The response spectral density is an important parameter which should be examined by a machine-tool analyst. A new approach for the calculation of response spectral density for a linear stationary random multi-degree-of-freedom system is presented. This method is based on condensing the system matrices and introducing a set of auxiliary variables. The response spectral density matrix obtained by using this new approach contains the spectral densities and the cross-spectral densities of the master degrees-of-freedom chosen. The new method requires significantly less computation time, as compared to conventional methods, for calculating response spectral densities associated with the selected number of degrees of freedom. To compare the computation time, three numerical examples are presented.

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