张晓志^*， 刘龙江， 曹玲， 李子欣

（  东北电力大学建筑工程学院，吉林 132012；  ）

摘要： 基于外行简谐波动模型、多项式插值理论、具有解析表达式的外插序列，导出 阶透射边界及其误差项与收敛的充分条件。利用外插序列的时空坐标满足同一直线方程的几何特征，完成简谐波动 阶透射边界向任意外行波动 阶透射边界的推广。依据外插序列的解析表达式，导出后者误差项的近似表达式和收敛性的充分条件。 阶透射边界的主部与 阶多次透射公式相同，但误差项的表达式不同，精度与收敛性的分析方法与结果也不同，误差项分析表明虚拟透射边界位移解的计算精度一般低于而不是高于内域位移解的计算精度。提出了与虚拟透射边界相关的频率放大倍数和虚拟波动频率的新概念，认为它们是影响虚拟透射边界近源失稳的关键因素，这一不同于传统的认识将导致不同于传统的研究思路和发展方向。
关键词： 固体力学；简谐波动；透射边界；任意波动；收敛性；失稳机制；虚拟波动频率

Zhang Xiaozhi^*， Liu Longjiang， Cao Ling， Li Zixin

（  College of Architecture Engineering ,Northeast Dianli University, Jilin 132012, China；  ）

Abstract： Based on outgoing harmonic wave model、polynomial interpolation theory and extrapolation sequence with analytical expression,the N-Order transmitting boundary and its error-term and the sufficien condition of convergence were derived. Using the geometric features that time-space coordinate of extrapolation sequence satisfies the same linear equation, the extension from N-Order transmitting boundary for harmonic waves to that for arbitrary outgoing wave was completed. According to analytical expression of extrapolation sequence，the approximate expression of error-term and the sufficien condition of convergence for the latter were derived. The principal part of N-Order transmitting boundary is similar to N-Order multi-transmitting formula，but the expression of error-term is different，both analysis method and result of the precision and convergence are different too，generally, the error-term analysis shows that computation accuracy of the displacement solution of virtual transmitting boundary is not higher but lower than that of the inner domain displacement solution. New conceptions of frequency amplification and virtual wave frequency were proposed which related to virtual transmitting boundary，and they are considered as the key factors effecting near source instability of virtual transmitting boundary, this recognition being different from the traditional will lead to multiple research thoughts and developments.

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