is utilized to derive the equilibrium equations. An analytical solution methodology is developed to derive closed forms for critical buckling loads. The developed solution procedure is implemented into a MATLAB software code. The accuracy of the developed procedure is verified by comparing obtained results with corresponding cases reported in the literature. Influences of different design variables on the electromechanical buckling behavior are explored through intensive parametric studies. Results obtained showed the significant effects of the flexoelectricity and the piezoelectric parameters on the size dependent buckling behavior of piezoelectric sandwich nanobeams with perforated core. Size dependent electromechanical as well as mechanical buckling behaviors could be controlled by adjusting these parameters. The developed procedure and the obtained numerical results are helpful in many technological and industrial applications as MEMS and NEMS. [ABSTRACT FROM AUTHOR]

In the present research, torsional buckling response of thick truncated conical shell panels supporting on Winkler-type elastic medium has been surveyed. The shell is constructed from a porous metal material reinforced by graphene platelets (GPLs) in which the porosity and volume weight fraction of nanofillers are graded along the thickness of shell. Three functions for porosity distribution and five patterns of GPLs are examined. To estimate the Young modulus of the shell, Tsai-Halpin micromechanical model, and for its mass density, extended rule of mixture is employed. Linear theory of 3D elasticity in conjunction with the virtual work principle and numerical graded finite element method (FEM) are applied to derive the state of equilibrium in pre-buckling mode. Torsional buckling forces are derived by applying nonlinear Green strains and by deriving geometric stiffness matrix of the system. The effect of various parameters such as coefficient of porosity, various distributions of porosity and different nanofiller patterns, weight fraction of graphene nanofillers, semi vertex angle of cone, span angle, stiffness of elastic medium and various boundary conditions on torsional buckling loads of functionally graded (FG) porous truncated conical panel reinforced by GPLs have been presented. The main purpose of this research is obtaining the best distribution of porosity and GPLs pattern and investigating the influence of adding nano particles on the torsional buckling forces of the shell. Results denote that employing GPL-X pattern in conjunction with porosity distribution 1 provides the maximum value of buckling loads. Besides by adding the nano particles, the amount of buckling loads will increase 100%. [ABSTRACT FROM AUTHOR]

Hyperelastic functionally graded materials have a wide range of application prospects in soft robotics and biomedical fields. This paper investigates the nonlinear free and forced vibrations of a hyperelastic functionally graded beam (HFGB) based on higher-order shear deformation beam theory. The geometrical nonlinearity is considered by using the von-Kármán’s nonlinear theory. The three-material-parameter free energy function named as Ishihara model is employed to characterize the hyperelastic material. The power-law gradient form along the thickness direction is adopted. The HFGB is resting on the elastic foundation. The Winkler, Pasternak and nonlinear stiffness coefficients are considered. The time-harmonic external force is applied to the HFGB. The nonlinear governing equations for the vibration of the HFGB are derived by using Hamilton’s principle, and are subsequently transformed into ordinary differential equations via Galerkin’s method. The nonlinear free vibration and primary resonance of the HFGB are investigated analytically by employing the extended Hamiltonian method and multiple scales method, respectively. The results indicate that the power-law index, slenderness ratio, material properties, and elastic foundation parameters have significant influences on the nonlinear frequency of free vibration as well as the frequency–response and force–response curves of forced vibration. The phase plane method is employed to analyze the system’s stability states under various excitation amplitudes. The relative error between the results of the current computational model and the published literature is less than 0.1 percent. [ABSTRACT FROM AUTHOR]

Environmental responses to deep excavations are combined results of numerous factors. The effects of some factors are relatively straightforward and can be considered carefully during the design. On the other hand, more features impact excavation-induced performances indirectly, making their influences difficult to be clearly understood. Unfortunately, the complexity and non-repeatability of practical projects make it impossible to thoroughly understand these issues through realistic deep excavation projects. Therefore, parametric studies based on repeatable laboratory and numerical tests are desired to investigate these issues further. This work examines the influence of several key features on excavation-induced displacements through a series of 3D numerical tests. The study includes the choice of soil constitutive models, the modeling method of the soil–wall interface, and the influences of various key soil parameters. The comparison shows that the MCC model can yield a displacement field similar to the HSS model, while its soil movement is greatly improved compared to the MC model. Both the soil–wall interface properties and soil parameters impact the excavation-induced displacement to a large extent. In addition, the influence mechanisms of these parameters are analyzed, and practical suggestions are given. The findings of this paper are expected to provide practical references to the design and construction of future deep excavation projects. [ABSTRACT FROM AUTHOR]

