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For structures with non-classical damping or closely distributed modes, it is not easy to apply the traditional modal analysis method 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 non-classical damping ratio and structures with very closely distributed modes is proposed. This method defines the generalized modes in state space, and uses the differential state variables estimated from measured acceleration responses to decompose modal responses. A Kalman filtering is utilized to calculate the linear transformation matrix of governing modes, and the linear transformation matrix is updated in the optimization process to maximize the performance index cooperated with a power spectral density of a target mode. For the verification of the proposed method, a numerical simulation is performed using a single degree of freedom (SDOF) system coupled with a tuned mass damper (TMD) which represents a non-classically 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 (ICA) method and the proper orthogonal decomposition (POD) method.

Mode decomposition, Non-classical damping, Closely distributed mode, Linear transformation matrix, Differential state variable, Averaged power spectrum