EI、Scopus 收录
中文核心期刊
Quick Search Issue Search Advanced Search
Volume 44 Issue 4
Turn off MathJax
Article Contents
Abstract
References
Related Articles
Xie Zhinan, Liao Zhenpeng. MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITS ELIMINATION——SH WAVE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 745-752. DOI: 10.6052/0459-1879-11-312
Citation: Xie Zhinan, Liao Zhenpeng. MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITS ELIMINATION——SH WAVE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 745-752. DOI: 10.6052/0459-1879-11-312
shu

MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITS ELIMINATION——SH WAVE

  • 1.

    Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China

  • 2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Funds: The project was supported by the National Natural Science Foundation of China (51108431, 51078337) and Research Group Fund of China Earthquake Administration.
  • Received Date: October 30, 2011
  • Revised Date: February 15, 2012
    Graphical Abstract
    • Abstract
  • To solve near-field wave problems by finite element method, absorbing boundary conditions were needed to simulate the unbound field robustly and efficiently. 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 efficient.
    • FullText(HTML)
    • References (27)
  • 廖振鹏. 工程波动理论导论 (第2版). 北京: 科学出版社, 2002 (Liao Zhenpeng. Introduction to Wav Motion Theories in Engineering (2nd edn). Beijing: Science Press, 2002 (in Chinese)
    Bérenger JP. Perfectly Matched Layer (PML) for Computational Electromagnetics. California: Morgan and Claypool Publishers, 2007
    Givoli D. Numerical Methods for Problems in Infinite Domains. Amsterdam: Elsevier, 1992
    Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bulletin of the Seismological Society of America, 1977, 67(6): 1529-1540
    Bayliss A, Turkel E. Radiation boundary conditions for wave-like equations. Communications on Pure and Applied Mathematics, 1980, 33(6): 707-725
    Liao ZP, Wong HL, Yang BP, et al. A Transmitting boundary for transient wave analyses. Scientia Sinica(Series A). 1984, 27(10): 1063-1076
    Higdon RL. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation. Mathematics of Computation, 1986, 47(176): 437-459
    Cerjan C, Kosloff D, Kosloff R, et al. A nonreflecting boundary conditions for discrete acoustic and elastic wave equations. Geophysics, 1985, 50(4): 705-708
    Sochaki I, Kubichek R, George J, et al. Absorbing boundary conditions and surface waves. Geophysics, 1987, 52(1): 60-71
    Bérenger JP. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 1994, 114(2): 185-200
    Grote MJ, Keller JB. Exact nonreflecting boundary conditions for the time dependent wave equation. SIAM Journal on Applied Mathematics, 1995, 55(2): 280-297
    Rowley CW, Colonius T. Discretely nonreflecting boundary conditions for linear hyperbolic systems. Journal of Computational Physics, 2000, 157(2): 500-538
    Komatitsch D, Martin R. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics, 2007, 72(5): SM155-SM167
    Hagstrom T, Mar-Or A, Givoli D. High-order local absorbing conditions for the wave equation: Extensions and improvements. Journal of Computational Physics, 2008, 227(6): 3322-3357
    Meza-Fajardo KC, Papageorgiou AS. On the stability of a non-convolutional perfectly matched layer for isotropic elastic media. Soil Dynamics and Earthquake Engineering, 2010, 30(3): 68-81
    Du XL, Zhao M. A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media. Soil Dynamics and Earthquake Engineering, 2010, 30(10): 937-946
    Zhao M, Du XL, Liu JB, et al. Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide. International Journal for Numerical Methods in Engineering, 2011, 87(11): 1074-1104.
    Liao ZP, Zhou ZH, Zhang YH. Stable implementation of transmitting boundary in numerical simulation of wave motion. Chinese Joural of Geophysics, 2002, 45(4): 554-568
    Liao ZP, Liu JB. Numerical instabilities of a local transmitting boundary. Earthquake Engineering & Structural Dynamics, 1992, 21(1): 65-77
    杜修力, 赵密, 王进廷. 近场波动模拟的人工应力边界条件.力学学报, 2006, 38(1): 49-56 (Du Xiuli, Zhao Mi, Wang Jinting. A stress artificial boundary in FEA for near-field wave problem. Chinese Journal of Theoretical and Mechanics, 2006, 38(1): 49-56 (in Chinese)
    谢志南. 波动数值模拟人工边界的稳定问题. [博士论文].哈尔滨: 中国地震局工程力学研究所, 2011 (Xie Zhinan. Stability problems of artificial boundary conditions in numerical wave simulation. [PhD Thesis]. Dalian: Institute of Engineering Mechanics, China Earthquake Administration, 2011 (in Chinese)
    廖振鹏,谢志南. 波动数值模拟的稳定性. 哈尔滨工程大学学报, 2011, 32(9): 1254-1261 (Liao Zhenpeng, Xie Zhinan. stability of numerical simulation of wave motion. Journal of Harbin Engineering University, 2011, 32(9): 1254-1261 (in Chinese)
    关慧敏,廖振鹏. 局部人工边界稳定性的一种分析方法. 力学学报,1996, 28(3): 376-380 (Guan Huimin, Liao Zhenpeng. A method for the stability analysis of local artificial boundaries. Acta Mechanica Sinica,1996, 28(3): 376-380 (in Chinese)
    景立平, 廖振鹏, 邹经湘. 多次透射公式的一种高频失稳机制. 地震工程与工程振动, 2002, 22(1): 7-13 (Jing Liping, Liao Zhenpeng, Zou Jingxiang. A high-frequency instability mechanism in numerical realization of multi-transmitting formula. Earthquake Engineering and Engineering Vibration, 2002, 22(1): 7-13 (in Chinese)
    Gustafsson B, Kreiss HO, Sundström A. Stability theory of difference approximations for initial boundary value problems II. Mathematics of Computation, 1972, 26(119): 649-686
    Trefethen LN. Group velocity interpretation of the stability theory of Gustafsson Kreiss and Sundstrom. Journal of Computational Physics, 1983, 49(2): 199-217
    Godunov S, Ryabenkii V. Spectral stability criteria for boundary value problems for non-self-adjoint difference equations. Russian Mathematical Surveys, 1963, 18(3): 1-12
    • Related Articles

