Application of the Homotopy Method to Solve Eigen Value in A Vibration Model

Abstract

Most mathematical models of natural phenomena are nonlinear model. One of the nonlinear problems is a problem of vibration which can be considered as an eigen value problem. Here, the nonlinear factor appeared due to the external forces applied to the system. The vibration problem in this study, was solved using the homotopy method. The homotopy method is analytical approach in the nonlinear problems within the series form. The terms of the series were obtained based on a recursive formula in a high deformation. A convergent solution of the series dependent on both the homotopy parameter and the coefficient of nonlinear factors appeared in the model.