Calculation of Nonlinear Normal Modes Using EPFM Method

In the last decade, nonlinear normal modes have attracted the attention of many researchers, and many methods and algorithms have been proposed to calculate them. Among the proposed methods, the combination of the shooting method and the continuation of the periodic solution is the strongest methods. However, the computational cost of the method has still limited its application. In this paper, an updated formula is used to reduce the computational costs of the method. Using this updated formula significantly reduced the computation time so that the computational speed of nonlinear normal modes increased tenfold. Also, as the power of nonlinear terms increases in the system, the efficiency of the updated formula increases. In order to evaluate the accuracy of the proposed method, a system with two degrees of freedom was studied, and it was observed that the results obtained are consistent with the results in other works.

Keywords:

Nonlinear Normal Modes , the Continuation of the Periodic Solution Method , Updated Formula