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The objective of this investigation is to propose a thermoelasticity model for analyzing the propagation of thermoelastic waves in a composite hollow circular cylinder with an LEMV/CFRP interface layer. The model incorporates a modified nonlocal couple stress theory and addresses the challenges associated with higher order time derivatives. The derivation results in three partial differential equations for the modified nonlocal couple stress of the cylinder in axisymmetric mode. Applying linear elasticity theory, the equations are solved to obtain frequency equations for the external surface of the cylinder under traction-free conditions, while ensuring continuity at the boundaries. The study explores the influence of variations in wave number and thickness on the frequency, temperature, and displacements within the field. To assess the impact of different thermoelasticity theories and nonlocal coupled stress parameters, the research utilizes tables and graphs for comparison and estimation. From the numerical evaluation, it is revealed that the impact of modified nonlocal couple stress parameter shows substantial effects on the physical quantities. [ABSTRACT FROM AUTHOR]

The main goal of this study is to examine the buckling properties of a composite material that combines graphene-origami-enabled features with magnetostrictive facesheets. The nonlocal theory, as developed by Eringen, has been used for the purpose of quantifying the small-scale parameter. However, the system being presented is based on the theoretical framework established by Winkler and Pasternak, which incorporates the analysis of a deformable medium. The use of a theoretical framework referred to as higher-order sinusoidal shear deformation theory has been utilized to formulate the governing equation. The governing equation is then solved via the Galerkin solution approach, while considering various boundary conditions. In order to assess the precision and effectiveness of the present inquiry, the findings are juxtaposed with the prevailing scholarly publications in the academic literature. Furthermore, this study aims to examine the impact of several factors, including as the weight fraction, hydrogen atom coverage, aspect ratio, and temperature, on the critical buckling load. The findings of the present investigation indicate that an increase in the weight fraction of graphene-origami-enabled material leads to an increase in the buckling load. The main aim of this study is to improve the understanding and predictive capability of engineers and designers about the phenomenon of buckling response. The aforementioned data have the potential to provide advantages in the advancement of nanoscale systems, including highly sought-after technologies such as sensors and actuators. [ABSTRACT FROM AUTHOR]

The main aim of this study is to examine the buckling behavior of a composite material that has both magnetostrictive capabilities and functionally graded facesheets. The effective material parameters of the functionally graded layer are determined using the power-law model. Eringen's nonlocal theory has been used for the quantification of the small-scale parameter. In contrast, the suggested system is based on the theoretical framework established by Winkler and Pasternak, which incorporates the analysis of an elastic medium. The use of higher-order sinusoidal shear deformation theory has been employed to derive the governing equation. This governing equation is then solved analytically using the Galerkin solution method, considering various boundary conditions. In order to assess the precision and effectiveness of the ongoing inquiry, the findings are juxtaposed with the existing literature articles. Furthermore, this study examines the impact of many factors, including aspect ratio, velocity feedback gain, and foundation, on the critical buckling load. The findings of the present research indicate that there is a positive correlation between the porosity volume parameter and the buckling load of the structure. The current study aims to provide engineers and designers with a better understanding and predictive capability about buckling response. This knowledge may be advantageous in the design of nanoscale systems, including highly sought-after technologies like as sensors and actuators. [ABSTRACT FROM AUTHOR]

The study explores the free vibration characteristics of hybrid laminated nanocomposite truncated conical shells and panels incorporating functionally graded graphene platelet-reinforced (FG-GPLs) and functionally graded carbon nanotube-reinforced (FG-CNTs) materials, advancing understanding in hybrid material applications. The structures are assumed to be supported by a two-parameter elastic foundation, and the study also considers the influence of CNT agglomeration. The estimation of CNT agglomeration effect is performed using a two-parameter agglomeration model based on the Mori–Tanaka approach, considering the random orientation of carbon nanotubes. By employing a combination of various control parameters, it becomes possible to determine the optimal mode for setting the natural frequency of the system. To ensure accurate calculations for both thin and thick shells, a third-order shear deformation theory is employed. The governing equations and boundary conditions are formulated based on Hamilton's principle. Numerical solutions are obtained through the systematic differential quadrature method, wherein the Kronecker delta function is employed. By introducing subtle adjustments to the governing equations, this method effectively minimizes computational volume and complexity, proving particularly advantageous for addressing problems characterized by higher degrees of freedom. To estimate the effective mechanical properties of the CNT-reinforced nanocomposite layers, the rule of mixtures is employed. Meanwhile, the Halpin–Tsai micromechanical model is utilized for calculating the properties of the GPL-reinforced nanocomposite layers. The presented study establishes convergence and accuracy through evaluation, considering various parameters such as CNTs volume fraction, GPLs mass fraction, different distribution patterns, different geometries under various boundary conditions, vertex angle of the cone, agglomeration characteristics of CNTs, and different stiffness of the elastic foundation. [ABSTRACT FROM AUTHOR]

