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.

本文提出了基于波的方法（WBM）作为一种新的半分析方法，以分析具有任意边界条件的磁电热弹性纳米束的波传播特性。根据蒂莫申科束理论和汉密尔顿原理，得到了与艾林根非局部理论有关的纳米束控制方程。位移和外部电势变量扩展为波动函数形式。根据几种类型边界条件的引入，构成了纳米束的总矩阵。通过二分法搜索总矩阵行列式的零位置，接收纳米束在任意边界条件下的固有频率。为了进一步说明所提出方法的计算正确性，将结果与参考文献中的解决方案进行比较。此外，提出了一系列数值示例，以研究各个参数对具有多个边界条件（例如束长和厚度，外部温升，磁和电势）的纳米束的自由振动特性的影响。本文提出了一些新的数值解和结论，为后续研究提供了基础。