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

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