In this paper, an analytical solution for exploring the buckling characteristics of functionally graded (FG) plate is presented based on a quasi-3D shear deformation theory. It is considered that the plate is subjected to different types of in-plane compressive load. The FG plate is placed on three-parameter foundation WinklerPasternak-Kerr. The overall material properties of FG plate are assumed to be varied across the thickness and are estimated through the Voigt micromechanical model. The governing equations are obtained on the base of the quasi-3D deformation theory that contain undetermined integral forms and involves only four unknowns to derive. Equations of motion are derived from the principal of virtual work and the analytical solution is used to determine the critical buckling loads. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the in-plane buckling are carried out, including the influence of boundary conditions, elastic foundation, plate geometric parameters and power law index. The results reveal that the critical buckling loads are strongly influenced by several parameters such as boundary conditions, elastic foundation parameters and geometric shape of the plate. [ABSTRACT FROM AUTHOR]

Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh–Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed. [ABSTRACT FROM AUTHOR]

The nonlinear vibration response of rectangular plates made of functionally graded porous materials (FGPs) induced by hygrothermal loading is investigated in this article using a numerical approach. The effect of elastic foundation on the vibrations is taken into account according to the Winkler–Pasternak model. Hygroscopic stresses produced due to nonlinear rise in moisture concentration are also considered. The temperature-dependent material properties of plate are computed based on the modified Voigt's rule of mixture and Touloukian experiments for even and uneven distribution patterns of porosity. Within the framework of the first-order shear deformation plate theory and von-Kármán nonlinearity, Hamilton's principle is utilized in order to derive the equations of motions. To achieve the temporal evolution of maximum lateral deflection of hygrothermally-induced plates, the generalized differential quadrature (GDQ) and Newmark integration methods are employed. Selected numerical results are presented to study the influences of temperature distribution, porosity volume fraction, moisture concentration, geometrical parameters, elastic foundation parameters and FG index on the geometrically nonlinear vibrations of FG porous plates with various boundary conditions. [ABSTRACT FROM AUTHOR]

To ensure the stability of broken surrounding rock under the influence of advance abutment pressure and the reliability of support system, the 21104 working face of Hulusu Coal Mine is taken as the research background. By means of theoretical calculation, numerical simulation and field measurement, a mechanical model of the elastic foundation beam for the deformation of the super front roof is established, the influencing factors of the bending deformation of the roof, the leading bearing pressure and the main controlling factors of the concentration coefficient are determined, and the advance grouting anchor cable reinforcement technology for broken surrounding rock is proposed. The results show that the roof elastic modulus only affects the roof deflection above the roadway, and the side elastic modulus controls the overall bending deformation of the roof. The advanced support pressure and concentration coefficient show a rapid increase followed by a slow increase trend with the advancement of the working face, and finally tend to stabilize. There is a 35 m high stress area in the grouting anchor cable reinforcement test face, the anchor cable has a high abundance coefficient, the surrounding rock deformation is low (

Vibration behaviors of elastically supported functionally graded (FG) sandwich beams resting on elastic foundations under moving loads are investigated. The transformed-section method is first applied to establish the bending vibration equations of FG sandwich beams, then the Chebyshev collocation method is used to study free and forced vibrations. Two types of sandwich beams with FG faces-isotropic core and isotropic faces-FG core are considered. The material properties of FG materials are assumed to vary across the beam thickness according to a simple power function. Regarding the free vibration analysis, bending vibration frequencies are calculated numerically by forming a matrix eigenvalue equation. As for the forced vibration analysis, the backward differentiation formula method is employed to solve the time-dependent ordinary differential equations to obtain the dynamic deformations of the beam. To ensure the accuracy of the proposed model, some calculated results are compared with those in the published literature. Parametric studies are then performed to demonstrate the effects of material gradient indexes, stack types, layer thickness ratios, slenderness ratios, excitation frequency and speed of moving loads, and foundation and support stiffness parameters on the dynamic characteristics of FG sandwich beams. [ABSTRACT FROM AUTHOR]