The main objective of this work is to examine the vibrational characteristics of a nanobeam exhibiting auxetic activity, achieved by the incorporation of a magnetostrictive material called Terfenol-D. The nanobeam is postulated to include three distinct layers, whereby the central layer is comprised of a magnetostrictive substance, while the outside layers are formed of auxetic material. On the other hand, the use of higher-order parabolic shear deformation beam theory is utilized to obtain the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. This work presents a thorough analysis and elucidation of the influence of several parameters, such as auxetic inclination angle, auxetic rib length, and feedback gain, on the investigated system. Based on current research, evidence suggests that adding auxetic facesheets to magnetostrictive beam results in decreasing dimensionless natural frequency. In order to establish the accuracy and dependability of the present study, a comparison examination has been undertaken to juxtapose our results with the existing body of scholarly literature. The results obtained from the present study have the potential to provide a valuable contribution to the advancement and improved understanding of nano-systems, namely nano-sensors and nano-actuators. Furthermore, the conclusions acquired from this study might potentially serve as a fundamental framework for future research. [ABSTRACT FROM AUTHOR]

The objective of this research is to manipulate the vibrational characteristics of a graphene-origami auxetic beam via the use of magnetostrictive materials. The use of higher-order parabolic shear deformation beam theory is utilized to determine the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. The results indicate that the integration of a graphene-origami auxetic core into a magnetostrictive beam results in an augmentation of the dimensionless natural frequency. Moreover, the results obtained might potentially serve as a preliminary stage for future research endeavors. In order to establish the accuracy and dependability of the present study, a comparison examination has been undertaken to juxtapose our results with the existing body of scholarly literature. The results of the present study have the potential to further the understanding and advancement of nanosystems, namely nanosensors and nanoactuators. Moreover, the results might perhaps serve as a preliminary stage for future inquiries. [ABSTRACT FROM AUTHOR]

This article analyzes the nonlinear vibrations of porous truncated conical polyvinylidene fluoride (PVDF) reinforced with Terfenol-D particles. The effective properties of the magneto-electro-elastic composite have been obtained using the Eshelby–Mori–Tanaka model. Also, the porosity in the composite is considered uniform. The governing equation of the system is derived based on the von Karman theory of nonlinear strains and the theory of first-order shear deformation by applying the principle of minimum energy potential and Hamilton's principle. These equations are solved using the generalized differential quadrature method. The effect of porosity, vertex angle, shell length, boundary conditions, and volume fraction of Terfenol-D will be discussed. Also, for validation, the obtained results were compared with those found in the literature, which was a good answer, along with the accuracy. Results show that the nonlinear to linear natural frequency ratio has a decreasing trend at the lower vertex angle. The present findings can serve as a reference point for subsequent assessments. [ABSTRACT FROM AUTHOR]

The functionalization of graphene aims at altering its material properties to encourage its use in various new applications. In the present research, an investigation on a functionalized graphene oxide (FGO) reinforced nanocomposite (NC) plate is performed once the plate is subjected to thermal loading. The reinforcement of the plate is done with multiple functionally graded (FG) distributions through the thickness, specifically, uniform (U), X, V, and O. This action is for the purpose of finding the most effective distributional strategy for functionalized graphene oxide with ameliorated vibrational characteristics. Also, the Winkler–Pasternak elastic substrate serves as the support for the plate construction. To describe the mechanical properties of the FG nanocomposite plate, the Halpin–Tsai model is employed and a more advanced higher order shear deformation model is used to take the impact of shear deformation into account. Next, Hamilton's principle is utilized to derive the governing equations of the plate structure. These governing equations are then solved for a simply supported functionalized graphene oxide-reinforced nanocomposite plate. Ensuing, several parametric studies are presented to better delineate the impact of numerous variants including FGO's weight fraction, distribution patterns, temperature raise, elastic substrate coefficients, and geometrical properties on the nanocomposite plates' fundamental frequency. Results of our study indicate that raising the temperature and aspect ratio can decrease the natural frequency of FGO-reinforced NC plates, while increase in the FGO's weight fraction and elastic foundation does the opposite. [ABSTRACT FROM AUTHOR]

