An alternative method for transient and random responses of structures subject to support motions

Abstract

In this paper, we propose the Stokes' transformation technique for extracting the finite part of divergent series resulting from modal dynamic analysis for support motion problems. From the computational point of view, Stokes' transformation is the best method as not only does it avoid calculating the quasistatic solution, it also has the same convergence rate as the mode acceleration method. It is found that the present method should only integrate a known series instead of solving a partial differential equation WIDE) for the quasistatic solution. The general formulation for a finite elastic body subjected to support motions is derived. Finally, two examples, a shear and a flexural beam subjected to multisupport motions, are analysed. Both derivations for transient and statistical responses are considered. The numerical results for random responses are compared with the quasistatic decomposition method proposed by Mindlin and Goodman and the exact solution by Tsaur. Good agreement is obtained.