Analysis of earthquake incitement and approximation of elastic spectrum by wavelet transform

Abstract eng:
This paper presents an analysis of the dynamic incitement of ground acceleration and suggests an approximation of the elastic earthquake response spectrum with the resonant response spectrum. The procedure is based on wavelet transform which separates acceleration into regular harmonic waves of different periods and shows the intensity of each wave in an accelerogram. Wavelet transform extracts a constant component a0 and series of fluctuating components a1, a1r, a2, a2r, …, an, anr from the dynamic incitement. The constant component a0 has the meaning of the constant value of acceleration. The first fluctuating component a1 has the highest intensity while the intensity of each following fluctuating components a2, a3, …, an decreases. The components a1r, a2r, …, anr represent the maximum value of each fluctuating components in dynamic incitement and show the possible resonant effect on single degree of freedom system with the period equal to the duration of the impulse. Wavelet transform performed on several acceleration records shows that the constant component has a significant intensity especially for low periods. The intensity of the constant and the first fluctuating component is approximately equal except for low periods. The limit value of the constant component when period T tends to zero gives peak ground acceleration. The response of the single degree of freedom system to the constant and all fluctuating components gives the components of the response acceleration spectrum. The total response acceleration spectrum consists of the responses to the constant and all fluctuating components. Under an assumption that constant and all fluctuating components have extremes at the same time, the extreme influence from the upper side are obtained for the value of the response acceleration spectrum. This spectrum is named resonant response acceleration spectrum. An approximation of the elastic acceleration spectrum with the resonant response acceleration spectrum based on simultaneously appearance of the extremes of the constant component a0 and two resonant fluctuating component a1r and a2r is suggested in the paper.

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