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In the current paper, analysis of torsional vibration behavior of non-circular nanorods made of auxetic honeycomb material is investigated for the first time. The triangular and elliptical cross-sections are selected to be analyzed. Moreover, one of the distinct properties of auxetic honeycomb materials is that they possess a negative Poisson's ratio, which can be effective on the design and analysis of structures. In order to capture a small size or scale effect, the constitutive relation of nanorods is modified based on Eringen's nonlocal elasticity theory (ENET). Hamilton's principle is employed to obtain the kinematic relation of nanoscale rods. The nonlocal derived governing equations of non-circular auxetic nanorods are solved by utilizing an analytical method with respect to different boundary conditions. In order to verify the correctness of obtained outcomes, the results are compared to previous investigations, and good agreement can be observable. The influences of various parameters such as both Clamped–Clamped (C–C) and Clamped-Free (C-F) boundary conditions, nonlocal parameters, inclined angles, and geometrical ratios are explored and illustrated in the framework of several figures, which can be seen in detail. [ABSTRACT FROM AUTHOR]

The current paper is devoted to investigate the free and forced vibrational responses of the multi-phase angle-ply laminated nanocomposite beam with focusing on the occurrence of resonance phenomenon. The influence of uniform thermal loading and three-parameter Kerr substrate which can affect the resonance behavior of the structure is surveyed. Utilizing a superior nanofiller with the name of Graphene Oxide (GO) together with the macro-scale Carbon Fibers (CFs) will constitute a novel multi-scale hybrid reinforcement for the polymer matrix. The combination of the Halpin–Tsai micromechanical model and extended rule of the mixture is implemented to estimate the effective properties of this multi-scale hybrid nanocomposite. Refined higher-order beam theory is employed to obtain the displacement fields and then with applying Hamilton's principle, the governing equations are derived and analytically solved via Galerkin's exact solution method. Also, the presented results are validated with reputed works in open literature. Furthermore, some tabulated and graphical results are provided to reveal the effects of various parameters such as fibers' orientation angle, weight and volume fractions of reinforcements, different boundary conditions, beam's slenderness ratio, Kerr substrate parameters, excitation frequency and temperature change on the dynamic behavior of the proposed structure. [ABSTRACT FROM AUTHOR]

The present article studies the two phase local/nonlocal deformation of magneto thermo electrical composite nano beam reinforced with graphene oxide powder (GOP). The controlling equation of motion and boundary conditions are derived via two phase elasticity in differential form conjunction with Hamilton's principle and Euler-Bernoulli beam model. The effect of a non-uniform magnetic and piezo electric field is incorporated with the governing equations by convoluting field quantities and displacement components. Then, Navier method is adopted to observe the influence of various boundary conditions on the dynamics of the beam. Comparison studies are performed to display the accuracy and efficiency of this analytical model. Further, the effects of magnetic field, GOP weight fraction, two phase parameter, external electric voltage, nonlocal parameter and temperature difference on the dimensionless frequency of GOP reinforced magneto piezo thermo elastic composite beams are thoroughly investigated and highlighted through tables and dispersion curves. [ABSTRACT FROM AUTHOR]

This study aims to control the vibrational behavior of an auxetic plate coated with magnetostrictive material. The kinematic relations of the plate, rested on a Winkler–Pasternak medium, are expressed based on the first-order shear deformation theory (FSDT). The governing equations are derived by employing the Hamilton's principle and solved analytically by applying the Navier's method. The effects of various parameters such as auxetic inclination angle, auxetic rib length, and feedback gain, on the control behavior of the system are monitored in detail. In order to exhibit the accuracy and validity of this study, our results are compared to those available in the literature. The results indicate that adding auxetic core to magnetostrictive plate results in increasing dimensionless natural frequency. The results obtained from this study can potentially contribute to the advancement of various applications such as the design and improvement of sensors, actuators, and vibration cancellation systems. Additionally, the obtained results could serve as a foundational basis for subsequent investigations. [ABSTRACT FROM AUTHOR]

