离散网格中相速度、群速度概念的注记

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英文篇名：A note of phase velocity and group velocity in discrete scheme 作者：马新生 ; 郑永路 ; 马完君 英文作者：Ma Xinsheng;Zheng Yonglu;Ma Wanjun;School of Earth and Space Sciences,University of Science and Technology of China;Key Laboratory of Earthquake Engineering and Engineering Vibration,Institute of Engineering Mechanics,China Earthquake Administration; 关键词：离散网格波动 ; 相速度 ; 群速度 英文关键词：wave motion in discrete grid;;phase velocity;;group velocity 中文刊名：JCJG 英文刊名：Building Structure 机构：中国科学技术大学地球和空间科学学院;中国地震局工程力学研究所中国地震局地震工程与工程振动重点实验室; 出版日期：2018-12-15 出版单位：建筑结构 年：2018 期：v.48 基金：国家科技支撑计划课题(2015BAK17B01);; 国家自然科学基金(51678539);; 黑龙江省级资助项目(GX16C006) 语种：中文; 页：JCJG2018S2067 页数：4 CN：S2 ISSN：11-2833/TU 分类号：347-350

摘要

针对离散网格波动的频散分析结果表明:离散网格中波的传播规律与连续模型中波的传播规律存在显著差异。数值离散将额外引入波传播的频散及耗散误差,其中频散误差可基于离散网格中波传播的相速度以及群速度加以描述。群速度亦是描述离散网格中能量传播的重要概念,且被广泛应用于离散模型数值稳定性分析。基于一维双向波动模型进一步阐明离散网格中波传播的相速度及群速度概念。除证实离散模型中波包和波前的传播速度由群速度描述这一常规认识外,明确指出单频简谐波在离散网格中是以相速度传播这一概念。因此,不能未加区别地认为离散网格中波传播速度均由群速度给出。研究结果对进一步分析离散网格中的波传播规律及误差分析具有参考价值。
        The dispersion analysis results show that there is a significant difference between the propagation rule of the wave and the wave propagation in the continuous model. The dispersion and dissipation errors of wave propagation were introduced in the numerical dispersion,and the dispersion error can be described based on the phase velocity and group velocity of wave propagation in the discrete grid. The group velocity is also an important concept describing the energy propagation in discrete grids and is widely used in the numerical stability analysis of discrete models. The concept of phase velocity and group velocity of wave propagation in discrete meshes is further clarified based on one-dimensional bidirectional wave model. In addition to confirming that the propagation velocity of wave packet and wave front in discrete model is described by group velocity,it is clear that single frequency harmonic wave propagates this concept in the discrete grid. Therefore,it cannot be considered that the wave propagation velocity in discrete meshes is given by group velocity. The results is of reference value for further analysis of wave propagation law and error analysis in discrete grids.

引文

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