Experimental Modal Analysis by using Dynamic Mode Decomposition

Abstract

In this paper, applicability of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems from their time-domain dynamic responses, i.e., experimental modal analysis is discussed. Of particular interest is its capability to extract modal parameters, i.e., natural frequencies, damping ratios and mode shapes, from measured time histories of displacement of discrete and distributed mechanical systems. First, theoretical background of DMD is briefly reviewed from the viewpoint of structural dynamics. It is shown that the modal parameters can be extracted from the DMD eigenvalues and the associated eigenvectors. The DMD is then applied to analytical solutions of transient response of discrete mass-spring-damper mechanical systems to discuss the applicability of the DMD to extract the modal parameters from the transient response. Furthermore, the effects of measurement errors on the identified modal parameters are discussed. With relatively large measurement errors, it is shown that DMD produces erroneous results especially for the damping ratios. Finally, DMD is applied to experimentally-obtained impulse response of displacement field of a cantilevered beam with many measurement points, and its modal parameters are extracted. It is shown that the modal parameters extracted by DMD are as accurate as the ones obtained by the existing modal parameter extraction method.