一种求解复波数域波动弥散方程的通用数值方法
发布时间：2018-07-21 09:52
【摘要】：波动弥散方程的求解是分析弹性波或声波问题时的一种比较常见的过程,求解所得的曲线即为弥散曲线。其方程形式一般是关于波数与频率的一个二元超越方程,当波数为复数时,方程实际为三元超越方程。这类方程没有解析解,由于方程的变量和参数涉及复数域,一般的数值求解方法也难以处理。本文提出了一种基于模值收敛性的数值方法,求解一般波动弥散方程复波数域内的解。首先论述了本方法的理论依据,然后介绍了其求解步骤,最后将本方法应用于求解复波数域波动弥散方程的具体算例。通过对比可以发现:本方法广泛有效地解决了复波数域内波动弥散曲线的求解问题,适用于不同形式波动弥散方程的求解。
[Abstract]:The solution of wave dispersion equation is a common process in the analysis of elastic wave or acoustic wave problem. The obtained curve is called dispersion curve. The equation is generally a binary transcendental equation about wavenumber and frequency. When the wavenumber is complex, the equation is actually a ternary transcendental equation. Because the variables and parameters of the equation are related to the complex field, the general numerical method is difficult to deal with. In this paper, a numerical method based on modular convergence is proposed to solve the solutions in complex wavenumber domain of general wave dispersion equations. First, the theoretical basis of this method is discussed, then the steps of its solution are introduced. Finally, the method is applied to the solution of wave dispersion equation in complex wavenumber domain. By comparison, it is found that this method can solve the problem of wave dispersion curve in complex wavenumber domain widely and effectively, and can be applied to the solution of wave dispersion equation in different forms.
【作者单位】： 南京航空航天大学航空宇航学院机械结构力学及控制国家重点实验室;
【基金】：国家自然科学基金(11502108;11232007;51405225) 中央高校基本科研业务费——南京航空航天大学杰出人才培育基金(NE2013101) 江苏省自然科学基金(SBK20140037;BK20140808)
【分类号】：O241.8
本文编号：2135142
[Abstract]:The solution of wave dispersion equation is a common process in the analysis of elastic wave or acoustic wave problem. The obtained curve is called dispersion curve. The equation is generally a binary transcendental equation about wavenumber and frequency. When the wavenumber is complex, the equation is actually a ternary transcendental equation. Because the variables and parameters of the equation are related to the complex field, the general numerical method is difficult to deal with. In this paper, a numerical method based on modular convergence is proposed to solve the solutions in complex wavenumber domain of general wave dispersion equations. First, the theoretical basis of this method is discussed, then the steps of its solution are introduced. Finally, the method is applied to the solution of wave dispersion equation in complex wavenumber domain. By comparison, it is found that this method can solve the problem of wave dispersion curve in complex wavenumber domain widely and effectively, and can be applied to the solution of wave dispersion equation in different forms.
【作者单位】： 南京航空航天大学航空宇航学院机械结构力学及控制国家重点实验室;
【基金】：国家自然科学基金(11502108;11232007;51405225) 中央高校基本科研业务费——南京航空航天大学杰出人才培育基金(NE2013101) 江苏省自然科学基金(SBK20140037;BK20140808)
【分类号】：O241.8
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