The nonlinear buckling response of laminated composite cylindrical shells reinforced with graphene nanoplatelets (GNPs) is studied in this paper. The functionally graded (FG) shell reinforced by GNPs is analytically studied under external pressure and uniform temperature rise loadings. It is also assumed that the GNP-reinforced laminated composite shell is in contact with an elastic foundation. Various types of profiles are employed for the GNP distribution patterns in the shell thickness including 10 nanocomposite layers. The nonlinear strain-displacement relations of the shallow cylindrical panel are established utilizing the third-order shear deformation shell theory. Governing equilibrium equations of the laminated GNP-reinforced composite shell are formulated employing the principle of virtual displacement. The coupled system of nonlinear differential equations is solved analytically for the hinged–hinged and fixed–fixed boundaries of the shell using a perturbation-based technique. Correctness of presented formulations and obtained solutions is proved by comparisons with results from previous studies for an isotropic cylindrical shell. Novel numerical results reveal that the material properties, geometrical characteristics and load parameters significantly affect on the buckling behavior of laminated composite cylindrical shells. [ABSTRACT FROM AUTHOR]

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Deep excavations clearly impact adjacent existing properties and threaten their operational safety. Predicting the deformation of existing infrastructure induced by nearby underground construction is the main concern of urban underground development. This paper presents an analytical calculation method for predicting underground pipe gallery deformations induced by adjacent deep excavations. First, the authors assume the existing pipe gallery to be nonexistent in the soil and propose a solution to calculate the excavation-induced vertical movements of the soil at the position of the existing pipe gallery. Thereafter, the authors simplify the existing pipe gallery as an elastic beam on a Winkler foundation to calculate its deformation. Finally, the method is verified by the good agreement found between the calculated result and the field measurement of the construction of the Shanghai Hongqiao CBD project. The proposed analytical method of this work can provide accurate evaluation results for similar engineering projects. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

The present study is the first attempt to investigate the free vibration behavior of the rectangular plate including two equal (twin) internal parallel piezoelectric inclusions (lying width-wise in the plate) utilizing the 3D exact equations of electroelasticity theory. For the solution, the finite element method is applied. By Hamilton's principle, the equation of motion and boundary conditions are obtained to derive the finite element equations using the electrical energy of the piezoelectric material and the mechanical energy of the structure. Lateral edge surfaces of the plate have zero electrical potential and are simply supported. Ideal contact conditions are satisfied by the interface surfaces between the elastic medium and piezoelectric (abbreviated as PZT) inclusions. After investigating the convergence and validation of the approach, the influence of various parameters on the natural frequencies of the plate behavior, such as the mutual effect of PZT inclusions, coupling effect between the electrical and mechanical fields, the effect of the size, location, material, and polled directions of the PZT inclusions, and the material of the elastic medium, is investigated. [ABSTRACT FROM AUTHOR]

AbstractThe present study is focused on the development of an analytical solution for the buckling analysis of carbon nanotube reinforced functionally graded (FG-CNTRC) laminated plates resting on Pasternak elastic foundation and subjected to different nonuniform edge loads. The analytical solution is formulated using a two-step procedure: First, an accurate in-plane stress solution is developed by superimposing three suitable Airy’s stress functions; second, the stress solution is utilized to compute the critical buckling loads using the Galerkin’s procedure. Results from parametric studies show that the buckling behavior of FG-CNTRC plates greatly depends on the type of nonuniform loads, plate configurations, and support parameters. [ABSTRACT FROM AUTHOR]

The nonlinear vibration analysis of functionally graded reinforced with graphene platelet (FG-GRC) porous truncated conical shells surrounded by the Winkler-Pasternak elastic foundation is presented in this paper. An improved model for evaluating the material properties of porous composites is proposed. Three types of porous distribution and three patterns of graphene nanoplatelets (GPLs) dispersion are estimated. Coupled with the effect of the Winkler-Pasternak elastic foundation, the nonlinear governing equations are developed by using the Hamilton principle. The Galerkin integrated technique is employed to obtain the linear and nonlinear frequencies of the shells. After the present method is validated, the effects of the pores, GPLs, the Winkler-Pasternak foundation, and the semi-vertex are investigated in detail. The results show that the linear frequency can be raised by increasing the values of the mass volume of the GPL and foundation parameters. In contrast, the ratio of nonlinear to linear frequency declines as the mass volume of the GPLs and foundation parameters rises. Furthermore, it is found that the minimum ratio of nonlinear to linear frequency can be obtained as the semi-vertex angle is about 55º, and the effect of porosity distribution on the linear and linear frequencies might be neglected. [ABSTRACT FROM AUTHOR]

