In order to identify the horizontal seismic motion owning the largest pulse energy, and represent the dominant pulse-like component embedded in this seismic motion, we used the adaptive wavelet transform algorithm in this paper. Fifteen candidate mother wavelets were evaluated to select the optimum wavelet based on the similarities between the candidate mother wavelet and the target seismic motion, evaluated by the minimum cross variance. This adaptive choosing algorithm for the optimum mother wavelet was invoked before identifying both the horizontal direction owning the largest pulse energy and every dominant pulse, which provides the optimum mother wavelet for the continuous wavelet transform. Each dominant pulse can be represented by its adaptively selected optimum mother wavelet. The results indicate that the identified multi-pulse component fits well with the seismic motion. In most cases, mother wavelets in one multi-pulse seismic motion were different from each other. For the Chi-Chi event (1999-Sep-20 17:47:16 UTC, Mw = 7.6), 62.26% of the qualified pulse-like earthquake motions lay in the horizontal direction ranging from ±15° to ±75°. The Daubechies 6 (db6) mother wavelet was the most frequently used type for both the first and second pulse components.
Summary
The time delay effect is prominent for the slender structures under the action of near‐fault pulse‐like earthquake excitation. It takes time for the earthquake motion to transfer from the base to other portions of the structure. This paper proposes an explicit‐based fiber line element with its analytical framework to capture the time delay effect when excitated by earthquake motion. The object‐oriented technique (C++) is used to code the integrated analysis framework. Newly designed classes are integrated to perform the explicit analysis parallelly. The nonlinear material model is also incorporated into the proposed element. The verification of the proposed element shows the time delay effect can be spotted inside the structure. The proposed element can provide a reasonable transient dynamic response under both static and dynamic loadings. The basic and higher vibration model can be aroused if the proper frequency is inputted. A slender reinforced concrete bridge pier is numerically modeled by the proposed element, and its seismic response characteristic under the action of the qualified multipulse near‐fault earthquake motion is analyzed. The results show the seismic response within the pier is transferred from bottom to top in a distinct time delay. In a statistical sense, the typical increasing ratio of relative displacement for S/R and P/S is 4.9% and 8.1%, respectively. Directly using the earthquake motion recorded at the seismic station may underestimate the seismic demand.
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