Time History Response of Multidegree-of-Freedom Systems

Abstract

In Chapter 7 the nonlinear analysis of a single degree-of-freedom system using the step-by-step linear acceleration method was presented. The extension of this method, with a modification known as the Wilson-θ method, for the so-lution of structures modeled as multidegree-of-freedom systems is developed in this chapter. The modification introduced in the method by Wilson et al. 1973 serves to assure the numerical stability of the solution process regardless of the magnitude selected for the time step; for this reason, such a method is said to be unconditionally stable. On the other hand, without Wilson’s modification, the step-by-step linear acceleration method is only condition-ally stable and for numerical stability of the solution may require such an extremely small time step as to make the method impractical if not impos-sible. The development of the necessary algorithm for the linear and nonlin-ear multidegree-of-freedom systems by the step-by-step linear acceleration method parallels the presentation for the single degree-of-freedom system in Chapter 7.