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In view of the increasingly prominent noise problem, more and more attention has been paid to the research of sound insulation materials and structures. This paper takes aluminum foam laminated structural plate as the research object. The numerical model of sound insulation was derived using equivalent parameter method, and the sound insulation performance of aluminum foam composite structural plate was tested using a standing wave tube. The experimental results show that the transfer loss of aluminum foam composite structure with 5 mm and 10 mm core layer thickness is increased by 10 dB and 17 dB on average compared with ordinary base aluminum plate. The calculated results of transfer loss in effective range are in good agreement with the experimental results. The error is only 2–5 dB at low frequencies. At the high-frequency stage, although the error increases slightly, the overall trend of the two changes is consistent. The degree of coincidence increases with the increase of frequency. It provides an important theoretical basis for the research direction of sound insulation theoretical model of aluminum foam laminated structure, and also lays a foundation for the optimization of subsequent mathematical model. [ABSTRACT FROM AUTHOR]

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]

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]

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]

Purpose: This work investigates the free vibration response of functionally graded (FG) nanocomposite laminated plates in thermal environments. The nanocomposite plies consist of a polymer matrix strengthened by nano-scale reinforcements, namely a graphene monolayer. This is a case of matrix/graphene mixture or in other words graphene-reinforced nanocomposite (GRNC). Besides the uniform distribution pattern of the graphene reinforcements, four piece-wise FG patterns are also considered to find out the best way to reinforce the nanocomposite plates. The FG distribution patterns are structured by varying the amount of the graphene nano-reinforcements from ply to ply. Methods: Material properties corresponding to the homogenization mixture are carried out using the extended Halpin-Tsai approach. Material properties of the GRNC plies are considered to be either temperature-dependent or temperature-independent. The governing equations of the laminated plate structure are derived based on the first-order shear deformation plate theory (FSDT). The validity of the internal computer program, developed using the finite element method (FEM), is examined by comparing the results obtained in this investigation with those reported in the open literature. Numerical analysis illustrates the effects of a broad range of influencing parameters on the mode shapes and associated natural frequencies of GRNC laminated plates when subjected to varying temperature fields. Results: Numerical results state that the free vibration behavior of the GRNC laminated plates is strongly affected by the variation of the environmental temperature as well as by the geometric parameters. In this context, considering the noteworthy results achieved in this paper, new ideas are proposed to offer innovative insights and novel design models for future real-life applications in polymeric nanocomposite structures. [ABSTRACT FROM AUTHOR]

Purpose: In this paper, the free vibration and dynamic response of laminated composite wave plate in a thermal environment are investigated by means of the mesh-free strong form method. Method: The wave plate is divided into several rectangular and cylindrical segments, and each segment is transformed into a square domain or equivalent cylindrical rectangular domain through a coordinate mapping technique to ensure numerical stability. The theoretical formulation of the individual segment is established using Hamilton's principle in the framework of first-order shear deformation theory (FSDT), and the thermal effects on the wave plate are considered by employing the thermo-elastic theory. The discretized equations are obtained directly from the strong forms of governing equations in which displacement components are approximated by a mes-hfree Tchebychev-radial point interpolation method (TRPIM) shape function. The formulation of the entire wave plate is obtained using coupling conditions between the segments. The harmonic distributed load and stationary/nonstationary stochastic excitation are considered as the external force. Results: Convergence and verification studies are performed to confirm the reliability and accuracy of the present formulation. Satisfactory agreements are achieved between the numerical results of the proposed method and those from the published literature. Finally, the effect of some parameters on the free vibration and dynamic response of laminated composite wave plate is presented. [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]

This paper presents a novel approach using Generative Adversarial Networks (GANs) to predict thermal stress distribution in binary composites. The composite plates, generated randomly, serve as the basis for finite element simulations that produce datasets for training the GANs. To enhance the training process, binary images representing composite architecture are combined with corresponding thermal stress distribution images, creating a unified dataset. Remarkably, the trained GANs exhibit a high level of accuracy in predicting thermal stress within the composites. The results underscore the potential of GANs in accurately predicting thermal stress, opening avenues for advancements in materials science. [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 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]

