Development of MAFVRO to randomly excited vibration systems to derive the natural frequencies and mode shapes

MAFVRO is one of the out-put only modal analysis methods which is able to determine the modal parameters of a vibration system through the free vibration responses. It is worth to note that most of the vibration systems are subjected to random excitations. Therefore, in such cases, the traditional MAFVRO cannot extract the modal parameters. In this study, the mentioned method is developed to randomly excited vibration systems. Then, the modified MAFVRO is applied to a randomly excited vibration system. The random excitation has been considered as a set of white noises which are applied to all masses of a discrete system. Then by employing the developed method, the estimated results have been compared with those obtained through the structural eigenvalue problem. Comparing the results reveals that the developed method can give the natural frequencies and mode shapes of a randomly excited system with a good accuracy, but it estimates the damping ratios lower than their exact values. In addition, the effect of the noise on the accuracy of the estimated modal parameters have been investigated.