A Linear Time-Varying Approximation Method to Nonlinear Structural Dynamic Systems

In order to obtain the response of nonlinear structural dynamic system effectively, a linear, time-varying approximation method is proposed in this paper. The technique is based on the replacement of the original nonlinear system by a sequence of linear time-varying systems, whose solutions will converge to the solution of the nonlinear problem in the global time domain. In this paper, the solutions of a nonlinear time-unvarying system and a nonlinear time-varying system are separately obtained by this iteration approach. This method is powerful for obtaining the accurate response of nonlinear structural system, and the only condition required for its application is a mild Lipschitz condition which must be satisfied by the nonlinear state matrix. Moreover, the choose of initial function is important for changing the convergence rate of this iteration technique. Results indicate that the closer the initial function is to the true nonlinear solution, the sooner this convergence will be achieved.