Background: The plate structure is one of the typical components of the mechanical system and its vibration research has attracted full attention. Graphene platelet is a new high-performance nano-reinforced filler and its emergence provides an opportunity to improve the vibration properties of conventional composite plate structures. Purpose: The free vibration characteristics of the three-phase composite thin plate reinforced synergistically by graphene platelets (GPLs) and carbon fibers are studied in this paper, and we also analyze the influences of the content changes of different reinforcements on the natural frequencies and mode shapes of the three-phase composite thin plate. Methods: The effective material properties of the three-phase composite material are calculated according to a combination of the Halpin–Tsai model and the micromechanics approach. The separation method of variables is used to obtain the natural frequencies and mode shapes of the three-phase composite thin plate under different boundary conditions. The accuracy of results from the separation method of variables is verified by comparison with the references. Conclusions: The synergistic effect of GPLs and carbon fibers can increase the natural frequencies of a composite thin plate under different boundary conditions. The mode shape transformation phenomena mostly appear in the higher order vibrations of the three-phase composite thin plate when the GPLs content increases. The appearance of mode shape transformation is accompanied by a change in the rate of frequency growth. These results have important theoretical significance for a widespread engineering application of the three-phase composite structure. [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]

Composite plates are susceptible to various damages in complex conditions and working environments, which may reduce the reliability of the structure and threaten equipment and personal safety. Thus, the implementation of a robust online Structural health monitoring (SHM) system for these composite structures becomes imperative. To enhance reliability and safety, we introduce a robust online SHM system anchored by our newly developed damage detection Bayesian neural network (DD-BNN). The main contribution of this study lies in the DD-BNN to perform precise and reliable damage detection and localization in composite plates using only one actuator-receiver pair without any signal/feature pre-processing and human intervention. The proposed DD-BNN model innovatively combines probabilistic modeling with deep learning to address uncertainty in Lamb wave-based damage detection and model performance for composite plates, featuring a specialized probabilistic layer trained through Bayesian inference to efficiently encapsulate and manage uncertainty in model weights and activation. Notably, our method significantly simplifies the SHM system design and manual operation requirements. In addition, this approach not only reduces overfitting but also enhances robustness to noise, as confirmed by experiments on perturbation analysis of Gaussian and Poisson noise. [ABSTRACT FROM AUTHOR]

Purpose: Three-dimensional thermal vibration analysis of functionally graded carbon nanotube (FG-CNT) reinforcement composite plates is performed for uniform, linear and sinusoidally temperature distribution. Methods: The reinforcement directions is considered through the thickness according to four reinforcement models as UD, FG-V, FG-O and FG-X are examined. As the components of the composite, the material properties of both the CNT forming the reinforcement phase and the polymer forming the matrix phase change depending on the temperature, and this is the focus of this study. The effective material properties of the FG-CNT reinforced composite are determined by the mixtures rule. The three displacements of the plates are expanded by a series of Chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions. The natural frequencies are obtained by the Ritz method. Results: It is shown that the numerical results of the current approach are compared with the results of other researchers for validation, the results appear to be in good agreement. The effects of the thickness-to-length ratio and different volume fraction distributions for cantilever (CFFF) boundary conditions in considered thermal environments are investigated. The effect of different boundary conditions such as clamped (CCCC), simply supported (SSSS), simply supported through the x-axis and clamped through the y-axis (SCSC) and simply supported through the x-axis and free through the y-axis (SFSF) is also examined. It is shown that the increase in the amount of temperature and the type of temperature distribution are effective on the decrease of frequencies. [ABSTRACT FROM AUTHOR]

The ice formation over the aerofoil structure of the aircraft wing has been an obstruction as they abrupt the airflow, acting as drag. The investigation will intend to determine ice accumulation on carbon fiber-reinforced polymer (CFRP), approximated as ice build-up on aircraft wings. The observation is carried out over quasi-isotropic composite laminates using ultrasonic-guided waves with a central working frequency regime of 100 kHz. The three-dimensional (3D) finite element (FE) simulations are performed to observe the scattering effect to explore the reflection site in the far field. This effect was quite prominent for different thicknesses of Glaze ice (G-Ice) and was found to be strongly linked with the wave propagation and dispersion effect. The scattering results for the reflection of Lamb mode, when it interacted with the G-Ice interface, were quite noteworthy along the angular region rather than on the center line, indicating that the scattering was more prominent due to the presence of a 45° or (− 45)-degree fiber orientation in that laminate. A similar but complex scattering phenomenon was observed for different stacking sequences where the wave propagation angle and its amplitude at the receiver nodes are found to be closely bound with the exponential decay in group/phase velocity for the ice thicknesses studied. The FE approach is verified, and the results are validated analytically. Analytically, we have investigated a much-closed approximation with the detectability obtained from three-dimensional studies. Where the dispersion study performed has also contributed to verifying the present investigation in the long wavelength limits. This study can reveal the various optimized locations for placing the sensor for ice detection and quantification, which can be further helpful for practical guided wave inspection in ice detection and its removal. [ABSTRACT FROM AUTHOR]

