Advanced parametric space-frequency separated representations in structural dynamics: A harmonic–modal hybrid approach

Abstract

This paper is concerned with the solution to structural dynamics equations. The technique here presented is closely related to Harmonic Analysis, and therefore it is only concerned with the long-term forced response. Proper Generalized Decomposition (PGD) is used to compute space-frequency separated representations by considering the frequency as an extra coordinate. This formulation constitutes an alternative to classical methods such as Modal Analysis and it is especially advantageous when parametrized structural dynamics equations are of interest. In such case, there is no need to solve the parametrized eigenvalue problem and the space-time solution can be recovered with a Fourier inverse transform. The PGD solution is valid for any forcing term that can be written as a combination of the considered frequencies. Finally, the solution is available for any value of the parameter. When the problem involves frequency-dependent parameters the proposed technique provides a specially suitable method that becomes computationally more efficient when it is combined with a modal representation.