This work is an attempt to examine the wave propagation of thermally loaded graphene platelets (GPL)s reinforced nanocomposite plates. Particularly, an analytical approach is made to determine the extent of wave dispersion in functionally graded nanocomposite plates reinforced with graphene platelets (GPL)s when thermal loading is added to the structure. Along with thermal loading, the plate structure is rested on an elastic foundation to derive a more realistic outcome. Variety of thermal loads with different temperature rises have been studies in the present research; these loads include: uniform temperature rise (UTR), sinusoidal temperature rise (STR), and linear temperature rise (LTR). Moreover, the nanocomposite (NC) plate is rested on a Winkler–Pasternak elastic foundation. GPL particles are dispersed in the polymer base along the thickness of the plate in four differing distribution patterns. Furthermore, Hamilton's principle along with refined higher-order plate theory is utilized to derive the governing equations of the problem. Afterwards, these differential equations are solved in an analytical format to attain the wave frequency, as well as, the phase velocity of GPL-reinforced NC plate. Before, assessing the impact of numerous parameters on the wave propagation characteristics of GPL-reinforced NC plate, our analytical model had been validated with previous studies. Results of this study indicates that the wave dispersion of NC plates reinforced with GPLs is heavily depended on parameters such as GPL distribution pattern, thermal loading type, GPL weight fraction and so on. [ABSTRACT FROM AUTHOR]

The primary focus of this study is to analyze the vibrational properties of a nanobeam with a porous structure, which is composed of a functionally graded material. Additionally, the nanobeam comprises a magnetostrictive substance known as Terfenol-D. The nanobeam is postulated to include three distinct layers, whereby the central layer is comprised of a magnetostrictive material, while the outside layers are built of functionally graded material. On the other hand, the use of higher-order parabolic shear deformation beam theory is utilized to get the kinematic relations. Moreover, Eringen's nonlocal theory is used to include the impact of small-scale phenomena. The governing equations are derived by the application of Hamilton's principle and then solved using analytical techniques. This study presents a thorough examination and elucidation of the influence exerted by several elements, such as aspect ratio, feedback gain, and gradient index, on the system being studied. Based on extant research, empirical evidence indicates that increasing the feedback gain results in a decrease in the natural frequencies. In order to establish the accuracy and dependability of our present study, we have undertaken a comparison examination of our results in relation to the existing body of the literature. The results of the present study have the potential to advance the understanding and progress in the field of nano-systems, namely nano-sensors and nano-actuators. [ABSTRACT FROM AUTHOR]

Our study employs the Timoshenko beam theory to thoroughly investigate the propagation of waves in auxetic metamaterial beams enabled by functionally graded graphene origami. This exploration is conducted while the Winkler–Pasternak foundation supports the beams. In addition, many distinct graphene origami (GOri) distribution patterns have been explored, and the results have been shown to be uniform and functionally graded across the thickness direction. The kinetic equations of auxetic metamaterial beams may be captured with the help of Hamilton's principle, which is applied here. The analytical solution of the governing equations for the auxetic metamaterial beam is determined based on the received information. Comparisons have been made between the effects that a wide variety of parameters have on the wave frequency and phase velocity of the auxetic metamaterial beam. These parameters include graphene distribution pattern and content, GOri folding degree, temperature, wave number, and elastic foundation coefficients. The crucial aspects of each figure have been identified through in-depth analysis and comparison of the results. [ABSTRACT FROM AUTHOR]

