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

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

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

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

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

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

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

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

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

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

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]

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]

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

This work is motivated by lack of research in the nonlinear dynamics and the instability of the double-walled nanobeams caused by the parametric excitation and also subjected to the thermo-magneto-mechanical loads. In this paper, firstly, a short double-walled nanobeam is modeled and embedded on a viscoelastic foundation. The double-walled nanobeam is subjected to an axial parametric force and the thermo-magneto-mechanical loads simultaneously. Secondly, based on the nonlocal elasticity and the nonlinear von Karman beam theories, the nonlinear governing equation of motion is derived. A class of nonlinear 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 parametric excitation, the thermo-magneto-mechanical loads, the viscoelastic foundation coefficients and the damping coefficient. The results emphasize that the outer layer of the nanobeam plays a significant role in the nonlinear instability of the system than the inner layer. [ABSTRACT FROM AUTHOR]

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton's principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors. [ABSTRACT FROM AUTHOR]

Present research is mainly devoted to show the effects of temperature change on the mechanical properties of in-plane waves propagating in a single-layered graphene sheet. Graphene sheet is assumed to be rested on an elastic medium. Influences of elastic substrate on the behavior of graphene sheet is modeled by the means of a two parameter elastic foundation. In addition, a trigonometric refined plate theory is applied to derive the kinematic relations. Also, a nonlocal strain gradient theory is utilized to show the size-dependency of graphene sheet. In the framework of Hamilton's principle, the nonlocal governing differential equations are derived. Moreover, an analytical approach is applied to find the unknowns of the final eigen value equation. At the end of the paper, it is tried to clarify the influences of each parameter by the means of some diagrams. [ABSTRACT FROM AUTHOR]

In this research, vibration characteristics of a flexoelectric nanoplate in contact with Winkler-Pasternak foundation are investigated based on nonlocal elasticity theory considering surface effects. This non-classical nanoplate model contains flexoelectric effect to capture coupling of strain gradients and electrical polarizations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, flexoelectric and surface effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Natural frequencies are verified with those of previous papers on flexoelectric nanoplates. It is illustrated that flexoelectricity, nonlocality, surface stresses, elastic foundation and boundary conditions affects considerably the vibration frequencies of piezoelectric nanoplates. [ABSTRACT FROM AUTHOR]

In this manuscript, a non-classical beam model is proposed based on the Eringen’s nonlocal elasticity theory for nonlinear vibration analysis of magneto-electro-hygro-thermal piezoelectric functionally graded (PFG) nanobeams rested in elastic foundation. The Hamilton’s principle is employed to derive the nonlinear motion equation and related boundary conditions within the framework of Euler-Bernoulli beam model with von-Karman type nonlinearity. The power-law distribution model is utilized to explain the continuous variation of material properties through the thickness of FG nanobeam. The Galerkin-based method is employed to discretize the nonlinear partial differential motion equations into a set of time-dependent ordinary differential equations. The numerical results are given to investigate the influence of various parameters such as nonlocal parameter, amplitude ratio, aspect ratio, power-law index, external voltage, temperature change, magnetic field, moisture effect and Winkler-Pasternak elastic foundations on the nonlinear frequency ratio of PFG nanobeam for various boundary conditions. It is expressly shown that the nonlinear frequency ratio of PFG nanobeam is significantly influenced by these effects. Some of the numerical results are compared with well-known literature, which are proved to be in good agreement. The presented results can serve as benchmarks for future nonlinear analysis of PFG nanobeams. [ABSTRACT FROM AUTHOR]

In this research a nonlocal strain gradient plate model is introduced for hygro-thermo-mechanical buckling analysis of double-layered graphene sheets in elastic medium. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. In fact, buckling load 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 hygro-thermal loading, nonlocal parameter, length scale parameter, elastic foundation, interlayer stiffness and boundary conditions on buckling characteristics a double-layer graphene sheet are studied. [ABSTRACT FROM AUTHOR]

