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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 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]

The high mechanical properties of auxetic materials with negative Poisson's ratio make them suitable for a variety of applications. This article investigated how the auxetic layer affects wave propagation and its effective characteristics in cylindrical sandwich shells. An analytical solution is established to describe wave propagation through wave frequency and wave velocity according to first-order shear deformable shell theory. Moreover, the Hamilton principle was applied. Then, the governing equation was solved by utilizing an analytical method. Different parameters such as auxetic cell angle inclined and dimensions on wave behavior were investigated. The final step is to conduct a numerical investigation. The results are reported in the form of several figures and analyze how each parameter influences wave propagation. [ABSTRACT FROM AUTHOR]

The purpose of present investigation is to study propagation of flexural wave in porous metal foam beams resting on Winkler–Pasternak foundation based upon refined higher-order shear deformable beam theory. Moreover, different types of porosity distribution through the thickness direction are probed namely; uniform, symmetric and asymmetric. The Hamiltonian approach is implemented to catch motion equations of porous metal foam beams. Then, the obtained governing equations of porous metal foam are solved analytically. The influences of different parameters such as various types of porosity distribution, porosity coefficient, slenderness ratio, wave number and elastic foundation coefficients on the variation of wave frequency, escape frequency and phase velocity are covered and presented within the framework of a group of figures which can be observed in detail. [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]

This paper elaborates on the wave propagation characteristics of a smart sandwich plate consisting of smart piezo composite layers on a plate’s upper and lower borders via an auxetic core. This study’s equation of motion was derived using a refined version of the Shear-deformation theory at a higher order, or HSDT. Additionally, detecting the properties of the auxetic core and piezoelectric composite layers employs a micromechanical model. The fundamental equations of the smart sandwich plates were formulated utilizing the Hamiltonian principle and Maxwell’s law. Then, the governing equations of a sandwich plate are solved using an exponential form and an analytical method. Furthermore, the phase velocity of the intelligent sandwich plate is provided based on the layer thicknesses of the auxetic core and thicknesses of intelligent piezoelectric composite layers. In addition, each figure calculates and presents the weight of the Winkler–Pasternak coefficient, the viscoelastic substances factor, the source of the outside electricity, and the volume percent of reinforcement in the matrix on the phase velocity. [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 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]

In the current investigation, the influences of waviness and agglomeration factor of nanofillers on wave dispersion of embedded nanocomposite beams reinforced with multi-walled carbon nanotubes (MWCNTs) is investigated for the first time. These beams are supported on Winkler–Pasternak elastic foundation. The effective mechanical properties of nanocomposite beam are estimated by employing a blend of a new form of Halpin–Tsai micromechanical model and rule of mixture. The kinematic and kinetic relations of nanocomposite beam are computed based upon refined higher-order shear deformation theory. Moreover, the governing equations are derived by utilizing the Hamiltonian approach. Afterward, an analytical method is used in order to solve the obtained governing equations. Effects of the wide range of variants such as volume fraction of MWCNTs, slenderness ratio, waviness factor, random orientation factor, agglomeration factor and elastic foundation coefficient on the variation of wave frequency and phase velocity have been illustrated comparatively. Furthermore, the results are thoroughly discussed to obtain the highlights of each figure. [ABSTRACT FROM AUTHOR]

Because of the time-dependent characteristics of the polymers, carbon nanotube (CNT)-reinforced polymer nanocomposites exhibit great viscoelastic nature. Besides, it also has advantages in strength and stiffness. Therefore, a sufficient understanding of their rheological behavior is necessary if the materials are to be used in the aerospace industry. The paper's objective is to track the vibrational responses of a multi-scale hybrid nanocomposite beam for the first time while accounting for the wavy form and the time dependency of the polymer. To do this, the homogenization process combines the mix-ture's rule with the modified Halpin-Tsai model. The results demonstrate that assigning a large value to the polymer's characteristic relaxation time may delay the structure's vibration suppression. Furthermore, the results show that hybrid nanocomposites made of wavy CNTs are unable to offer optimal frequencies in comparison to those produced from straight CNTs. [ABSTRACT FROM AUTHOR]

In this paper, a machine-learning model is utilized to estimate the temperature-dependent moduli of neat, thermally reduced graphene and covalently functionalized graphene/epoxy nanocomposites. In addition, the governed mathematical expressions have been used to solve the buckling problem of beams fabricated from such nanocomposites in the presence of a thermal gradient. In order to do so, an energy-based method including the shear deformable beam hypothesis is used. The beam structure is rested on the Winkler–Pasternak substrate. The reported verifications demonstrate the impressive precision of the presented ML model, as well as the buckling response of the under-study structures. Finally, in the framework of some numerical case studies, the impact of several parameters on the buckling of nanocomposite beams is depicted. The results of this study delineate that temperature has a vital role in the determination of the critical buckling load that the nanocomposite structures can endure. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling problem of a multi-scale hybrid nanocomposite shell for the first time while the cylinder is supposed to be rested on an elastic substrate. The constituent material is considered to be made from a polymeric matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers' agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing the Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube-reinforced (CNTR) nanocomposite are coupled with those of carbon fibers (CFs) within the framework of a modified rule of the mixture. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the static form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin's method to obtain the buckling load of the structure for both simply supported and clamped boundary conditions. The results indicate on the fact that if the agglomeration effects are ignored, the designed nanocomposite system may fail under low static excitations. Also, it is better to avoid from the construction of a large number of small clusters to make the nanocomposite structure more powerful against buckling mode failure. [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]

