Keywords: modal truncation error, residual flexibility, nonclassical damping, steady-state response, modal superposition method, harmonic response..

In this paper, an adaptive modal correction method is presented to calculate the steady-state responses of non-proportionally damped systems by only using lower available modes. It is shown that the steady-state responses can be exactly expressed as a power-series expansion in terms of the available modes and system matrices. However, a series-truncation problem is encountered in engineering applications. To this end, a criterion of determining the number of the power-series terms is presented to process the necessary accuracy, and an adaptive accuracy control is presented to handle the series-truncation problem. It is shown that, the convergence of the adaptive modal correction method is much faster than the mode superposition method and the computational cost of the proposed method is much less than that of the direct frequency response method. Finally, a sandwich damping structure is used to show that, the adaptive modal correction method yields good trade-off between the accuracy and the computational efficiency.

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