It is clear that there is a relationship between time and space in nanostructures that are always attacked by waves with wavelengths within the intrinsic characteristic length of the nanostructure. Also, the viscoelastic behavior of nanostructures is affected by this relationship between nonlocal time and nonlocal space. It is worth noting that the conventional tempo-spatially decoupled nonlocal viscoelasticity does not give accurate results regarding the viscoelastic response of these structures. Hence, herein and for the first time, a novel fractional nonlocal time–space strain gradient viscoelasticity is implemented to be able to give a correct answer in addressing the dispersion of elastic waves inside functionally graded material (FGM) viscoelastic nanoplates. The constructive equations of this theory are based on the theory of nonlocal strain gradient elasticity. The properties of the FGM studied in this research are obtained by the power-law model, and the kinematic relations are extracted based on the refined higher-order plate theory. Subsequently, motion equations are written using Hamilton's principle and solved analytically. The results of this work reveal that an increase in the nonlocal parameter can reduce the loss factor in a remarkable way due to the coupling between the nonlocalities in the spatial and temporal domains. [ABSTRACT FROM AUTHOR]

There is a correlation between nonlocal time and space in the nanostructures which are attacked by waves whose length lies in the range of the nanostructure's intrinsic characteristic lengths. This temporal–spatial coupling affects the viscoelastic behaviors of the nanostructures. In such a case, the conventional tempo-spatially decoupled nonlocal viscoelasticity is not able to provide accurate dynamic responses. To resolve this problem, the present paper focuses on the development of a novel fractional nonlocal time–space strain gradient viscoelasticity and shows its application in the wave propagation analysis of functionally graded material (FGM) nanobeams. The fractional constitutive equations are derived on the basis of the combination of the well-known nonlocal strain gradient elasticity and fractional nonlocal time–space hypotheses. The motion equations of the beam-type elements are presented on the basis of the refined higher-order beam theory and Hamilton's principle. With this newly developed nonlocal theory, the governing equations of the nanobeam are extracted. Afterward, an analytical wave solution will be utilized to achieve the loss factor of the problem. The results of this work reveal that an increase in the nonlocal parameter can reduce the loss factor in a remarkable way due to the coupling between the nonlocalities in the spatial and temporal domains. [ABSTRACT FROM AUTHOR]

This research is concerned with the analysis of wave propagation of multi-scale hybrid composite beams subjected to various types of thermal loading. Carbon fiber (CF) and carbon nanotube (CNT) are assumed as reinforcements that are distributed in the matrix. The homogenization process is performed exerting the Halpin–Tsai model and the rule of mixture. Different types of temperature rise, namely, uniform, linear and sinusoidal temperature rise are presumed to present a more trustworthy thermal analysis. The beam is rested on Winkler–Pasternak foundation. A refined trigonometric shear deformable beam theory is used to compute the kinetic relations without any external shear correction coefficient. Governing equations are derived implementing Hamilton's principle and then solved analytically. Eventually, the effects of different parameters, such as CNT's weight fraction, the volume fraction of CF, elastic foundation, different types of temperature rise, etc., on wave frequency and phase velocity. are provided numerically in the framework of a set of illustrations. [ABSTRACT FROM AUTHOR]

The current investigation examines the vibrational properties of porous truncated conical structures made from a composite material consisting of polyvinylidene fluoride (PVDF) reinforced with Terfenol-D particles. The effective properties of the magneto-electro-elastic composite were determined using the Eshelby–Mori–Tanaka model. The governing equation of the system is obtained by applying the principles of minimal potential energy and Hamilton's principle to the first-order shear deformation theory. The equations are solved utilizing the generalized differential quadrature technique. This study aims to examine the interconnections among the volume percentage, vertex angle, shell length, boundary conditions, and porosity of Terfenol-D. Moreover, to validate the results, a comprehensive analysis was performed by comparing them with the existing body of literature, resulting in a favorable and accurate agreement. The results demonstrate a consistent decrease in the linear natural frequency as the vertex angle gradually increases. The findings derived from this study have the potential to serve as a reference point for future analyses. [ABSTRACT FROM AUTHOR]

This study aims to examine the dynamic characteristics of a sandwich composite nanoplate when exposed to a nano damper–spring–mass stimulator. The composite structure consists of a core layer composed of magnetostrictive material, accompanied by upper and lower facesheets made of functionally graded material (FGM). Moreover, the proposed framework is designed to be based on a visco-Pasternak medium. The governing equations of nanoplates are derived using the higher-order shear deformation theory (HSDT) and Hamilton's principle. In the end, Navier's solution is utilized to solve partial differential equations, while the Laplace transform is employed for solving ordinary differential equations. Subsequently, a thorough investigation is conducted with a primary focus on examining the impact of different parameters on the dynamic response of the continuous system. The findings indicate that the incorporation of the damper–spring–mass system into the nanoplate has a notable impact on its natural frequency. The results can serve as reference points for the effective development of nanosensors, nanoresonators, drug delivery systems, and biosensors. [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]

