Modal analysis of mdof system by using free vibration response data only

Conventional modal testing requires the actuator and sensor to perform FRF measurement so as to determine the structural modal parameters. This paper presents a new idea of experimental modal analysis by only using the structural free vibration response due to initial conditions. If the structural displacement can be measured, the displacement response matrices that are the discrete-time-domain data for all measured dofs can be formulated. The velocity and acceleration response matrices can then be calculated by finite difference methods. With the input of these response matrices to the developed algorithm, the system natural frequencies and their corresponding mode shapes can be determined simultaneously. Numerical examples for a 3-dof and 10-dof systems are presented, to show, respectively, the feasibility and effectiveness of the developed method. Results show the proposed method is very promising. Only the structural displacement response in free vibration condition need to be measured and as the input to the modal parameter extraction algorithm such that all of the structural modal frequencies and mode shapes of the system can be determined successfully. The presented idea can also be extended and applied to the general structure with non-proportional damping case. The proposed methodology can therefore enhance the structural modal analysis technique.