An efficient time/frequency domain algorithm for modal analysis of non-linear models discretized by the FEM

Abstract The present paper describes an efficient time/frequency domain approach for modal analysis of non-linear models discretized by the FEM. An efficient recurrence relationship for displacement and velocity, based on the Green’s function of the model and its time derivative, is presented in both a time and a frequency domain context. In the time domain procedure the Green’s function related terms are analytical; in the frequency domain procedure the fundamental terms are indirectly evaluated, taking into account steady-state responses of the system. The pseudo-force method is adopted in order to deal with the model non-linearity. Results for the time/frequency domain approaches discussed here showed the same level of accuracy as those obtained by the Newmark/Modified-Newton algorithm at a lower computational cost.

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