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]

Free oscillation analysis of shells consisted of multi-scale hybrid nanocomposites is carried out with regard to the destroying effect of the nanofillers' agglomeration on the system's dynamics. The equivalent material properties of the hybrid nanocomposite are obtained in the framework of a bi-level micromechanical procedure. The influence of existence of agglomerated carbon nanotubes (CNTs) on the stiffness of the nanocomposite is included with the aid of the Eshelby-Mori-Tanaka method. Thereafter, the first-order shear deformation theory (FSDT) of the shells will be combined with the dynamic form of the principle of virtual work to reach the Euler-Lagrange equations of the problem. Next, the governing equations will be extracted from the Euler-Lagrange ones by using the constitutive equations of the nanocomposite. To obtain the natural frequencies of the system for shells with clamped and simply supported ends, the Galerkin's method is hired. The validity check reveals that the utilized methodology is powerful enough to predict the frequency behaviors of nanocomposite shells. According to the results, it can be inferred that the hybrid nanocomposite shells may be involved in resonance phenomenon in low-range frequencies if the impact of the CNTs' aggregation is neglected. Obviously, the volume fraction of the CNTs inside the inclusions plays a magnificent role in the determination of the system's dynamic behavior. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the wave propagation analysis of multi-scale hybrid nanocomposite plates by considering the influences of the aggregation of the nanoparticles. For the constituent materials of the plate, a polymeric matrix is supposed to have macro- and nano-reinforcements dispersed in it. The well-known micromechanical methods, such as Eshelby-Mori-Tanaka model and the rule of the mixture, are exerted to compute the effective material properties of the nanocomposite plate. Also, a refined higher-order shear deformation theory is implemented to obtain the motion relations. Besides, the governing equations are derived by employing the principle of Hamilton. Then, the analytic method is used to solve the obtained governing equations of structure and finally wave frequency and phase velocity are calculated. The effects of the various parameters on the variation of phase velocity and wave frequency of the multi-scale nanocomposite plates are examined. The presented results demonstrate that the mechanical response of the system can be decreased, while the nanotubes are covered by clusters. [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]

This investigation deals with wave propagation analysis of porous metal foam resting on the Kerr substrate in the thermal environment within the framework of the refined higher-order plate theory. Different types of temperature rise are studied namely; uniform, linear and sinusoidal temperature rise. The pores are distributed through the thickness symmetrically and asymmetrically. The principle of Hamilton is employed in order to reach motion equations of porous metal foam plates. Next, governing equations of porous metal foam are derived for a refined inverse cotangential shear deformation plate and then solved analytically. The effects of various parameters including porosity coefficient, various types of porosity distribution, different types of temperature rise, length to thickness ratio, shape function, wave number and linear and shear layers of Kerr substrate on the variation of wave frequency and phase velocity of metal foam plate are covered and presented within the framework of a group of figures which can be observed in detail. [ABSTRACT FROM AUTHOR]

This article aims to investigate buckling characteristics of a functionally graded magneto-electro-thermo-elastic nanoshell based on nonlocal strain gradient theory (NSGT). Accounting for nonlocal and strain gradient size-dependency, NSGT has two scale coefficients. The nanoshell is subjected to external electric, magnetic, mechanical, and thermal fields. The temperature distributions are considered as uniform and linear thorough the nanoshell thickness. All material properties including elastic, piezoelectric, and magnetic properties are defined based on a power-law distribution type. Seven coupled governing equations are derived for the nanoshell based on Hamilton's rule and then solved applying Galerkin's approach. The dependency of the buckling behavior of the nanoshell on applied thermal load, temperature distribution, electric voltage, magnetic potential, material gradient index, scale parameters, and shear deformation will be explored. [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 article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques. [ABSTRACT FROM AUTHOR]

The present article is proposed to capture the influences of carbon nanotubes' agglomeration on the natural frequency behaviors of multi-scale hybrid nanocomposite plates for the first time. The constituent material, which is a hybrid nanocomposite, is consisted of both macro- and nano-scale reinforcing fibers dispersed in a polymer matrix. 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 plate theorem. Next, the derived equations will be solved in the framework of Galerkin's well-known analytical method to reach the fundamental frequency. It is worth mentioning that the influence of various boundary conditions is included. Once the validity of the presented results is proven, a set of numerical examples are presented to explain how each variant can affect the plate's natural frequency. Communicated by Wei-Chau Xie. [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]