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years. Bamboo fibers are renowned for their good mechanical properties, abundance, and short cycle growth. As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications, this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite (BFRC) beams on the elastic foundation. Three different functionally graded (FG) layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness. The elastic properties of the composite are determined with the law of mixture. Employing Hamilton's principle, the governing equations of motion are obtained. The generalized differential quadrature method (GDQM) is then applied to the equations to obtain the results. The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions, elastic foundation stiffness values, and boundary conditions (BCs) and slenderness ratio of the beam change. Furthermore, a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials, demonstrating the significant enhancements in both vibration and buckling responses, with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-⟡) fiber distribution. Eventually, the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite (CNTRC) beams found in the literature, indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams. [ABSTRACT FROM AUTHOR]

In this paper, the effect of coefficient of viscous damping on the dynamic analysis of Euler-Bernoulli beam resting on elastic foundation was investigated using Integral-Numerical method which reduces to an ordinary differential equation with series representation of Heaviside function. The dynamic responses of the beam in terms of normalized deflection and bending moment has been investigated for different velocity ratios under moving load and moving mass conditions. Generally, closed-form solution to the generalized mathematical model for prismatic beam was computed by means of symbolic programming approach through MAPLE 18. Results obtain revealed that the presence of an elastic foundation and the provision of sufficient reinforcement in beams and beam-like structure reduces vibration intensity and ensure safe passage of load and prolong the beam life. [ABSTRACT FROM AUTHOR]

In engineering design methods, it is assumed that the structure is located on a fixed base, and the effects of the soil environment on the structural response are generally ignored. However, research showed that the environment of the soil and the structure can interact with each other. This phenomenon is called soilstructure interaction effect. Therefore, the soil environment should be modeled in structural analysis. There are different methods for soil modeling. One of the practical methods is to use separate springs to model the soil environment. In this article, the effect of the number of floors and the period of the structure on the soil springs' stiffness has been investigated. In this regard, three-dimensional structures with the number of floors 1, 3, 5, 10 and 15 were modeled in Opensees software with continuous soil environment. Then, from the results of the structural analysis, the reaction of the soil under the foundation was calculated and relations were presented to determine the stiffness of the soil. These relationships are dependent on the structure's period. [ABSTRACT FROM AUTHOR]

Present research with the aid of multivariate analysis of variance explores the closed-form dynamics of the poroelastic nanocomposite sandwich plate. Additionally, graphical optimization of the system's vibration by proper adjusting the involved parameters is provided by employing response surface methodology. p-value and F-value tests are executed to determine the contribution percentage of each parameter on the dynamics of the structure. The nanocomposite face-sheets are made of graphene-platelets reinforced polymer. The main relations governing the dynamics of the initially stressed sandwich system are defined in the background of theory known as linear poroelasticity. Bidirectional format of discrete singular convolution approach (2D-DSCA) is employed in order to determine the design-points' dynamic performance. Validity of the applied solution procedure is tested through comparison with the outcomes of the first-rate articles. In this research, it is revealed that the graphical optimization is a reliable way to determine the proper adjustment of the parameters for achieving the optimum vibration performance. Moreover, it is observed that the aspect ratio of the plate is the most decisive factor in the free oscillation response of the sandwich plate compared with other factors whose influence are examined in the present article including GPL's weight-fraction, GPL's dispersion patterns, in-plane initial stresses, and the poroelasticity coefficient. [ABSTRACT FROM AUTHOR]

Large deflection nonlinear bending of functionally graded (FG) porous cylindrical panels reinforced with graphene platelets (GPLs) on a Pasternak-type elastic foundation is examined by developing a reliable and effective 2D meshfree-based nonlinear numerical method. The large displacement field is express by the first-order shear deformation theory (FSDT) and the von Kármán nonlinearity, and approximated by 2D natural element method (NEM) in conjunction with the stabilized MITC3+ shell concept and the shell surface–rectangular grid geometry transformation. The nonlinear simultaneous equations are solved by a load incremental Newton–Raphson scheme. The developed nonlinear numerical method is justified from by comparing with the reference solutions, and the load–deflection and bending moment of FG-GPLRC porous cylindrical panels on elastic foundation are scrutinizingly examined. Four different symmetric GPL distribution patters (except for FG-Λ) and three different symmetric porosity distributions are considered and their combined effects on the nonlinear bending behavior are investigated, as well as the effects of foundation stiffness and GPL amount. Also, the results are compared with those of FG CNT-reinforced porous cylindrical panels. [ABSTRACT FROM AUTHOR]

