Abstract
Wavelet frame expansions are utilized to introduce ‘‘wavelet response functions’’ (WRF). The convolution integral is replaced by an efficient synthesis scheme by incorporating multiresolution and wavelet frame expansion concepts. Wavelet frame expansion is used to partition a wide spectral range into multiresolution frequency bands. The response from each resolution level is obtained by using a sampling interval that is matched with the bandwidth. The contributions coming from different resolution levels are combined to construct the overall system response. In the applications, the attention is focused on the synthesis of the transient time-domain vibration response of proportionally damped (Bn=η, fn, n=modes) wideband linear systems. Naturally, such systems, having impulse response durations that are inversely proportional to the modal bandwidths (Tmaxn= 2.2/Bn), require a multiresolution synthesis scheme during the construction of their transient response, which involves fast-decaying high-frequency components that are superimposed on top of slowly decaying low-frequency modal responses. The proposed construction technique averts the time-domain aliasing problem associated with the DFT schemes. The effectiveness of the wavelet frame synthesis scheme is demonstrated by considering the construction of the transient vibration response of a finite dispersive system.
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