This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small ...This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.展开更多
The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identica...The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.展开更多
文摘This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.
文摘The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.
文摘传递矩阵法(transfer matrix method,TMM)是研究结构振动时常用的计算方法,但在计算大跨度输流管路高频横向振动时,TMM存在数值不稳定的现象,制约了其进一步应用。基于无量纲化计算结果得到的子单元划分准则的全局传递矩阵法(global transfer matrix method,GTMM)、混合能传递矩阵法(hybrid energy transfer matrix method,HETMM)和结合变精度算法的传递矩阵法(variable precision algorithm-transfer matrix method,VPA-TMM)等三种方法解决了这一问题。GTMM是最常用的TMM计算稳定性改进方法;HETMM系首次从层状介质中的波传播计算扩展到管路系统的振动分析领域,计算矩阵的维度和形式不随子单元数的变化而变化,计算时间最短;VPA-TMM无需进行子单元划分,可以看作是从根源上解决了TMM的长跨度高频计算失稳问题,但计算时间会大幅度增加。
