Mode decomposition of structures with closely distributed modes and nonclassical damping

Abstract

It is difficult to apply traditional modal analysis methods to structures with nonclassical damping or closely distributed modes, because the damping matrix is not diagonalized by the modal matrix obtained from the mass and stiffness matrices. In this paper, a new mode decomposition method for structures with nonclassical damping and very closely distributed modes is proposed. This method defines the generalized modes in state space and uses differential state variables constructed from measured acceleration responses to decompose modal responses. A Kalman filtering approach is utilized to calculate the linear transformation matrix of governing modes, and the linear transformation matrix is updated in the optimization process of the objective functions integrated with the power spectral density of a target mode. The two performance functions are proposed to maximize the energy at a certain mode and to minimize the differences between the decomposed modal power spectrum and averaged power spectrum, assuming that each mode has a monochromatic signature with one natural frequency and one damping ratio. To verify the proposed method, a numerical simulation is performed using a single degree of freedom system coupled with a tuned mass damper that represents a nonclassically damped system with closely distributed modes. The results from the simulations show that the proposed method estimates the modal responses more precisely than conventional mode decomposition methods such as the independent component analysis method.