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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 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, nonlocal beam theory is utilized for vibration analysis of hygro–electro–thermo–mechanical of functionally graded material (FGM) nanobeam by consideration of magnetic field and preload. Moreover, the material properties are considered to vary corresponding to the thickness of nanobeam in the framework of power-law distribution. Differential equations are derived by means of Hamilton principle in the framework of Euler–Bernoulli beam theory. The derived governing differential equations are solved by differential transformation method (DTM) which demonstrates to have high precision and computational efficiency in the vibration analysis of nanobeams. Numerical results are presented for various boundary conditions. A detailed parametric study is conducted temperature to examine the effects of the nonlocal parameter, voltage and, elastic mediums, power-law index, aspect ratio, preload, magnetic field and moisture effect on vibration characteristics of functionally graded nanobeam. Numerical results are presented in this paper to serve as benchmarks for future analyses of nanotubes. [ABSTRACT FROM AUTHOR]

In the present paper, the vibrational and buckling characteristics of nanotubes with various boundary conditions are investigated considering the coupled effects of nonlocal elasticity and surface effects, including surface elasticity and surface tension. The nonlocal Eringen theory is adopted to consider the effect of small scale size, and the Gurtin-Murdoch model the surface effect. Hamilton's principle is employed to formulate the governing equation and differential transformation method (DTM) is utilized to obtain the natural frequency and critical buckling load of nanotubes with various boundary conditions. The results obtained match the available ones in the literature. Detailed mathematical derivations are presented and numerical investigations are performed. The emphasis is placed on the effects of several parameters, such as the nonlocal parameter, surface effect, aspect ratio, mode number and beam size, on the normalized natural frequencies and critical buckling loads of the nanotube. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects. Numerical results are presented which may serve as benchmarks for future analysis of nanotubes. [ABSTRACT FROM AUTHOR]