  • Related Articles

    [1]Xu Yazhou, Tian Rui. A PSEUDO-SPECTRAL METHOD FOR THE GENERALIZED DENSITY EVOLUTION EQUATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2415-2422. DOI: 10.6052/0459-1879-23-633
    [2]Chen Jianbing, Zhang Shenghan. PROBABILITY DENSITY EVOLUTION ANALYSIS OF NONLINEAR RESPONSE OF STRUCTURES WITH NON-UNIFORM RANDOM PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 136-144. DOI: 10.6052/0459-1879-13-174
    [3]Ren Limei, Xu Wei. FIRST PASSAGE PROBABILITIES OF STRUCTURAL DYNAMICS SYSTEM BASED ON DOMAIN DECOMPOSITION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 421-425. DOI: 10.6052/0459-1879-12-355
    [4]Jiang Chao, Zhang Zhe, Han Xu, Bai Yingchun. AN EVIDENCE-THEORY-BASED RELIABILITY ANALYSIS METHOD FOR UNCERTAIN STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 103-115. DOI: 10.6052/0459-1879-12-040
    [5]Chaos control of form iterative algorithm in structural reliability analysis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 647-654. DOI: 10.6052/0459-1879-2007-5-2006-501
    [6]Xiaojun Wang, Zhiping Qiu, Zhe Wu. Non-probabilistic set-based model for structural reliability[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 641-646. DOI: 10.6052/0459-1879-2007-5-2006-629
    [7]Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(1): 127-133. DOI: 10.6052/0459-1879-2006-1-2005-054
    [8]FORM in structural reilianbility analysis and chaotic dynamics[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(6): 799-804. DOI: 10.6052/0459-1879-2005-6-2004-244
    [9]The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(2). DOI: 10.6052/0459-1879-2004-2-2003-202
    [10]TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES BASED ON RELIABILITY 1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(3): 277-284. DOI: 10.6052/0459-1879-1998-3-1995-127

  • Cited by

    Periodical cited type(1)

    1. 彭宗桓 ，盛建龙 ，叶祖洋 ，李硕 . 基于t-SNE-AMARS-MPM的空间变异性边坡可靠度分析及大变形破坏模式研究. 力学学报. 2024(11): 3274-3289 . 本站查看

    Other cited types(0)

Catalog

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1867) PDF downloads (1005) Cited by(1)
    Related

    Download Center

    Author Center

      Copyright © Editorial Office of the Chinese Journal of Mechanics   京ICP备05039218号-1

      Address：15 Beishihuan Xi Lu, Haidian District, Beijing, China   China Pos：100190

      Tel：010-62536271

      Email：lxxb@cstam.org.cn

      Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return