Development of "modal analysis free vibration response only" method for randomly excited systems

Abstract

Modal analysis free vibration response only (MAFVRO) is one of the output-only modal analysis methods which is able to determine the modal parameters of a vibration system by the free vibration responses. However, most of the vibrating systems are subjected to random excitations, and in such cases, the traditional MAFVRO cannot extract the modal parameters. In this study, the traditional MAFVRO method has been developed to randomly excited vibration systems by using some modifications. In order to verify the accuracy of modified MAFVRO, this method is applied to vibration analysis of a cantilever beam and a vehicle suspension system which are subjected to the random white noise excitation. The estimated results are compared with the exact solution obtained from the structural eigenvalue problem. Comparing the results reveals that the developed method can estimate the natural frequencies and mode shapes of a randomly excited system with a good accuracy. In addition, the effect of the measurement noise on the estimated modal parameters is investigated.

Modal Identification of damped vibrating systems by iterative smooth orthogonal decomposition method

“…Although the POD algorithm is very simple and efficient, it can only be applied to systems with uniform mass distribution ( M = m I ) or with mass distribution known in prior. To overcome this limitation, several covariance matrices based methods have been proposed, such as the modal analysis by free vibration response only method (MAFVRO) (Rezaee et al, 2015; Wang and Cheng, 2008), nonsymmetric state-variable decomposition (Feeny and Farooq, 2008) and the smooth orthogonal decomposition (SOD) (Chelidze and Zhou, 2006; Farooq and Feeny, 2008; Hu et al, 2018). Their common feature is that the covariance matrices of response data are used to construct different generalized eigenvalue problems (EVPs) and obtain modal parameters by solving the EVPs.…”