This research employs a multiple scales perturbation approach to evaluate the nonlinear wave propagation behaviors of a doubly curved sandwich composite piezoelectric shell with a flexible core in a hygrothermal environment. Stress and strain calculations for the flexible core and face sheets are carried out using Reddy's third-order shear deformation theory (TSDT) and third-order polynomial theory, respectively. The study explores the synergistic effects of a multilayered shell, flexible core, and magneto-rheological layer (MR) in revealing the nonlinearity of both in-plane and vertical moment within the core. The Halpin–Tsai model is employed to derive the properties of polymer/carbon nanotube/fiber (PCF) and polymer/graphene platelet/fiber (PGF) three-phase composite shells. The governing equations for the multiscale shell are derived using Hamilton's formulation. The research investigates temperature variations, diverse distribution patterns, curvature ratios, and magnetic fields through numerical analysis, presenting the results graphically and prior research has demonstrated the accuracy of these methods. Notably, these factors exert significant influence on the frequency-amplitude curves of the smart structure. [ABSTRACT FROM AUTHOR]

The present article studies the finite element modeling of wave propagation characteristics in a nonlinear thermal piezoelectric hygroscopic nanoporous metal foam nanobeam. The symmetry 1, symmetry 2, and uniform type of nanoporosity patterns are employed in this study. The controlling equation of motion is derived via a modified trigonometric beam model in higher order. The effect of a piezo electric field is incorporated with the governing equations by convoluting field quantities and displacement components. The Rayleigh–Ritz finite element method is adopted to observe the dynamic response of the nanobeam. Comparison studies are performed to display the accuracy and efficiency of this analytical model. Further, the effects of piezoelectric strain, porosity coefficient, moisture concentration, slenderness ratio, and thickness to diameter ratio on the critical buckling load of metal foam nanobeams are thoroughly investigated and highlighted by Tables and dispersion curves. [ABSTRACT FROM AUTHOR]

In this paper, the vibration problem of a rectangular plate rested on a viscoelastic substrate and consisting of porous metal foam is solved via an analytical method with respect to the influences of various porosity distributions. Three types of porosity distribution across the thickness are covered, namely uniform, symmetric and asymmetric. The strain–displacement relations of the plate are assumed to be derived on the basis of a refined higher-order shear deformation plate theory. Then, the achieved relations will be incorporated with the Hamilton's principle in order to reach the Euler–Lagrange equations of the structure. Next, the well-known Galerkin's method is utilized to calculate the natural frequencies of the system. The influences of both simply supported and clamped boundary conditions are included. In order to show the accuracy of the presented method, the results of present research are compared with those reported by former published papers. The reported results show that an increase in the porosity coefficient can dramatically decrease the frequency of the plate. Also, the stiffness of the system can be lesser decreased, while a symmetrically porous metal foam is used to manufacture the plate. [ABSTRACT FROM AUTHOR]

In this research, electrically characteristics of a graphene nanoplatelet (GPL)-reinforced composite (GPLRC) microdisk are explored using generalized differential quadrature method. Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin–Tsai micromechanics is used to acquire the elasticity of the structure, whereas the variation of thermal expansion, Poisson's ratio, and density through the thickness direction is determined by the rule of mixtures. Hamilton's principle is implemented to establish governing equations and associated boundary conditions of the GPLRC microdisk joint with PIAC. The compatibility conditions are satisfied by taking perfect bonding between the core and PIAC into consideration. Maxwell's equation is employed to capture the piezoelectricity effects. The numerical results revealed the important role of ratios of length scale and nonlocal to thickness, outer-to-inner ratio of radius ( R o / R i ), ratio of piezoelectric to core thickness (hp/h), and GPL weight fraction ( g GPL ) on the critical voltage of the system. Another important consequence is that by increasing R o / R i , the critical voltage of the smart structure increases more intensely in comparison with the g GPL . [ABSTRACT FROM AUTHOR]

In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers' number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure decreases but in higher value of length scale parameter this matter is inverse. Finally, influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature and frequency of the laminated composite nanostructure are investigated. [ABSTRACT FROM AUTHOR]

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton's principle is employed to establish the governing equations of motion, which is finally solved by generalized differential quadrature method (GDQM) and perturbation method (PM). Finally, the results show that FG patterns, different orientation angle of the fiber, the VF and WCNT parameters, axial load, nonlinear temperature gradient, and applied temperature of the top surface play an essential impact on the linear and nonlinear dynamic responses of the MHCD. The more significant outcome of this research is that the effects of the VF, WCNT, θ , and β parameters on the nonlinear frequency of the MHCD can be considered at the higher value of the large deflection parameter and the effect of negative axial load on the dynamic responses of the structure is more intensive. As an applicable result show that the best functionally graded (FG) pattern for serving the highest nonlinear dynamic response of an MHC reinforced annular plate is FG-A. [ABSTRACT FROM AUTHOR]