The goal of the present research is an investigation of the smart control and wave propagation examination of a graphene nanoplatelets reinforced (GPLRC) cylindrical micro-shell covered with piezoelectric layers as the sensor and actuator (PLSA) in the framework of an analytical method. The stress and strain components are given based on the first-order shear deformable theory (FSDT), and for accessing the size effects, the nonlocal strain gradient theory is used for obtaining the correct results. The material properties of the GPLRC micro-shell are modeled via modified Halpin–Tsai and the rule of the mixture. The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. The governing equations of the electrically micro-shell are derived via Hamilton's principle. This work concludes that the PD controller, wave number, applied voltage, and weight fraction of graphene nanoplatelets (GPL) have a significant influence on the wave propagation of the GPLRC cylindrical micro-shell. The remarkable result is that consideration of the PD controller leads to expand the stable area and improve the dynamic behaviors of the smart system. [ABSTRACT FROM AUTHOR]

Negative Poisson's ratio (NPR) auxetic metamaterials are attracting significant attention because of their peculiar and interesting mechanical features. Using geometrically von-Karman nonlinear factors and Mindlin plate theory, a smart multiscale hybrid (GPL/CF/PVDF) sandwich plate with a unique two-type functionally graded graphene origami auxetic (FG-GOA) is investigated here for its nonlinear vibrational behavior. The present properties of the electro-elastic layers were established using the Halpin–Tsai (HT) model and rule of mixing (ROM). Hamilton's principle, Maxwell's law, and the nonlinear factors of von Karman are used to determine the governing equations for the piezo plate. The subsequent step is to use the generalized differential quadrature (GDQ) technique to discretize the equations of motion for the sandwich plate. Results show that smart FG-GOA plates exhibit hardening nonlinearity. Nonlinear ratios of frequencies and natural frequency of the intelligent plate are also measured by electric voltage, the weight fraction of GPL, and the volume fraction of carbon fibers. Furthermore, the effect of the porosity coefficient, GOri folding degree, the FG-GOA core height, and the smart hybrid nanocomposite (SHNC) layer's height on frequency ratio and nonlinear natural frequency were calculated and displayed for each figure. [ABSTRACT FROM AUTHOR]

This paper describes the nonlinear vibration of a novel smart plate with an auxetic metamaterial core and piezoelectrically actuated multiscale hybrid nanocomposite porous layers (GPL/CF/PVDF) using Reddy's higher-order shear deformation theory (HSDT). Using the rule of mixture (ROM) and Halpin–Tsai model (HT), the current properties of electroelastic layers were determined. Smart plate equations are detected using Hamilton's principle, Maxwell's law, and von Karman nonlinearity terms. The generalized differential quadrature method (GDQM) is then employed to discretize the governing equations of a sandwich plate for various boundary conditions. In addition, the smart plate's nonlinear frequency ratio and nonlinear natural frequency are detected using the angle of auxetic cell, the electric voltage, and the graphene nanoplatelet weight fraction. In addition, the influence of the porosity constant, the thickness of the auxetic core, and the thickness of the smart graphene-reinforced hybrid nanocomposite layer on (ω nl / ω l) and ω nl were computed and presented in each figure. [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 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]

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]

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]

In the present study, the free vibration of functionally graded graphene platelet‐reinforced (FG‐GPLs) and functionally graded carbon nanotube‐reinforced (FG‐CNTs) hybrid laminated nanocomposite truncated conical shells and panels are analyzed. Multi‐layers truncated conical shell and panel of pure FG‐CNTs, pure FG‐GPLs and hybrid CNTs‐GPLs reinforcement were evaluated. In light of its high accuracy in the calculation of thin and thick shells, a third‐order shear deformation theory is adopted. The governing equations and boundary conditions is derived using Hamilton's principle and is solved numerically using the systematic differential quadrature method (DQM) which uses Kronecker delta function. The effective mechanical properties of the CNT‐reinforced nanocomposite layers are estimated using the rule of mixtures, whereas those of the GPL‐reinforced nanocomposite layers is calculated using the Halpin‐Tsai micromechanical model. Convergence and accuracy evaluation of the presented study are confirmed and a number of parameters, including the CNTS volume fraction, GPLs mass fraction, distribution patterns (i.e., Uniform distribution (UD), Functionally graded O‐distribution (FG‐O), Functionally graded X‐distribution (FG‐X), Functionally graded V‐distribution (FG‐V) and FG‐A), different boundary conditions and the vertex angle of the cone, are investigated. The results obtained in this article for the combination of two different materials, GPLs and CNTs, showed that in controlling the natural frequency of the system, without changing the percentage of fiber and only by changing the arrangement, very wonderful results can be achieved. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response. [ABSTRACT FROM AUTHOR]