A finite element method using a 9-node isoparametric plate bending element, incorporating the effects of transverse shear based on the first-order shear deformation theory, is proposed for the free vibration analysis of rectangular cut-out plates resting on an elastic foundation. The elastic foundation is modeled on the Winkler and the Pasternak type, and equations of motion are obtained using the principle of virtual work. To account for the parabolic strain variation through the thickness, a shear correction factor of 5/6 is used, and the effect of rotary inertia has been included in the formulation. The present formulation is compared with established results obtained using analytical methods, with and without rotary inertia, and the max variation observed is 2.24% without rotary inertia and 0.02% with rotary inertia. Cut-out plates are validated with results obtained using the finite element method, and the max variation observed between established results and present formulation is 1.3%. Establishing the accuracy of the current formulation, new results are obtained for rectangular cut-out plates resting on an elastic foundation of various stiffness parameters. The effect of incrementing cut-out dimensions and different layouts of cut-outs in the plate on the free vibration response of plates resting on an elastic foundation is investigated, along with the effects of varying aspect ratios and thickness-to-side ratios. [ABSTRACT FROM AUTHOR]

Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz's method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to use the higher-order isogeometric analysis (IGA) to study the vibration behaviour of sandwich plates with an auxetic honeycomb core and two different functionally graded materials (FGM) skin layers (namely h-FGS plates) resting on an elastic foundation (EF) under double blast loading. Reddy's HSDT is used due to its simplicity and efficiency. The foundation model incorporates two parameters as springer stiffness (k1) and the shear layer stiffness (k2). The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the vibration characteristics of h-FGS plates is carried out in detail. The obtained results are expected to be useful for calculating and designing h-FGS plates in practice.

Excessive vibration has always been a serious problem for conical shell structures, while the application of the graphene-based free-constrained layer (GFCL) based on carbon fiber-reinforced composite (CFRC) structure is a novel way to improve structural performance. An analytical model for vibration and dynamic characteristics of the GFCL-CFRC conical shell resting on the Winkler–Pasternak elastic foundation with arbitrary boundary conditions is constructed, and four types of GFCL porosity distribution and GFCL dispersion pattern are considered in this model. The multi-segment technique and virtual spring technique are utilized to simulate arbitrary boundary conditions. Then, the first-order shear deformation theory (FSDT) and Hamilton's principle are employed to obtain the motion equation of the GFCL-CFRC conical shell, and the motion equation of the GFCL-CFRC conical shell is solved by the Ritz method. In conclusion, the dispersion mode of GFCL, thickness ratio of GFCL, and fiber angle have influence on the dynamic performance. With a reasonable design, the dynamic performance of the GFCL-CFRC conical shell can be further improved. [ABSTRACT FROM AUTHOR]

