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透射边界高频失稳机理及其消除方法——SH波动
引用本文:谢志南,廖振鹏.透射边界高频失稳机理及其消除方法——SH波动[J].力学学报,2012,44(4):745-752.
作者姓名:谢志南  廖振鹏
作者单位:1. 中国地震局工程力学研究所, 哈尔滨 150080; 2. 哈尔滨工程大学船舶学院, 哈尔滨 150001
基金项目:国象自然科学基金,中国地震局优秀团队研究基金
摘    要:用有限元法求解近场波动问题,须选取人工边界条件以实现对无限域稳定、高效的数值模拟. 该文探讨了SH波导 有限元数值模拟中透射边界引发的高频失稳问题. 从离散模型出发,分析了内节点与人工边界节点运动方程频散曲线之间的匹配关系,揭示了高频失稳的一种机理,即二者相互耦合所 得计算方案支持自发从人工边界向计算区域内行进的高频波动. 提出通过调整内节点运动方程以改变这一匹配关系,从而消除失稳的措施. 理论分析与数值结果表明该措施能有效地消除高频振荡失稳.

关 键 词:人工边界条件  数值失稳  波动  有限元  频散曲线  群速度
收稿时间:2011-10-31
修稿时间:2012-02-16

MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITSELIMINATION-SH WAVE
Xie Zhinan,Liao Zhenpeng.MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITSELIMINATION-SH WAVE[J].chinese journal of theoretical and applied mechanics,2012,44(4):745-752.
Authors:Xie Zhinan  Liao Zhenpeng
Institution:1. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China; 2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract:To solve near-field wave problems by finite element method,absorbing boundary conditions were needed to simulate the unbound field robustly and effciently.Taking numerical simulation of wave motion in SH waveguide as an example,high-frequency instability caused by transmitting boundary were discussed.Directly from discrete model,mechanism of instability was found by analyzing the matching relationship of motion equations of interior nodes and nodes on absorbing boundary.Results showed that instability was caused by high frequency wave,which was allowed to enter continuously from the absorbing boundary into the computational region without excitation.Thus an approach of eliminating such instability was proposed by adjusting the motion equations of interior nodes to change the matching relationship.Theoretical and numerical results showed that the present approach was effcient.
Keywords:absorbing boundary condition  numerical instability  wave motion  finite element  dispersioncurve  group velocity
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