Simulation of the time histories of second-order wave effects is often performed by quadratic transformation of a wave time history. By the present approach, the quadratic transformation of waves is approximated by linear combinations of the products of component wave time records and their Hilbert transforms. The computational efficiency is greatly enhanced. The efficient quadratic transformation of a time history is for the time domain solution of structural dynamic response, and can also be used as a post-processor of the frequency domain solution for obtaining statistic parameters of dynamic response.

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