This article investigates vibrational behavior of a multi-phase nanocrystalline nanobeam resting on Winkler-Pasternak foundation and subjected to a longitudinal magnetic field in the framework of nonlocal couple stress and surface elasticity theories. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, couple stress and surface effects are omitted. Hamilton’s principle is employed to derive the governing equations and the related boundary conditions which are solved applying differential transform method. The frequencies are compared with those of nonlocal and couple stress based beams. It is showed that vibration frequencies of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, magnetic field, surface effect, nonlocality and boundary conditions. [ABSTRACT FROM AUTHOR]

This article deals with the wave propagation problem of nanosize double-layered plates while subjected to a longitudinal magnetic field. To achieve more reliable answers, nonlocal strain gradient theory (NSGT) is utilized which takes into account both decreasing and increasing influences of small scale. Moreover, Kirchhoff plate theory is reviewed and incorporated with the Hamilton’s principle to obtain the equations of motion for each nanoplate. Afterwards, the equations of motion are mixed with those of NSGT in order to derive the nonlocal governing equations of nanoplates. Then, the achieved equations are solved analytically to reach the wave frequency and phase velocity values of propagated waves. Accuracy of the introduced model is verified by setting a comparison between this research and former published attempts. Finally, influence of each parameter on the wave dispersion answers of double nanoplate systems is shown in some diagrams. [ABSTRACT FROM AUTHOR]

In this article, wave dispersion responses of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation and exposed to thermal load are presented based on nonlocal strain gradient theory. Mori-Tanaka model has been considered to express the gradual variation of material properties across thickness. Governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton’s principle in context of Euler-Bernoulli theory. Dispersion relations of rotating FG nanobeam are analytically derived by solving an eigenvalue problem. Obviously, numerical results indicate that different parameters such as angular velocity, gradient index, temperature change, wave number, and nonlocality parameter have significant influences on wave characteristics of rotating FG nanobeams. Hence, results of this research can provide useful information for the next generation studies and accurate deigns of nanomachines including nanoscale molecular bearings and nanogears. [ABSTRACT FROM AUTHOR]

This study employs the nonlocal and surface elasticity theories to explore the buckling characteristics of piezoelectric nanobeams incorporating flexoelectricity effects. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Considering the flexoelectricity effects, the piezoelectric nanobeams can tolerate higher buckling loads compared with conventional ones, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectrically actuated piezoelectric nanobeams in magnetic field for the first time. Hamilton’s principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical-based solution. 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 parameter, surface elasticity, temperature rise, beam thickness and various boundary conditions on the buckling characteristics of magnetically affected flexoelectric nanobeam. [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 this research, vibration analysis of axially preloaded nonlocal flexoelectric nanobeams considering surface and magnetic field effects is performed. The main propose of present paper is to fill the gap in previous analyzes of flexoelectric nanobeams in which nonlocal and surface effects are ignored. Flexoelectricity in a nanobeam results in larger vibration frequencies than a typical piezoelectric nanobeam. Via Galerkin's technique, the governing equations of the flexoelectric nanobeam are numerically solved. The vibration frequency of the nanobeam is validated with previous one in the literature. The illustrative results demonstrate the influences of the flexoelectricity, nonlocal stress field, surface energy, magnetic field, axial load and beam thickness on vibrational characteristics of a nanosize preloaded flexoelectric beam. [ABSTRACT FROM AUTHOR]

In this paper, electromechanical buckling behavior of size-dependent flexoelectric nanoplates is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between strain gradients and electrical polarizations. Flexoelectric nanoplates can tolerate higher buckling loads compared with conventional piezoelectric nanoplates, especially at lower thicknesses. The flexoelectric nanoplate is in contact with a two-parameter elastic foundation, which consists of infinite linear springs and a shear layer. Nonlocal elasticity theory of Eringen is applied in the analysis of flexoelectric nanoplates for the first time. The residual surface stresses which are usually neglected in the modeling of flexoelectric nanoplates are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical solution which satisfies various boundary conditions, the governing equations obtained from Hamilton's principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effect, plate geometrical parameters, elastic foundation and boundary conditions on the buckling characteristics of flexoelectric nanoplates are explored. [ABSTRACT FROM AUTHOR]

