Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

In this article, wave based method (WBM) is proposed as a new semi-analytical method to analyze the wave propagation characteristics of the magneto-electro-thermo-elastic nanobeams with arbitrary boundary conditions. According to the Timoshenko beam theory and Hamilton principle, the governing equations of the nanobeam which are related to Eringen’s nonlocal theory are obtained. The displacement and external potential variables are expanded as wave function forms. In the light of the introduction of several type boundary conditions, the total matrix of the nanobeam is constituted. Searching the zero locations of the total matrix determinant by the bisection method, the natural frequencies of the nanobeam under arbitrary boundary conditions are received. To further illustrate the calculation correctness of the presented method, the results are compared with the solutions in reported references. Furthermore, a series of numerical examples are proposed to investigate the effect of each parameter on the free vibration characteristics of the nanobeam with several boundary conditions, such as beam length and thickness, external temperature rise, magnetic and electric potential. Some new numerical solutions and conclusions are presented in this paper to provide the basic foundation for subsequent research.