Size-dependent hygro–thermo–electro–mechanical vibration analysis of functionally graded piezoelectric nanobeams resting on Winkler–Pasternak foundation undergoing preload and magnetic field.

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]