In this article, an elastic foundation is used to study the characteristics of flexural edge waves propagating on a piezoelectric structure. The nonlocal elasticity theory is introduced to investigate the microscale effect on edge wave propagation. The traditional Kirchhoff plate hypothesis is used to determine the kinematics of the piezoelectric plate. By considering the sinusoidal waveform, a closed-form dispersion relation can be obtained. In the context of a flexural edge wave on a piezoelectric plate, an analytical and graphical comparison between the two boundary conditions (i.e. short circuit and open circuit) is discussed. In the presence of nonlocal elasticity, the dispersion relation is implied as an implicit function of frequency and wave number. A significant difference occurred between the dispersion curves for piezoelectric plates with different foundations and nonlocal parameters. Due to the Pasternak elastic foundation, an increasing rate of the fundamental mode of frequency is observed at the traction-free edge of a thin, semi-infinite piezoelectric plate. In contrast, the nonlocal elasticity tends to decrease this fundamental frequency mode for a particular wave number value. The corresponding phase velocity decreases rapidly within a short range of wave numbers. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to use the higher-order isogeometric analysis (IGA) to study the vibration behaviour of sandwich plates with an auxetic honeycomb core and two different functionally graded materials (FGM) skin layers (namely h-FGS plates) resting on an elastic foundation (EF) under double blast loading. Reddy's HSDT is used due to its simplicity and efficiency. The foundation model incorporates two parameters as springer stiffness (k 1) and the shear layer stiffness (k 2). The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the vibration characteristics of h-FGS plates is carried out in detail. The obtained results are expected to be useful for calculating and designing h-FGS plates in practice. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we have introduced, for the first time, a novel integral quasi-3D higher-order shear deformation theory (HSDT) employing a third-order shape function. This approach is employed to analyze the free vibration characteristics of a cracked porous functionally graded material (FGM) beam supported on a three-parameter elastic foundation (Winkler/Pasternak/Kerr). This new Quasi HSDT introduces a stretching effect that surpasses the capabilities of FSDT and other HDST. The employed shape function satisfies the conditions of shear stress nullity at both the higher and lower facets without the need for correction factors. The study incorporates a mathematical model representing Winkler/Pasternak/Kerr foundation types into the Hamiltonian to derive the equations of motion. The FGM beam studied in this paper is assumed to be composed of materials with a distribution that varies according to a power law along its height. Our results are compared with previous studies and we reinforce our findings with a parametric study assessing the impact of crack attributes on the natural frequencies of the FG plate. This study presents an advanced integral quasi-3D HSDT, applied for the first time, to analyze the behavior of FG beams resting on a three-parameter foundation. [ABSTRACT FROM AUTHOR]

AbstractThis article presents an analytical technique for determining the free vibration response of a rectangular tank. It is assumed that this structure has a flexible foundation and rigid walls. The effects of beneath soil are considered by using Winkler and Pasternak foundations. To verify the authors’ responses, the finite element solutions are also compared with the analytical results. Additionally, a closed-form approximate relationship is provided in this research work to determine the first natural frequency of the tank resting on a deformable foundation. In order to find the effect of various parameters, such as the stiffness of the elastic foundation and tank dimensions, on the natural frequencies of this system, a sensitivity analysis is also carried out. [ABSTRACT FROM AUTHOR]

The nanoplates have been used extensively in electronic devices, during the working process they can be affected by external forces. To enhance the working performance of mechanical systems, flexoelectric effects are usually added, therefore, it is necessary to study the mechanical behavior of these material structures under the effect of these effects. This is the first research to examine the vibration response and static buckling of variable flexoelectric nanoplates using the FEM and novel shear deformation theory type hyperbolic sine functions, where the thickness is adjusted by linear and nonlinear rules. This is a simple theory, which does not need any shear correction factors, while the mechanical responses of the structures are still described exactly. The numerical results of this work are compared with those of the analytical approach and other methods. Then, the influences of geometrical and material parameters on the free vibration and static bucking of the structure are explored. The data shows that the flexoelectric effect has a strong effect on the free vibration and static bucking behavior as well as the vibration mode shapes of the nanoplates. The working performance is increased when taking into account the effect of flexoelectricity. This work also shows that for each changing rule of plate thickness, the flexoelectric effect also significantly changes the mechanical response of the plate. This is an important suggestion in the design and use of plate structures in engineering practice. [ABSTRACT FROM AUTHOR]

Today, due to the many applications of sandwich beams in industry, studying the forced vibrations of these structures is important. In these structures, amplifiers are used to improve mechanical properties. In this paper, metal-based graphene (copper) is used to improve the mechanical properties. This research uses a functionally graded (FG) graphene-reinforced copper-based composite (GRCC) sandwich beam and FG soft porous core, subjected to two moving loads and located on an elastic foundation. The equations are derived using Soldatos' higher-order shear deformation theory in axial and transverse directions. The exact problem under the magnetic field is solved using the Laplace method, which has not been done. The advantages of this method are the simplicity of solving and reducing to zero the error percentage that exists in numerical solutions. The results are compared with previous works. Finally, the effect of various parameters such as magnetic, porosity coefficient, elastic constant, thickness ratio, and velocity of moving load on the dynamic response of the sandwich beam is investigated. It should be noted that the results can be used to construct this type of structure. [ABSTRACT FROM AUTHOR]