In this paper, analytical functions for the estimation of the temperature-dependent behaviors of poorly and highly dispersed graphene oxide reinforced nanocomposite (GORNC) materials are studied in the framework of a machine learning-based approach. The validity of the presented models is shown comparing the results achieved from this modeling with those reported in the open literature. Also, the application of the obtained functions in solving the thermal buckling problem of beams constructed from such nanocomposites is demonstrated based on an energy-based method incorporated with a shear deformable beam hypothesis. The verification of the results indicates that the presented mechanical model can approximate the buckling behaviors of nanocomposite beams with remarkable precision. It can be realized from the results that the temperature plays an indispensable role in the determination of the buckling load which can be endured by the nanocomposite structure. [ABSTRACT FROM AUTHOR]

This work is motivated by little research in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates. This paper, using an analytical approach, presents bifurcations in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates caused by the parametric excitation. An axial parametric load is applied to excite the system, while the reinforced piezoelectric nanoplate is under an applied electric voltage, simultaneously. The governing equations of motion for the reinforced piezoelectric nanoplate embedded on a visco-Pasternak foundation are derived using the nonlocal elasticity theory, Hamilton's principle, and nonlinear von Karman theory. A class of nonlinear the Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The numerical results are performed, while the emphasis is placed on investigating the effect of the applied electric voltage, visco-Pasternak foundation coefficients, and the parametric excitation. It is found that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of the natural frequency. [ABSTRACT FROM AUTHOR]

Present paper is proposed to capture the influences of carbon nanotubes' agglomeration on the stability behaviors of multi-scale hybrid nanocomposite beams within the frameworks of refined higher order beam theories for the first time. In this research, a mixture of macroscale and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multi-scale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby–Mori–Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher order beam theorem. Next, the derived equations will be solved in the framework of Galerkin's well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included, too. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the structure's stability endurance. [ABSTRACT FROM AUTHOR]

The present study mainly investigates the effect of the residual surface stress and the applied electric voltage on the nonlinear dynamic instability of the viscoelastic piezoelectric nanoresonators under parametric excitation. In fact, great attention is given to the influence of the residual surface stress on the nonlinear instability of the system. Numerical examples are treated which show various bifurcations. By means of a bifurcation analysis, it is shown that the instability of the system can be significantly affected by considering the residual surface effect. The results also show that a discontinuous bifurcation is always accompanied by a jump. Finally, stable and unstable regions in dynamic instability of viscoelastic piezoelectric nanoplates are addressed. [ABSTRACT FROM AUTHOR]

The present study mainly investigates surface effect on nonlinear dynamic instability of viscoelastic nanoplates under parametric excitation. In fact, great attention is given to the influence of residual surface stress on nonlinear dynamic behavior of the system. To achieve this goal, the governing equation of motion is derived by modeling a nanoplate embedded on a visco-Pasternak foundation and then, applying surface effect relations, nonlocal elasticity and nonlinear von Karman theories and Hamilton's principle, respectively. Galerkin technique and multiple time scales method are also used to solve the equation. A class of nonlinear Mathieu–Hill equation is established to determine the bifurcations and the regions of nonlinear dynamic instability. The numerical results are performed, while the emphasis is placed on investigating the effect of residual surface stress, visco-Pasternak foundation coefficients, and parametric excitation. It is shown how residual surface stress leads to high values of amplitude response. Finally, stable and unstable regions in dynamic instability of viscoelastic nanoplates are addressed. [ABSTRACT FROM AUTHOR]

In this article, the bending analysis of flexoelectric functionally graded (FG) microbeams according to nonlocal elasticity theory is verified. To this end, higher order refined beam theory has been used. The foundation of FG microbeam includes Winkler-Pasternak layer. Hamilton’s principle is used to obtain the governing equations based on the nonlocal theory and solved employing an analytical solution. The model is designed in such a way that the properties change continuously. A parametric study is presented to inquire the nonlocal parameter, power-law hygro-thermal-loadings, flexoelectric effect, transverse external loading, on the bending characteristics of FG microbeam. It is found that boundary conditions, flexoelectric effect, nonlocal parameter, power-law index and beam geometrical parameters have notable effects on dimensionless deflection of FG microscale beams. [ABSTRACT FROM AUTHOR]

