Application of the differential transformation method to the solution of a damped system with high nonlinearity

This paper employs the differential transformation method to investigate the response of a damped system with high nonlinearity. The accuracy and validity of the proposed method are demonstrated through its application to the solution of a dynamic system with various values of power-form nonlinearity. The numerical results indicate that the amplitude decays more rapidly at higher values of nonlinearity, particularly at higher values of the damping coefficient. It is shown that the current results are in excellent agreement with those provided by the Runge–Kutta method. Therefore, the method presented in this study provides an effective scheme for determining the solutions of a damped vibration problem with high nonlinearity.