A laminated composite plate designed is supposed to be used under different end supports. The elastic foundation is one of such conditions. The strength of the laminated composite plates can be enhanced by altering constituents or by the addition of filler materials. For localized strengthening of laminated composite plates, such as at particular layers, it is not cost-effective to strengthen the whole structure. So, the laminated composite plates are strengthened at a particular layer by adding the fillering materials, for example, graphene or flyash. The addition of these filler materials in a particular region sometimes causes agglomeration. Agglomeration of filler materials causes adverse effects such as stress concentration or strain aging. In theoretical formulation, Eringen's nonlocal principle is applied to account for the impact of agglomeration. In the current study, neat epoxy glass laminated composite plates as well as rectangle laminated composite plate variants with outer layer graphene, core layer graphene, functionally graded laminated composite plate, laminated composite plates exclusively rich in graphene, and laminated composite plates only rich in flyash are taken into consideration. Using a layer-wise model, the fifth-order shear deformation theory is applied. The laminated composite plates are assumed to rest on an elastic foundation. The consequence of elastic coefficient of foundation on procured parameters such as fundamental frequencies, stress parameters, center deflections, and buckling performance is determined. For this purpose, computerized programs are developed using MATLAB and validated first for isotropic material. Further, the work is extended to study these effects on the laminated composite plate variants. [ABSTRACT FROM AUTHOR]

The present paper deals with the modal analysis of sigmoid functionally graded (S-FGM) rectangular plate resting on elastic foundation by using the dynamic stiffness method (DSM). The DSM is formulated based on the exact solutions of the governing differential equations, and thereby it results in the very accurate computation of the natural frequencies. To obtain the DSM results for thicker plates, the study incorporates first-order shear deformation theory (FSDT) which includes the important effects of transverse shear deformation and rotatory inertia. The governing equations and the associated natural boundary conditions are derived using Hamilton's principle, and the solution is sought in the Levy form where two opposite edges of the plate are simply supported. The present study also contributes by highlighting mistakes in the classical plate theory (CPT)-based DSM formulation published in a recent work and presents a correct CPT-based mathematical formulation. For both these cases, the frequency-dependent dynamic stiffness matrix of the S-FGM plate gives rise to the transcendental eigenvalue problem, which is solved by using the Wittrick and Williams algorithm. Comparison with the available literature establishes the accuracy of the method. In addition, a parametric study is presented for various geometric and stiffness parameters of the elastically supported S-FGM plates using both CPT- and FSDT-based formulations, and accurate frequency results are reported. [ABSTRACT FROM AUTHOR]

Sandwich-Structured Composites (SSCs) are widely used in lightweight construction, especially in the aerospace sector, due to their high specific stiffness and strength. Therefore, it is important to develop their quality by using new techniques. Today, nanotechnologies offer new perspectives for the reinforcement of construction materials. This paper assumes that the reinforcement of the sandwich shell is performed by CNT reinforced face sheets with a uniform or Functionally Graded (FG) distribution of CNTs. The effective properties of the Carbon Nanotubes Reinforced Sandwich-Structured Composite (CNT-RSSC) shells are calculated using the rule of mixture. This study presents novel exact analytical formulas to predict the critical buckling load of the CNT-RSSC shells resting on elastic foundations based on Donnell cylindrical shell theory. These analytical formulas provide the most meaningful answer because we get an equation showing us exactly what happens with each variable. The effects of various parameters on the buckling stability of the RSSC shells are examined. [ABSTRACT FROM AUTHOR]

We consider the problem of bending of a three-layer shallow shell resting on an elastic foundation under the action of a transverse load. It is assumed that the lower and upper layers are made of functionally graded materials and the filler is made of an isotropic material (metal or ceramic). For the mathematical modeling of the problem, we use the refined first-order Timoshenko-type theory of plates that takes into account the presence of bending strains. The elastic foundation of the shell is modeled by a Pasternaktype two-parameter model. The effective elastic properties of the functionally graded materials vary according to the power law. The proposed algorithm for solving the problems of bending is based on the application of the R-functions theory and the Ritz variational method. The developed software, which realizes the proposed approach, is verified by analyzing test problems posed for rectangular plates and shallow shells with different schemes of arrangement of the layers and various characteristics of the elastic foundation. The efficiency of the method is demonstrated by an example of a shell with hexagonal hole and circular notches on the sides. We consider various conditions of fastening of the hole and the outer contour of the shell. The influence of the gradient index and the characteristics of elastic foundation on the maximum value of deflection are analyzed. The obtained results are presented in the form of tables and plots. They are used to study functionally graded plates and shallow shells on an elastic foundation with complex shape in the plan. [ABSTRACT FROM AUTHOR]