Purpose: In comparison to traditional, constant stiffness laminates, variable stiffness composite laminates (VSCL) with curvilinear fibres represent an extra analysis effort. It is the purpose of this work to present and test a relatively simple optimisation procedure, in order to find the maximum fundamental frequency of vibration in bending and in in-plane vibrations. It is also intended to explain why certain fibre paths lead to higher frequencies. Methods: The optimisation is performed using a genetic algorithm (GA), which is described in detail. The bending and the in-plane plate models are based on the p-version Finite Element Method. Each model requires a small number of degrees of freedom, an important feature because applying the GA involves the solution of a large number of eigenvalue problems. In order to support the physical interpretation of the optimal designs, mode shapes and stress fields corresponding to some optimal solutions are illustrated. Results: Single- and multi-layer plates with different boundary conditions and fibre path types are studied. Fibre paths that lead to maximum fundamental frequencies are found and justified. The consequences that maximising the first frequency has on the higher-order modes of vibration are studied. Conclusion: The proposed optimisation and modelling methods are effective. Curvilinear fibres with the characteristics considered led to the maximum first natural frequency of vibration in a few cases, but not all. Particularly in in-plane vibrations, curvilinear fibres can provide major gains in comparison to straight fibres. The increase in the vibration frequency is accompanied by, overall, larger stresses. [ABSTRACT FROM AUTHOR]

An experimental analysis was conducted to investigate the use of external steel plates as tensile reinforcement in concrete beams with prefabricated cages and its failure pattern. A prefabricated cage with an external steel plate as tensile reinforcement and stirrups welded directly to the steel plate was used as the rebar cage for the reinforced concrete beam. This work aims to explore the feasibility of external steel plates as tension reinforcement in terms of their bending behavior and deformability till the failure stage. Twelve specimens with the same beam geometry and concrete grade were used. The ultimate load, load–deflection characteristics, and crack pattern have been studied with respect to the control beam. There are four sets of specimens, which are control beam, plate-reinforced concrete beam, control beam with bent-up bar, and plate-reinforced concrete beam with bent-up bar. Two approaches have been taken in this study: an in-house experimental investigation incorporating theoretical analysis and a numerical simulation utilizing finite element approach (FEA). The obtained experimental data indicated a firm agreement of around 94.7–100% with that of the reference beam with the reduction of crack width, number of cracks, and compressive strain on the steel plate-reinforced beams. [ABSTRACT FROM AUTHOR]

The modal testing and numerical results on free vibration behavior of completely free woven fiber glass/epoxy-laminated composite shallow shell panels are presented in this investigation. The finite element numerical model is established by a doubly curved shell model on the basic of first-order shear deformation theory (FSDT). Vibration study of the composite shell panels is carried out using a quadratic eight-noded isoparametric element. The modal testing experiments are carried out using FFT analyzer with PULSE software to determine natural frequencies of woven fabric glass/epoxy composite cylindrical shell panels under free–free boundary condition. The first four natural frequencies of completely free woven fabric glass/epoxy laminated cylindrical shell panels are obtained for different curvature ratios, sequences of lamination and number of laminate layers. The modal test values illustrate an excellent concurrence with the numerical values and will serve as bench mark for future investigators in the present area. [ABSTRACT FROM AUTHOR]

Purpose: The current analytical study is devoted to examining the nonlinear free vibration behavior of the laminated nanocomposite cylindrical shells containing multi-scale hybrid reinforcements once a nonlinear three-parameter substrate surrounds the structures. The multi-phase material of the structures includes polymeric matrix, nano-scale GOPs, which are uniformly distributed through the thickness of each layer and macro-scale carbon fibers with various orientation angles. Methods: The effective material properties of each multi-phase nanocomposite layer are calculated by implementing the modified Halpin–Tsai micromechanical scheme together with the extended rule of the mixture in a hierarchy. After that, with an incorporation of the improved Donnell's shell theory and Hamilton's principle, the governing equations are derived. Then by adopting a two-step solution technique, these nonlinear equations are transferred to one ordinary differential equation via Galerkins' method, and in the next step, the nonlinear frequencies of the structure are obtained by employing the multiple scale technique. Results: In the framework of various graphical results, a parametric analysis is conducted in detail to reveal the influences of the different parameters such as nonlinear foundation parameters, carbon fibers' orientation angles, GOPs' weight, and carbon fibers' volume fractions and length-to-radius ratios on the nonlinear vibration characteristics of the multi-phase laminated nanocomposite cylindrical shell. Conclusions: The results declare that the addition of the GO nanofillers along with the CFs and also embedding the structure on the nonlinear substrate can significantly enhance the vibrational behavior of the multi-phase laminated nanocomposite cylindrical shell. [ABSTRACT FROM AUTHOR]