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Adaptive mode superposition and acceleration technique with application to frequency response function and its sensitivity

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摘要

An adaptive mode superposition and acceleration technique (AMSAT) is proposed and implemented into the computation of frequency response functions (FRFs) and their sensitivities. Based on the mode superposition and mode acceleration methods for the FRFs, m-version, s-version, and ms-version adaptive schemes are presented. In these schemes, the error resulted from the mode truncation and/or series truncation is, at first, estimated at every specific frequency, respectively. Then, one more mode (called m-version), or one more level of the series (called s-version), or the combination (called ms-version) is included in the computation of the FRF when its error is greater than the error tolerance. The new FRF is recalculated and its error is re-evaluated. This procedure is repeated until all the errors fall below the specified value. Although only the implementation of FRFs and their sensitivities is demonstrated in this paper, the proposed adaptive technique may be applied to the computation of dynamic responses in time domain and their sensitivities, sensitivity of eigenpairs, modal energy, etc. One numerical example is included to demonstrate the application of the proposed adaptive schemes. The results show that the present schemes work very well. The s- and ms-version adaptive schemes are much more efficient than m-version scheme. Since the intention of this paper is to propose these new procedures, the damping, particularly the non-classical damping, is not included due to the complexity.

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