Methods of dynamic analysis in the frequency domain are presented in this paper which are particularly suitable for the analysis of structural systems with frequency dependent properties and with hysteretic damping. These systems are typically found in interaction systems such as soil-and fluid-structure interaction systems. An alternative formulation, other than using a discrete Fourier Transform (FT) pair, for the calculation of the response of single degree-of-freedom (SDOF) systems and formulations for multi-degree-of-freedom (MDOF) systems are detailed addressed. These formulations are extended for the analysis of non-linear systems which only recently have been analysed through frequency domain methods. The response analysis, in the frequency domain, for initial conditions, which is important for nonlinear analysis, is clarified. An iterative procedure for the modal analysis, in the frequency domain, of systems with nonproportional and hysteretic damping is presented. There are provided examples of linear and nonlinear analysis by frequency domain methods.

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