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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 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]