This paper investigates wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler-Bernoulli beam model by using an analytical approach. The nonlocal beam model has a length scale parameter and captures the size influences. Material properties are spatially graded according to sigmoid distribution. A derivation of the governing equations for the wave propagation analysis of nanoscale S-FGM beams is conducted. Then, the dispersion relations between wave frequency and phase velocity with the wave number is investigated. It is found that wave propagation characteristics of nonlocal S-FGM beams are influenced by various parameters including length scale parameter, material graduation, elastic foundation parameters and magnetic field intensity. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration characteristics of smart shear deformable plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials are investigated considering various boundary conditions by using an analytical method for the first time. Porosities possibly occur inside functionally graded materials (FGMs) during fabrication because of technical problems that lead to creation of micro-voids in these materials. Magneto-electro-elastic properties of FGM plate are supposed to vary through the thickness direction according to a modified power-law model in which the porosities with even and uneven distributions are approximated. The governing differential equations of porous FGM plate under magneto-electrical field are formulated through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions and plate side-to-thickness ratio on natural frequencies of the porous MEE-FG plate are investigated and discussed in detail. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases. [ABSTRACT FROM AUTHOR]

The vibration problem of a nonlocal magneto-electro-elastic functionally graded (MEE-FG) nanoplate lying on two-parameter elastic foundation under different boundary conditions is examined through a trigonometric plate formulation. Based on power-law model, graded material properties of the nanoplate are described. Employing Hamilton's principle, the formulation of shear deformable MEE-FG nanoplates lying on elastic substrate is presented. Admissible functions are provided to satisfy various boundary conditions and analytically solving the governing equations. Effects of elastic substrate, axial magneto-electrical load, various edge conditions, nonlocality parameter and material gradation on vibration frequencies of a MEE-FG nanoscale plate are studied. It is observed that vibration response of MEE-FG nanoplates is prominently influenced by these parameters. [ABSTRACT FROM AUTHOR]

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

In this paper, wave propagation analysis of functionally graded size-dependent nanobeams embedded in elastic foundation exposed to a longitudinal magnetic field is conducted based on nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also the presence of cutoff and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated. [ABSTRACT FROM AUTHOR]

This article deals with the free vibration investigation of nonlocal strain gradient-based viscoelastic functionally graded (FG) nanobeams on viscoelastic medium considering surface stress effects. Nonlocal strain gradient theory possesses a nonlocal stress field parameter and a length scale parameter for more accurate prediction of mechanical behavior of nanostructures. Surface energy effect is incorporate to the nonlocal strain gradient theory employing Gurtin-Murdoch elasticity theory. Thermo-elastic material properties of nanobeam are graded in thickness direction using power-law distribution. Hamilton's principal is utilized to obtain the governing equations of FG nanobeam embedded in viscoelastic medium. The effects of surface stress, length scale parameter, nonlocal parameter, viscoelastic medium, internal damping constant, thermal loading, power-law index and boundary conditions on vibration frequencies of viscoelastic FGM nanobeams are discussed in detail. [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]

Free vibration analysis is presented for a simply supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third-order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher-order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design. [ABSTRACT FROM AUTHOR]

In the present study, thermo-electro-mechanical vibration characteristics of both sigmoid and power-law functionally graded piezoelectric (FGP) nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier-type solution for the first time. Three kinds of thermal loading, namely uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness according to power-law and sigmoid distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, different material compositions, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams. The results should be relevant to the design and application of the piezoelectric nanodevices. [ABSTRACT FROM AUTHOR]

In this article, combined effect of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is investigated by developing various refined beam theories which capture shear deformation influences needless of any shear correction factor. The material properties of FG nanobeam are temperature dependent and change gradually along the thickness through the power-law model. Size-dependent description of the nanobeam is performed applying nonlocal elasticity theory of Eringen. Nonlocal governing equations of embedded FG nanobeam in hygro-thermal environment obtained from Hamilton's principle are solved analytically. To verify the validity of the developed theories, the results of the present work are compared with those available in the literature. The effects of various hygro-thermal loadings, elastic foundation, gradient index, nonlocal parameter, and slenderness ratio on the vibrational behavior of FG nanobeams modeled via various beam theories are explored. [ABSTRACT FROM AUTHOR]

