A Semi Analytical Method For Electro-Thermo-Mechanical Nonlinear Vibration Analysis of Nanobeam Resting On the Winkler-Pasternak Foundations With General Elastic Boundary Conditions

Abstract

This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler–Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.