A class of nonlinear Mathieu–Hill equation is established to determine the bifurcations and the regions of nonlinear dynamic instability of a short double-walled nanobeam, while the emphasis is placed on investigating the effect of residual surface stress on instability. To achieve this goal, first, a short double-walled nanobeam is modeled and embedded on a viscoelastic foundation and subjected to an axial parametric force. Second, based on the nonlocal elasticity and nonlinear von Karman beam theories, the nonlinear governing equation of motion is derived. Finally, Galerkin technique and multiple time scales method are used to solve the equation. Numerical examples are treated which show various discontinuous bifurcations. Also, infinitely stable and unstable solutions are addressed. [ABSTRACT FROM AUTHOR]

This article explores that the study on bending of magneto-electric-elastic nanobeams relies on nonlocal elasticity theory. The Vlasov's model foundation utilizes the silica aerogel foundation. The guiding expressions of nonlocal nanobeams in the considered framework are used extensively and where parabolic third-order beam theory is achieved after using Hamilton's principle. Parametric work is introduced to scrutinize the influence of the magneto-electro-mechanical loadings, nonlocal parameter, and aspect ratio on the deflection characteristics of nanobeams. It is noticed that the boundary conditions, nonlocal parameter, and beam geometrical parameters have significant effects on dimensionless deflection of nanoscale beams. [ABSTRACT FROM AUTHOR]

In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton's principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums. [ABSTRACT FROM AUTHOR]

In this article, the damping forced harmonic vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam embedded in viscoelastic foundation is evaluated based on nonlocal strain gradient elasticity theory. The viscoelastic foundation consists of Winkler–Pasternak layer. The governing equations of nonlocal strain gradient viscoelastic nanobeam in the framework of refined shear deformable beam theory are obtained using Hamilton's principle and solved implementing an analytical solution. In addition, a parametric study is presented to examine the effect of the nonlocal strain gradient parameter, magneto-electro-mechanical loadings, and aspect ratio on the vibration characteristics of nanobeam. From the numerical evaluation, it is revealed that the effect of electric and magnetic loading on the natural frequency has a predominant influence. [ABSTRACT FROM AUTHOR]

In this study postbuckling behaviors of multiscale composite sandwich doubly curved piezoelectric shell with a flexible core and MR layers by employing Homotopy Perturbation Method in hygrothermal environment has been investigated. By using Reddy third shear deformable theory the face sheets and third-order polynomial theory of the flexible core the strains and stresses are obtained. A mathematical model for the multiscale composite layered shell with a flexible core and magnetorheological layer (MR) that incorporates the nonlinearity of the in-plane and the vertical displacements of the core is assumed. Three-phase composite shells with polymer/Carbon nanotube/fiber and polymer/Graphene platelet/fiber either uniformly or non-uniformly based on different patterns according to Halpin–Tsai model have been considered. The governing equations of multiscale shell have been derived by implementing Hamilton's principle. Meanwhile, simply supported boundary conditions are employed to the shell. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, different parameters such as temperature rise, various distribution patterns, magnetic fields and curvature ratio are considered in this article. It is found these parameters have significant effect on the frequency–amplitude curves. [ABSTRACT FROM AUTHOR]

An analytical answer to the buckling problem of a composite plate consisted of multi-scale hybrid nanocomposites is presented here for the first time. In other words, the constituent material of the structure is made of an epoxy matrix which is reinforced by both macro- and nanosize reinforcements, namely, carbon fiber (CF) and carbon nanotube (CNT). The effective material properties such as Young's modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin–Tsai model. To present a more realistic problem, the plate is placed on a two-parameter elastic substrate. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived using the classical theory of plates. Finally, the governing equations are solved analytically to obtain the critical buckling load of the system. Afterward, the normalized form of the results is presented to emphasize the impact of each parameter on the dimensionless buckling load of composite plates. It is worth mentioning that the effects of various boundary conditions are covered, too. To show the efficiency of presented modeling, the results of this article are compared to those of former attempts. [ABSTRACT FROM AUTHOR]

