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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]

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]

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]

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