Modal analysis by free vibration response only for discrete and continuous systems

This work aims to develop the algorithm for modal analysis by free vibration response only (MAFVRO), in particular for the general or non-proportional viscous damping system model. If the structural displacement or acceleration response due to free vibration can be measured, the system response matrices, including the displacement, velocity and acceleration, can be obtained through numerical differential or integration methods. These response matrices can then be applied to the developed MAFVRO method to determine the structural modal parameters. The numerical differential and integration methods are introduced and adopted to establish the modal parameter prediction program for the non-proportional damping model of MAFVRO. This work also shows the applications of MAFVRO to the multiple degree-of-freedom (mdof) systems and the cantilever beam, respectively. Both the discrete and continuous systems are demonstrated for the feasibility of the MAFVRO algorithm. The developed method uses the free vibration output response only and can obtain the structural modal parameters successfully.