This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori-Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton's principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition. [ABSTRACT FROM AUTHOR]

In this paper, free vibration characteristics of functionally graded (FG) nanobeams based on third-order shear deformation beam theory are investigated by presenting a Navier-type solution. Material properties of FG nanobeam are supposed to change continuously along the thickness according to the power-law form. The effect of small scale is considered based on nonlocal elasticity theory of Eringen. Through Hamilton's principle and third-order shear deformation beam theory, the nonlocal governing equations are derived and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results for FG nanobeams as compared to some cases in the literature. The numerical investigations are presented to investigate the effect of the several parameters such as material distribution profile, small-scale effects, slenderness ratio and mode number on vibrational response of the FG nanobeams in detail. It is concluded that various factors such as nonlocal parameter and gradient index play notable roles in vibrational response of FG nanobeams. [ABSTRACT FROM AUTHOR]

In this paper, free vibration analysis of a rotating Mori-Tanaka-based functionally graded (FG) beam is investigated based on Timoshenko beam theory. The physical neutral axis position for the mentioned FG beam is determined. By using a semi-analytical differential transformation method (DTM), the governing differential equations are transformed into recurrence relations and the boundary conditions are converted to algebraic equations. The material properties of the rotating FG beam are supposed to vary across the thickness direction based on Mori-Tanaka micromechanics model. In the classical beam theory, the effects of transverse shear deformation and rotary inertia are not taken into consideration, while the Timoshenko beam model takes these effects into account. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of rotating FG beams. The good agreement between the results of this article and those available in the literature validated the presented approach. The detailed mathematical derivations are presented, and numerical investigations are performed, while the emphasis is placed on investigating the effect of functionally graded microstructure, mode number, slenderness ratios, rotational speed and hub radius and boundary conditions on the normalized natural frequencies of the rotating FG beam in detail. It is explicitly shown that the vibration behavior of a rotating FG beam is significantly influenced by these effects. [ABSTRACT FROM AUTHOR]

In this paper, the effects of various surface parameters on free vibration behavior of nanobeams are investigated in the presence of nonlocal effect. The Gurtin-Murdoch model is employed for incorporating the surface parameters including surface density, surface tension and surface elasticity, while the Eringen's nonlocal elasticity theory takes into account the effect of small scales. The governing equations of motion are obtained for different materials such as aluminum and silicon with various boundary conditions. The high-precision semi-analytical differential transformation method is utilized to solve the governing equations. Then, by transforming the governing differential equations and boundary conditions into algebraic equations, the natural frequencies are obtained. The objective of the present study is to explore comprehensively the effect of different combination of various surface effects on nonlocal vibrational behavior of nanobeams for the first time. It is explicitly shown that the vibration characteristics of a nanobeam are significantly influenced by these surface effects. Moreover, it is shown that by increasing the size of beam, the influence of surface effects reduce to zero, and the natural frequency reaches its classical value. Numerical results are also presented to serve as benchmarks for future analyses of nanobeams. [ABSTRACT FROM AUTHOR]

In this study, the thermal effect on the free vibration characteristics of embedded Single-walled carbon nanotubes (SWCNTs) based on the size-dependent Reddy higher order shear deformation beam theory subjected to in-plane thermal loading is investigated by presenting a Navier-type solution and employing a semi-analytical Differential transform method (DTM) for the first time. In addition, the exact nonlocal Reddy beam theory solution presented here should be useful to engineers designing nanoelectromechanical devices. The smallscale effect is considered based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle, and they are solved by applying DTM. Numerical results reveal that the proposed modeling and semi-analytical approach can provide more accurate frequency results of the SWCNTs compared to analytical results and some cases in the literature. The detailed mathematical derivations are presented, and numerical investigations are performed, whereas emphasis is placed on investigating the effect of several parameters such as small-scale effects, boundary conditions, mode number, thickness ratio, temperature change, and Winkler spring modulus on the natural frequencies of the SWCNTs in detail. The vibration behavior of SWCNTs is significantly influenced by these effects. Results indicate that the inclusion of size effect results in a decrease in nanobeam stiffness and leads to a decrease in natural frequency. Numerical results are presented to serve as benchmarks for future analyses of SWCNTs. [ABSTRACT FROM AUTHOR]

