Modal Analysis Using the Singular Value Decomposition

Abstract

Many methods exist for identifying modal parameters from experimental transfer function measurements. For frequency domain calculations, rational fraction polynomials have become the method of choice, although it generally requires the user to identify frequency bands of interest along with the number of modes in each band. This process can be tedious, especially for systems with a large number of modes, and it assumes the user can accurately assess the number of modes present in each band from frequency response plots of the transfer functions. When the modal density is high, better results can be obtained by using the singular value decomposition to help separate the modes before the modal identification process begins. In a typical calculation, the transfer function data for a single frequency is arranged in matrix form with each column representing a different drive point. The matrix is input to the singular value decomposition algorithm and left- and right-singular vectors and a diagonal singular value matrix are computed. The calculation is repeated at each analysis frequency and the resulting data is used to identify the modal parameters. In the optimal situation, the singular value decomposition will completely separate the modes from each other, so that a single transfer function is produced for each mode with no residual effects. A graphical method has been developed to simplify the process of identifying the modes, yielding a relatively simple method for computing mode shapes and resonance frequencies from experimental data.