The nonlinear vibration behavior and dynamic instability of Euler–Bernoulli nanobeams under thermo-magneto-mechanical loads is the main objective of the present paper. Firstly, a short Euler–Bernoulli nanobeam is modeled and exposed to an external parametric excitation. Based on the nonlocal continuum theory and nonlinear von Karman beam theory, the nonlinear governing differential equation of motion is derived. Secondly, to transport the partial differential equation to the ordinary differential equation, Galerkin method is applied. Then, multiple scales method, as an analytical approach, is used to solve the equation. At the end, modulation equation of Euler–Bernoulli nanobeams is obtained. Then, to evaluate the dynamic instability of the system, trivial and nontrivial steady-state solutions are discussed. Emphasizing the effect of parametric excitation, for considering the instability regions, bifurcation points are studied and investigated. As a result, it can be observed that the damping coefficient plays an effective role as well as parametric excitation in stability and frequency response of the system. [ABSTRACT FROM AUTHOR]

This research develops a nonlocal couple stress theory to investigate static stability and free vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton's principle and they are solved applying Chebyshev–Ritz method which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation and various boundary conditions on natural frequencies and buckling loads of FG nanobeams in detail. [ABSTRACT FROM AUTHOR]

In this research, thermal vibration analysis of a graphene oxide powder-reinforced (GOPR) nanocomposite embedded plate is carried out once the plate is exposed to different types of thermal loading. The plate is reinforced with various functionally graded (FG) distributions through the thickness, namely uniform, X, V, and O in a comparative way to find out the most efficient model of GOPs' distribution for the purpose of improving vibrational behaviors of the structure. Also, the Halpin–Tsai micromechanical model is employed to describe the material properties of an FG nanocomposite plate. The shear deformation effects are taken into account using a refined higher order shear deformation plate theory. Moreover, the governing equations of the structure have been derived using Hamilton's principle and then solved analytically for a simply supported GOPR nanocomposite plate. Besides, detailed parametric studies are procured to show the influences of different variants on the natural frequency of the nanocomposite plates. Presented results reveal that the frequency responses of the nanocomposite plates in a thermal environment dramatically depend on the distribution pattern of the GOPs. [ABSTRACT FROM AUTHOR]

Due to rapid development of process manufacturing, composite materials with porosity have attracted commercial attention in promoting engineering applications. For this regard, in this research wave propagation-thermal characteristics of a size-dependent graphene nanoplatelet-reinforced composite (GNPRC) porous cylindrical nanoshell in thermal environment are investigated. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the laminated composite cylindrical nanoshell in thermal environment have been evolved using Hamilton's principle and solved with the assistance of the analytical method. For the first time, wave propagation-thermal behavior of a GNPRC porous cylindrical nanoshell in thermal environment based on NSGT is examined. The results show that by increasing the thickness, the effect of porosity on the phase velocity decreases. Another important result is that by increasing the value of the radius, the difference between the minimum and maximum values of the phase velocity increases. Finally, influence of temperature change, wave number, angular velocity and different types of porosity distribution on phase velocity are investigated using the mentioned continuum mechanics theory. As a useful suggestion, for designing of a GPLRC nanostructure should be attention to the GNP weight function and radius, simultaneously. [ABSTRACT FROM AUTHOR]

In this paper, surface and thermal effects on the vibration characteristics of viscoelastic functionally graded (FG) nanobeams embedded in a viscoelastic foundation are investigated based on nonlocal strain gradient elasticity theory and Euler-Bernoulli beam model. The present model contains two parameters to capture the size effects in which the stress is considered for not only the nonlocal stress field but also the strain gradients stress field. Gurtin-Murdoch elasticity theory is incorporated into the nonlocal strain gradient theory to develop a nonclassical beam model including the surface effects. The viscoelastic foundation consists of a Winkler-Pasternak layer together with a viscous layer of infinite parallel dashpots. A power-law model is adopted to describe a continuous variation of material properties of the FG nanobeam. The governing equations of nonlocal viscoelastic FG nanobeams are obtained using Hamilton's principle and solved implementing an analytical solution for simply supported and clamped-clamped boundary conditions. The results are validated with those available in the literature. The effects of linear, shear and viscous layers of foundation, structural damping coefficient, surface elasticity, nonlocal parameter, length scale parameter, temperature change, power-law exponent, and slenderness ratio on the frequencies of viscoelastic FG nanobeams are examined. [ABSTRACT FROM AUTHOR]

A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem. The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently, the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic base excitation are presented. [ABSTRACT FROM AUTHOR]