Electro-thermo-mechanical nonlinear free vibration of nanobeam resting on the winkler-pasternak foundations based on nonlocal elasticity using differential transform method

Abstract

This study presents electro-thermo-mechanical nonlinear vibration of nanobeam resting on the Winkler-Pasternak foundations. The nanobeam is considered as an Euler–Bernoulli beam together with von Karman assumptions are employed to model the geometrical nonlinearity where embedded on an elastic foundation which is simulated by spring constant of the Winkler-model and the shear constant of the Pasternak-model. The corresponding governing equations are obtained using Hamilton’s principle considering nonlinear strains. In order to obtain the nonlinear frequency for simply supported mechanical boundary condition at two ends of the nanobeam, differential transform method (DTM) is used in conjunction with a program. By applying this technique, the nanobeam’s natural frequencies can be easily obtained and a rapidly convergent sequence is obtained during the solution. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, temperature change, spring constants and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. To verify the results some comparisons are presented between differential transform method results and open literature to show the accuracy of this new approach. It has been discovered that the DTM does not necessitate small perturbation and is also suitably precise to both linear and nonlinear problems in physics and engineering.