In this study, the applicability of differential transformation method (DTM) in investigations on vibrational characteristics of functionally graded (FG) size-dependent nanobeams is examined. The material properties of FG nanobeam vary over the thickness based on the power law. The nonlocal Eringen theory, which takes into account the effect of small size, enables the present model to be effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle. The obtained results exactly match the results of the presented Navier-based analytical solution as well as those available in literature. The DTM is also demonstrated to have high precision and computational efficiency in the vibration analysis of FG nanobeams. The detailed mathematical derivations are presented and numerical investigations performed with emphasis placed on investigating the effects of several parameters, such as small scale effects, volume fraction index, mode number, and thickness ratio on the normalized natural frequencies of the FG nanobeams. The study also shows explicitly that vibrations of FG nanobeams are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams. [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]

In the present article, the hygro-thermal wave propagation properties of single-layered graphene sheets (SLGSs) are investigated for the first time employing a nonlocal strain gradient theory. A refined higher-order two-variable plate theory is utilized to derive the kinematic relations of graphene sheets. Here, nonlocal strain gradient theory is used to achieve a more precise analysis of small-scale plates. In the framework of the Hamilton’s principle, the final governing equations are developed. Moreover, these obtained equations are deemed to be solved analytically and the wave frequency values are achieved. Some parametric studies are organized to investigate the influence of different variants such as nonlocal parameter, length scale parameter, wave number, temperature gradient and moisture concentration on the wave frequency of graphene sheets. [ABSTRACT FROM AUTHOR]

In this present work the critical loading of magneto-electro-viscoelastic-hygro-thermal (MEVHT) piezoelectric nanoplates embedded in a viscoelastic foundation are investigated. Via two variable shear deformation plate theory displacement are obtained. The governing equations of nonlocal viscoelastic nanoplate are driven by using Hamilton's principle and solved by an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermo-magneto-electro-mechanical loadings and aspect ratio on the critical loading of MEVHT nanoplates. It is found that the critical loading is quite important to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the hygro-thermal loading. [ABSTRACT FROM AUTHOR]

The original version of this article unfortunately contained a mistake. Farzad Ebrahimi was not listed among the authors. [ABSTRACT FROM AUTHOR]

In this study, we evaluated the involvement of N-methyl- d-aspartate receptor (NMDAR)/nitric oxide (NO) system on the antidepressant-like effects of paroxetine in the mouse forced swimming test. Swim sessions were conducted by placing mice in individual glass cylinders filled with water for 6 min. The duration of behavioral immobility during the last 4 min of the test was evaluated. Paroxetine (8 and 16 mg/kg, intraperitoneal [i.p.]) significantly reduced the immobility times of mice, whereas lower doses (2 and 4 mg/kg) had no effect. NMDA antagonists MK-801 (0.1 and 0.25 mg/kg, i.p.) and ifenprodil (1 and 3 mg/kg, i.p.) and the NO synthase inhibitor NG- l-arginine methyl ester (L-NAME; 30 and 100 mg/kg, i.p.) significantly decreased the immobility time. Lower doses of MK-801 (0.01 and 0.05 mg/kg), ifenprodil (0.1 and 0.5 mg/kg), and L-NAME (10 mg/kg) had no effect. Combined treatment of subeffective doses of paroxetine (4 mg/kg) and MK-801 (0.05 mg/kg), ifenprodil (0.5 mg/kg), and L-NAME (10 mg/kg) robustly exerted an antidepressant-like effect. The noneffective dose of a NO precursor l-arginine (750 mg/kg, i.p.) prevented the antidepressant-like effect of paroxetine (30 mg/kg). We suggested, for the first time, a possible role for NMDAR/NO signaling in the antidepressant-like effects of paroxetine, providing a new approach for the treatment of depression. [ABSTRACT FROM AUTHOR]