Modal parameter identification using state space mode isolation

Multiple degree of freedom (MDOF) methods for modal parameter extraction in current use deal with all of the modal parameters in a simultaneous fashion in the process of matching measured data to analytical forms. In contrast, the mode isolation algorithm exploits the fact that each mode has unique characteristics that can be used to isolate it from the contribution of other modes. The present work extends the algorithm to use state-space modes as the analytical foundation. The paper describes how modal parameters are identified and then refined in a recursive manner. One of the issues of primary importance for a modal identification is the number of modes that significantly contribute to the measured response. Most MDOF algorithms require an a priori guess of the number of significant modes, or degrees of freedom, of the system. Several MDOF methods address this matter by utilizing peak counting of amplitude-frequency plots to identify the number of modes. However, such estimation becomes problematic for systems that exhibit modal coupling. In contrast, the mode isolation method offers a simple and consistent modal extraction methodology that is inherently automatic in nature. A prototypical system is used to demonstrate that it is not limited by the presence of modal coupling. A cantilever beam with three attached spring-mass-damper systems is tuned such that the bandwidths of two resonances are commensurate with the natural frequency separation. Differing levels of noise are imposed on the simulated time-domain response, which is then transformed to the frequency domain. The simulated data is used to illustrate the results of the algorithmic steps. The natural frequencies and damping ratios that result from the procedure are found to match the analytical system properties, with an error that is less than the noise level that was added.