Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform

The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.