Keywords: modal truncation error, residual flexibility, nonclassical damping, frequency response analysis, modal superposition method, sensitivity, harmonic response, design sensitivity analysis..

This paper is aimed at including the influence of the higher-order modes to the frequency response sensitivities of non-classically viscously damped systems. An accurate modal superposition method (AMSM), which only involves the available modes and system matrices, is presented to accurately calculate the frequency response sensitivities of non-classically damped systems. The AMSM is maintained in the original-space without having to involve the state-space equations of motion. The convergence condition only requires that all the modes whose resonant frequencies lie within the range of the excitation frequencies must be used for mode superposition. So it is easy to satisfy and the AMSM easily converges to the exact results. The computational complexity of the AMSM and the direct frequency response method (DFRM) is evaluated and compared. It is shown that the errors of the sensitivities calculated using the mode displacement method (MDM) are significant. The AMSM can reduce the modal-truncation error very rapidly. That is, the AMSM can give almost the same accuracy with the exact results of the DFRM, but save much computational cost. Therefore, the AMSM yields good trade-off between the accuracy and the computational complexity.

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