In the current work, wave propagation in simply supported (S-S) functionally graded (FG) beam is investigated while the beam is exposed to magneto-thermal environments and embedded on two-parameter elastic foundation. The mechanical properties of the structure are supposed to vary through the thickness via the exponential and power law function. The governing equations of the motion are derived by implementing Hamilton's principle on the basis of refined higher order beam theory which can capture the shear deformation effect. Two novel metal and ceramic with interesting properties named Osmium and Silicon Carbide (SiC) are used as materials of this structure. The thermal loadings are applied to the structure with various temperature changes namely uniform, linear and sinusoidal, through the thickness. Influences of the wide range of parameters such as magnetic field intensity, slenderness ratio, various thermal loadings, exponential- and power-law exponents and elastic foundation coefficient on the wave frequency and phase velocity of the FG beam have been illustrated comparatively and the results are thoroughly discussed to obtain the highlights of each figure. [ABSTRACT FROM AUTHOR]

In this article, wave propagation of the sandwich composite beam with tunable electro-rheological (ER) fluid core is investigated. The sandwich composite beam is made of three layers consisting of the basic layer, ER fluid core, and the limiter layer. ER fluid core embedded withindoors the basic and limiter layers. The upper and lower layers are constructed of the elastic materials. Hamilton's principle is utilized for deriving the governing equations of motion. Using an analytical solution, the wave frequency and the phase velocity can be gathered by solving eigenvalue problem. Moreover, the effect of different parameters such as electric field, core-to-top layer thickness ratio, and thickness of ER core is investigated on the wave dispersion characteristics. [ABSTRACT FROM AUTHOR]

The present paper is mainly focused on analyzing wave propagation of sigmoid functionally graded (SFG) piezoelectric nanobeams rested on an elastic foundation on the basis of the nonlocal elasticity theory. The small-scale influence is taken into account by employing Eringen's nonlocal elasticity theory (ENET). Zinc oxide and Lithium niobate are supposed to be constituent materials of the nanoscale structure. Although the common power-law formulation has been used to determine electromechanical properties of functionally graded piezoelectric in the reported investigations, the sigmoid power-law formulation is employed in order to characterize the distribution of electromechanical properties in the current paper. Hamilton's principle and the Euler–Bernoulli beam theory, which is also known by classic beam theory, are applied to derive nonlocal governing equations of piezoelectric nanobeam. Afterward, the obtained nonlocal governing equations are solved via the analytical method. Eventually, the effect of various parameters, such as wave number, nonlocal parameter, gradient index, slenderness ratio, elastic foundation coefficients, and electric voltage on the variation of wave frequency and phase velocity of SFG piezoelectric nanobeam, is examined and also, the obtained result is presented in a group of illustrations that can be found in detail. [ABSTRACT FROM AUTHOR]

The present article aims to clarify the effect of the nanoflow on the nonlinear dynamic instability of graphene sheets under parametric excitation. To achieve this aim, the graphene layer is added to a visco-Pasternak foundation then, the resulting nanostructure is subjected to the nanoflow and a parametric axial force, simultaneously. The nonlocal elasticity and the nonlinear von Karman theories and Hamilton's principle are combined in this article, which lead to the governing equation of motion. A class of nonlinear Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The main conclusion to be drawn is that nanoflow directly influences the amplitude response of the system. This investigation contains analysis of how the nanoflow affects the nonlinear instability of nanostructures including the graphene sheets which can be provided useful information for the next investigations in field of nano electromechanical system. [ABSTRACT FROM AUTHOR]

