Time History Response of Multi-Degree-of-Freedom Systems

Abstract

The nonlinear analysis of a single-degree-of-freedom system using the step-by-step linear acceleration method was presented in Chap. 6. The extension of this method with a modification known as the Wilson-θ method, for the solution 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 conditionally stable and for numerical stability of the solution it may require such an extremely small time step as to make the method impractical if not impossible. The development of the necessary algorithm for the linear and nonlinear multidegree-of-freedom systems by the step-by-step linear acceleration method parallels the presentation for the single-degree-of-freedom system in Chap. 6.