This composition presents a multi-phase-lags thermos-elasticity model for the thermos-elastic wave propagation reaction of a composite hollow circular cylinder with the interface layer LEMV/CFRP (Linear Elastic Material with void/Carbon Fiber Reinforced Polymer) using new modified couple stress theory. Three partial differential equations of the modified couple stress and multiphase lag model of composite hollow cylinder are derived for axisymmetric mode and solved exactly using linear theory of elasticity. The frequency equations are achieved for the traction free outer surface with continuity conditions at the interfaces. The influences of changing wave number and thickness on the field quantities like frequency, temperature, displacements, are investigated. Some comparisons are tabulated and presented graphically to estimate the effects of various thermos-elasticity theories and coupled stress parameter. [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]

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 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]

This paper investigates the wave propagation behavior of a high-speed rotating laminated nanocomposite cylindrical shell. The small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the cylindrical laminated composite nanoshell in a thermal environment were obtained using Hamilton's principle and solved by the analytical method. For the first time in this study, the wave propagation behavior of a high-speed rotating nanocomposite cylindrical shell is studied based on classic, strain gradient, nonlocal and nonlocal strain gradient theories (4 continuum theories) with considering the calibrated values of the nonlocal constant and material length scale parameter. The results show that wave number, angular velocity, and different types of laminated composites have an important role in the phase velocity of the nanocomposite structure using mentioned continuum mechanics theories. Another significant result is that in the higher values of angular velocity, three layers of laminated composite has the highest phase velocity in comparison with the other layers. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques. [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]

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]

This is the first research on the smart control and frequency analysis of a cylindrical sandwich nanoshell in the framework of the numerical-based generalized differential quadrature method (2D-GDQM). The current sandwich smart nanostructure is made of a honeycomb core and piezoelectric face sheets as sensor and actuator (PFSA). For modeling the size-dependent nanoshell, nonlocal stress-strain gradient theory (NSGT) is presented. Also, this nanostructure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. Also, the current structure rotates around its axial direction. The stresses and strains are obtained using the higher-order shear deformation theory (HSDT). The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. Governing equations and boundary conditions of the cylindrical sandwich nanoshell are obtained by implementing Hamilton's principle. The results show that the geometry of honeycomb core, PD controller, velocity of fluid flow, length to radius ratio (L/R), and applied voltage and have a significant influence on the frequency characteristics of a cylindrical sandwich nanoshell. Another important consequence is that applying the PD controller leads to an increase in the critical velocity of fluid flow in the smart nanostructure. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear vibrational behaviors of doubly-curved functionally graded piezoelectric (FGP) microshells in thermal environments have been studied. The doubly-curved microshell has been modeled by using modified couple stress and thin shell theories. The microshell has two material constituents which are piezoelectric materials and their gradation is described using power-law functions. Temperature fields are considered to be uniform, linear, and nonlinear. A closed-form of nonlinear vibration frequency has been obtained by analytically solving the governing equations using the Harmonic balance method. It will be demonstrated that nonlinear vibrational frequency of doubly-curved microshell relies on couple stress influence, material gradation, curvature radius, center deflection, and electrical field. [ABSTRACT FROM AUTHOR]

In this study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with assistance of the generalized differential quadrature method (GDQM). Besides, for the validation of the results, the results of the current model are compared to the results acquired from analytical method. The results show that, viscoelastic foundation, patterns of GPL distribution, nonlocal parameter, length scale parameter, layers' numbers, boundary condition as well as GPL weight function have considerable impact on the stability of the GPLRC cylindrical microshell. Another significant result is that; for C-F B.Cs, at the higher value of the l / R parameter, the influence of the g GPL on the dimensionless buckling load of the structure is much more remarkable in comparison with the lower one which in results section is investigated in detail. The results of the present investigation would be informative for design and fabrication of the microactuators and microsensors. [ABSTRACT FROM AUTHOR]

A comparative study of Love-type wave vibrations in a distinct piezoelectric (PE) material thin film with a highly and weakly dielectric interface with an elastic pre-stressed elastic plate is investigated analytically. Using the PZT-2, PZT-4, PZT-5H, LiNbO3 and BaTiO3 numerical data for the PE material, we achieved significant outcomes of PE and flexoelectric effect in the study. Dispersion equations are achieved analytically for both electrically open and short cases together with highly and weekly conducting interfaces in the transcendental complex form. Outcomes specify that microstructures having flexoelectricity has a significant influence on dispersion features. The existence of flexoelectricity shows that complex phase velocity with a positive imaginary part increases the phase velocity of considered waves with time. Numerical results are highlighted graphically and validated with existing results. The present study is a prior attempt to show the flexoelectricity influence with weekly and highly conducting interfaces and also to show that the outcomes are significant to obtain better surface acoustic wave device's performance. [ABSTRACT FROM AUTHOR]