An analytical approach is developed in this paper to investigate the wave propagating in graphene oxide powder (GOP) reinforced nanocomposite plates under thermal loading. The plate is embedded on a two parameter elastic substrate to make this research more realistic. The structure is exposed to thermal loadings with various temperature rises such as sinusoidal temperature rise (STR), linear temperature rise (LTR) and uniform temperature rise (UTR). The governing differential equations are derived via incorporation of the Hamilton's principle and refined higher order plate theory then solved analytically to obtain the wave frequency and phase velocity of the GOP reinforced nanocomposite plate. The GOPs are dispersed in a polymeric matrix through the thickness of the plate by considering different functionally graded (FG) patterns. Moreover, the effective material properties of the structure are predicted on the basis of Halpin–Tsai micromechanical scheme. Furthermore, the accuracy of the present model is verified with previous works and also the influences of various parameters on the wave propagation behavior of the structure are covered too. The graphical results declare that wave propagation in GOP reinforced nanocomposite plates dramatically depends on these parameters. [ABSTRACT FROM AUTHOR]

In this paper, a sandwich composite plate with tunable magneto-rheological (MR) fluid core is utilized for analyzing the wave propagation. Sandwich composite plate is made of three layers consisting of the base layer, MR layer and the limiter layer. MR layer is embedded within the base and the limiter layers. Moreover, the upper and the lower layers are made of the elastic materials. This structure is also located on a viscoelastic substrate. At first, for achieving the governing equations of motion, Hamilton's principle and classical plate theory (CLPT) are utilized. Then, exerting an analytical solution, the wave frequency and phase velocity of the propagated waves can be gained by solving eigenvalue problem. By investigating the effect of the magnetic field, the results emphasize that the magnetic field intensity is most important factor for changing the value of the wave dispersion characteristic. Besides, results indicate by enhancing the core-to-top layer thickness ratio, the wave frequency decreases because MR fluid core is softer in comparison to the elastic layers, Hence, MR fluid core operates similar damper. At the end, the effect of the other parameters such as thickness of MR layer, Winkler, Pasternak and damping coefficients are also discussed. [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]

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]

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]

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]

This study presents an investigation of the wave propagation of a rectangular sandwich composite plate with tunable magneto-rheological fluid core. The constituent parts of this rectangular sandwich composite plate are the base layer, magneto-rheological fluid core, and limiter layer. Magneto-rheological fluid core is embedded within the base and limiter layers. Also, the upper and lower layers are made of elastic materials. For obtaining the governing equations of motion, Hamilton's principle and classical plate theory are used. After that, applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gained by solving eigenvalue problem. By investigating the effect of the magnetic field, the results emphasize that the magnetic field intensity is the most important factor for changing the value of the wave frequency and phase velocity. Besides, results show by enhancing the core-to-top layer thickness ratio, the wave frequencies reduce because magneto-rheological fluid core is softer in comparison to elastic layers. Therefore, magneto-rheological fluid layer operates similar to a damper. At the end, the influence of the thickness of magneto-rheological fluid core on the phase velocity is also discussed. [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 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 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]

Herein, the thermo-magneto-elastic wave dispersion answers of rotary functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler–Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters. [ABSTRACT FROM AUTHOR]

This research presents the agglomeration effect of reinforcements on wave propagation analysis of multi-scale hybrid nanocomposite shell based on first-order shear deformable theory (FSDT) of shell for the first time. The nanocomposite shell is consist of carbon fiber (CF) as macro reinforcement, carbon nanotubes (CNTs) as nanoreinforcement and epoxy as an initial matrix. Eshelby-Mori-Tanaka method and rule of mixture are implemented in order to predict the equivalent mechanical properties of nanocomposite shell. To derive the motion equation of shell, FSDT is applied and governing equations are attained by employing Hamilton's principle. Dispersion solution is calculated by solving eigenvalue problem and also analytical method is utilized to solve the governing equations and finally wave frequency and phase velocity of nanocomposite shell can be achieved. In detail, several illustrations are presented which influence various parameters such as longitudinal and circumferential wave number, the volume fraction of CF, volume fraction of CNTs inside the cluster and so on are investigated. Communicated by Chandrika Prakash Vyasarayani. [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]

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]

