Application of the differential transformation method to non-linear shock damper dynamics

This paper adopts the differential transformation method (DTM) to non-linear shock damper dynamics with non-linear spring and non-linear damping. The principle of differential transformation is briefly introduced and is then applied in the derivation of a set of difference equations for the problem. The solutions are subsequently solved by a process of inverse transformation. The time responses of the equations are presented for two cases and the current results are then compared with those derived from the established Runge-Kutta method in order to verify the accuracy of the proposed method. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the proposed differential transformation method is a powerful and efficient tool for solving non-linear problems.