对瑞利波频散曲线计算中高频数值溢出的处理

Treating of numerical overflow in high frequencies for computing Rayleigh wave dispersion curves

任何一种求解瑞利导波频散曲线的解析方法都会出现高频数值溢出现象,如何避免Abo-Zena,Menke和张碧星等研究的传递矩阵法计算中的高频数值溢出,这是本文研究的核心问题.传递矩阵法中的频散方程是一个实方程,可用二分法求根.当传递矩阵中与频率有关的指数项的指数部分的模趋近很大时,用"-1"或者"-i"代替指数部分,并令传递矩阵中与频率无关的项为0,则不影响频散函数的正负性,即不影响频散方程的求根.在计算机上编制计算时进行如此处理后,可从根本上解决传递矩阵法计算中高频数值的溢出问题,模拟计算结果也验证了方法的正确性和可行性.

There was numerical overflow in high frequencies when computing Rayleigh guided waves by any analytic approach.Presented a method to solve the numerical overflow in high frequencies for transmission matrix approach which studied by Abo-Zena,Menke and Bixing Zhang,et al.The dispersion equation in the bisect-method could be solved,because it was a real equation.When the modulus of an exponent which related to frequencies was very big in the transmission matrix,the exponent could be replaced by "-1",or "-i",an...