Application of the taylor differential transformation method to viscous damped vibration of hard and soft spring system

Recently nonlinear elements such as structures with different tension and compression moduli, supports with motion-limiting stops, and mechanical systems having clearances or snubbers, have been widely used to obtain better performance in vibration controls. When a spring is stretched or compressed beyond the linear range, the restoring force increases at a greater rate than the deformation for a “hardening spring” and at a smaller rate for a “softening spring”. Hence, such a simple mass-spring oscillator is to be regarded as a nonlinear system. The purpose of this paper is to introduce the application of the Taylor differential transformation method to the viscous damped vibration of a hardening and softening spring system. The method introduced in this paper offers advantages over most other methods in its generality, efficiency, accuracy and ease-of-use for calculating the dynamic response of the nonlinear system. The computation of the Taylor differential transformation is complex and difficult probably, but, in the practical application, its advantages are very evident, especially for nonlinear systems and the time-dependant parameter systems. The computationally accurate and the quickly converging calculation by a computer with the Taylor differential transformation method are very salient.