Determination of dynamic characteristics of lattice structure using dynamic mode decomposition

Abstract

In this work, dynamic mode decomposition (DMD) was applied as an algorithm for determining the natural frequency and damping ratio of viscoelastic lattice structures. The algorithm has been developed based on the Hankel alternative view of Koopman and DMD (HAVOK-DMD). In general, the Hankel matrix is based on time-delay embedding, which is meant for the hidden variable in a time series data. Vibration properties of a system could be then estimated from the eigenvalues of approximated Koopman operator. Results of the proposed algorithm was firstly validated with those of the traditional discrete Fourier transform (DFT) approach and half power bandwidth (HPBW) by using analytical dataset of multi-modal spring-mass-damper system. Afterwards, the algorithm was further used to analyze dynamic responses of viscoelastic lattice structures, in which data from both experimental and numerical finite element (FE) model were considered. It was found that the DMD based algorithm could accurately estimate the natural frequencies and damping ratios of the examined structures. In particular, it is beneficial to any dataset with limited amounts of data, whereby experiments or data gathering processes are expensive.