黏弹性层状介质中瑞雷波的本征值求解

Eigenproblem of Rayleigh wave in multilayered viscoelastic medium

摘要:

为解决黏弹性层状介质中瑞雷波本征值求解中的漏根问题，提出了一种新的求解方法.通过分析以往方法中漏根和多根的原因，提出采用一系列初值虚部进行搜根后将结果合并，并去掉虚部大于实部的根.由此给出了本征值求解的流程图，在实例计算中采用此方法成功求解了黏弹性层状介质中瑞雷波的本征值.结果表明，在利用该方法在求解过程中不存在漏根和多根问题.在黏弹性层状介质中瑞雷波的本征值求解时采用搜根初值加密并剔除虚部大于实部的根的方法可以有效避免漏根和多根问题.

Abstract:

To avoid the root lost problem in the former methods, a new method of solving the eigenproblem of Rayleigh wave in multilayered viscoelastic medium. The reason of root-lost and pseudo-root phenomenon is analyzed. From this, a series of different initial imaginary parts are employed, and the roots whose imaginary part is larger than real part are omitted. A flowchart of solving the eigenproblem is presented based on this, and the eigenproblem of Rayleigh wave in multilayered viscoelastic medium in an example is successfully solved with the method. The results show that there is no root-lost and pseudo-root phenomenon when solving the eigenproblem with the method. In the eigenproblem of Rayleigh wave in multilayered viscoelastic medium, root-lost and pseudo-root phenomenon can be avoided by employing a series of different initial imaginary parts and omitting the roots whose imaginary part is larger than real part.