發(fā)布時間：2019-05-11 18:03

【摘要】：將邢浩潔和李鴻晶提出的多次透射公式(multi-transmitting formula,MTF)的譜元格式應用于均勻介質中線彈性SH波動問題的譜元模擬.假定緊鄰人工邊界的一層譜單元為具有直線邊界的四邊形單元,以保證每個人工邊界節(jié)點都唯一對應一條指向內(nèi)域的離散網(wǎng)格線.人工邊界節(jié)點在某時刻的位移由該離散網(wǎng)格線上的節(jié)點在前若干時刻的位移確定,按照MTF譜元格式進行計算.通過平面波以一定角度傳播的外源問題算例和點源脈沖自由擴散的內(nèi)源問題算例,驗證了方法的可行性以及對實際復雜波動問題的適用性.通過不同類型初值問題算例,在時域內(nèi)分析了插值多項式階次、人工波速和透射階次三個參數(shù)對反射誤差的影響.結果表明:插值多項式階次較高的格式會表現(xiàn)出更好的精度,但總體上對反射誤差的影響較小;人工波速對反射誤差具有顯著影響,當人工波速小于介質物理波速時反射誤差較大,而當人工波速等于或稍大于介質物理波速時反射誤差處于較低水平;透射階次對反射誤差具有決定性影響,表現(xiàn)在不失穩(wěn)的情形下提高透射階次能夠迅速降低反射誤差,但內(nèi)源問題從三階MTF開始出現(xiàn)飄移失穩(wěn),外源問題從二階MTF開始出現(xiàn)輕微的飄移失穩(wěn).
[Abstract]:The spectral element scheme of multiple transmission formula (multi-transmitting formula,MTF) proposed by Xing Haojie and Li Hongjing is applied to the spectral element simulation of elastic SH wave problem in the middle line of homogeneous media. It is assumed that a layer spectral element adjacent to the artificial boundary is a Quadrilateral element with a straight line boundary to ensure that each artificial boundary node has a unique discrete grid line pointing to the inner domain. The displacement of the artificial boundary node at a certain time is determined by the displacement of the node on the discrete grid line at the previous time, and calculated according to the MTF spectral element scheme. The feasibility of the method and its applicability to complex wave problems are verified by an example of exogenous problem propagated by plane wave at a certain angle and an example of internal problem of free diffusion of point source pulse. Through the examples of different types of initial value problems, the effects of interpolation order, artificial wave velocity and transmission order on reflection error are analyzed in time domain. The results show that the format with higher interpolation order will show better accuracy, but it has little effect on the reflection error as a whole. The reflection error is larger when the artificial wave velocity is less than the medium physical wave velocity, while the reflection error is lower when the artificial wave velocity is equal to or slightly greater than the medium physical wave velocity. The transmission order has a decisive effect on the reflection error. Increasing the transmission order without instability can reduce the reflection error rapidly, but the internal problem begins to appear drift instability from the third order MTF. The external problem begins with the slight drift instability of the second order MTF.
【作者單位】： 南京工業(yè)大學土木工程學院;
【基金】：國家自然科學基金資助項目(51278245)
【分類號】：O241.82
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本文編號：2474723