Basic Theory and Numerical Tools

This chapter offers an overview of the theoretical foundations and the standard numerical methods for solving structural dynamics problems, with emphasis placed firmly on the latter. Starting with the analysis of single degree of freedom (SDOF) systems both in the time and in the frequency domain, it includes sections on the computation of elastic and inelastic response spectra, filtering in the frequency domain, the analysis of nonlinear SDOF systems and the generation of spectrum compatible ground motion time histories. Discrete multi-degree of freedom (MDOF) systems, condensation techniques and damping models are considered next. Both modal analysis (“response modal analysis”) and direct integration methods are employed, focussing especially on the behaviour of MDOF systems subject to seismic excitations described by response spectra or sets of specific ground motion time histories. Detailed descriptions of the software used for solving the numerous examples presented complete with full input-output parameter lists conclude the chapter.