In this research, a free vibration study of a biaxially compressed magneto-electro-elastic functionally graded (MEE-FG) nanoplate resting on an elastic substrate is carried out according to a trigonometric plate formulation. Spatially graded MEE properties of the nanoplate are described according to a power-law distribution. Eringen’s nonlocal elasticity model is utilized to incorporate the small-scale influences. The distributions of magneto-electrical potentials in the thickness direction are considered as a combination of cosine and linear variations. The governing equations of the present plate model are obtained employing Hamilton’s principle. Some admissible functions are introduced to satisfy different boundary conditions and solving these equations. It is indicated that vibration frequencies of the MEE-FG nanoplate are dramatically affected by biaxial compression, magnetic potential, electric voltage, elastic substrate, small-scale parameter, and material gradation. [ABSTRACT FROM AUTHOR]

This article is concerned with the thermo-mechanical vibration behavior of flexoelectric nanoplates under uniform and linear temperature distributions. Flexoelectric nanoplates have higher natural frequencies than conventional piezoelectric nanoplates, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric nanoplates for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions, which are solved applying the Galerkin-based solution. A comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameters, surface elasticity, temperature rise, plate thickness, and various boundary conditions on the vibration frequencies of thermally affected flexoelectric nanoplate. [ABSTRACT FROM AUTHOR]

In this article, nonlocal free vibration analysis of curved functionally graded piezoelectric (FGP) nanobeams is conducted using a Navier-type solution method. The model contains a nonlocal stress field parameter and also a nonlocal strain-electric field gradient parameter to capture the size effects. Inclusion of these nonlocal parameters introduces both stiffness-softening and stiffness-hardening effects in the analysis of curved nanobeams. Nonlocal governing equations of curved FGP nanobeam are obtained from Hamilton's principle based on the Euler–Bernoulli beam model. The results are validated with those of curved FG nanobeams available in the literature. Finally, the influences of electric voltage, length scale parameter, nonlocal parameter, opening angle, material composition, and slenderness ratio on vibrational characteristics of nanosize curved FG piezoelectric beams are explored. These results may be useful in accurate analysis and design of smart nanostructures constructed from piezoelectric materials. [ABSTRACT FROM AUTHOR]

This paper develops a nonlocal strain gradient plate model for damping vibration analysis of visco-elastically coupled double-layered graphene sheets. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. In fact, frequency increment due to the strain gradient effect is neglected in all previous papers related to double-layer graphene sheets. Governing equations of a nonlocal strain gradient double-layer graphene sheet on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as damping coefficients, nonlocal parameter, length scale parameter, elastic foundation, interlayer stiffness and boundary conditions on vibration characteristics a double-layer graphene sheet are examined. [ABSTRACT FROM AUTHOR]

In the present article, a nonlocal strain gradient plate model is developed for damping vibration analysis of viscoelastic graphene sheets under hygor-thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on viscoelastic substrate are derived via Hamilton’s principle. Differential Quadrature Method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. [ABSTRACT FROM AUTHOR]

In this paper, free vibration of functionally graded (FG) size-dependent nanobeams is studied within the framework of nonlocal Timoshenko beam model. It is assumed that material properties of the FG nanobeam, vary continuously through the thickness according to a power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The non-classical governing differential equations of motion are derived through Hamilton's principle and they are solved utilizing both Navier-based analytical method and an efficient and semi-analytical technique called differential transformation method (DTM). Various types of boundary conditions such as simply-supported, clamped-clamped, clampedsirnply and clamped-ffee are assumed for edge supports. The good agreement between the presented DTM and analytical results of this article and those available in the literature validated the presented approach. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The obtained results show the significance of the material graduation, nonlocal effect, slenderness ratio and boundary conditions on the vibration characteristics of FG nanobeams. [ABSTRACT FROM AUTHOR]

The analysis of wave propagation behavior of a magneto-electro-elastic functionally graded (MEE-FG) nanobeam is performed in the framework of classical beam theory. To capture small-scale effects, the nonlocal elasticity theory of Eringen is applied. Furthermore, the material properties of nanobeam are assumed to vary gradually through the thickness based on power-law form. Nonlocal governing equations of MEE-FG nanobeam have been derived employing Hamilton's principle. The results of present research have been validated by comparing with those of previous investigations. An analytical solution of governing equations is utilized to obtain wave frequencies, phase velocities and escape frequencies. Effects of various parameters such as wave number, nonlocal parameter, gradient index, axial load, magnetic potential and electric voltage on wave dispersion characteristics of MEE-FG nanoscale beams are studied in detail. [ABSTRACT FROM AUTHOR]