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Generalized Analytical Dispersion Equations for Guided Rayleigh-Lamb waves and Shear Horizontal (SH) waves in Corrugated Waveguides
International Journal of Solids and Structures ( IF 3.4 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.ijsolstr.2020.05.026
Vahid Tavaf , Sourav Banerjee

Abstract Corrugated waveguides are periodic structures that exhibit important acoustic features. Features like acoustic bandgaps exhibit the ability to filter acoustic and ultrasonic frequencies. By varying the mean thickness, corrugation height, and periodicity, one can tune the propagating wave modes in the guide and thus can modify the bandgaps. This study aims to obtain a generalized Rayleigh–Lamb equation for corrugated waveguides such that a single equation is sufficient for both flat waveguides such as plates as well as corrugated and tapered plates. Further, the objective was to understand the effects of the corrugation height, periodicity, and mean thickness such that a physics-based predictive design of wave filters can be achieved. Instead of applying the Bloch–Floquet theorem to the displacement function directly, which is conventional, the theorem is applied to the scalar and vector wave potentials obtained from Helmholtz decomposition. The governing equations from these relationships after applying boundary conditions were then solved using a logical root-finding algorithm. To verify the generalized expressions guided wave band structure for a plate was obtained using Rayleigh–Lamb equation and compared with the generalized form setting the corrugation height to zero. The analytical solutions are then validated through a comparison with the results obtained from a rigorous finite element simulation. Finally, the effects on the propagating and evanescent wave modes due to the corrugation height and periodicity are studied for future reference.

中文翻译:

波纹波导中引导瑞利-兰姆波和剪切水平 (SH) 波的广义解析色散方程

摘要 波纹波导是具有重要声学特征的周期性结构。声学带隙等特征表现出过滤声学和超声波频率的能力。通过改变平均厚度、波纹高度和周期性,可以调整波导中的传播波模式,从而可以修改带隙。本研究旨在获得波纹波导的广义 Rayleigh-Lamb 方程,这样一个方程就足以适用于平板波导(如板)以及波纹和锥形板。此外,目标是了解波纹高度、周期性和平均厚度的影响,以便可以实现基于物理学的滤波器预测设计。不是将 Bloch-Floquet 定理直接应用于位移函数,这是传统的,该定理适用于从亥姆霍兹分解获得的标量和矢量波势。然后使用逻辑求根算法求解应用边界条件后来自这些关系的控制方程。为了验证广义表达式,使用瑞利-兰姆方程获得了板的导波带结构,并与将波纹高度设置为零的广义形式进行比较。然后通过与从严格的有限元模拟获得的结果进行比较来验证解析解。最后,研究了波纹高度和周期性对传播和渐逝波模式的影响,以备将来参考。然后使用逻辑求根算法求解应用边界条件后来自这些关系的控制方程。为了验证广义表达式,使用瑞利-兰姆方程获得了板的导波带结构,并与将波纹高度设置为零的广义形式进行比较。然后通过与从严格的有限元模拟获得的结果进行比较来验证解析解。最后,研究了波纹高度和周期性对传播和渐逝波模式的影响,以备将来参考。然后使用逻辑求根算法求解应用边界条件后来自这些关系的控制方程。为了验证广义表达式,使用瑞利-兰姆方程获得了板的导波带结构,并与将波纹高度设置为零的广义形式进行比较。然后通过与从严格的有限元模拟获得的结果进行比较来验证解析解。最后,研究了波纹高度和周期性对传播和渐逝波模式的影响,以备将来参考。为了验证广义表达式,使用瑞利-兰姆方程获得了板的导波带结构,并与将波纹高度设置为零的广义形式进行比较。然后通过与从严格的有限元模拟获得的结果进行比较来验证解析解。最后,研究了波纹高度和周期性对传播和渐逝波模式的影响,以备将来参考。为了验证广义表达式,使用瑞利-兰姆方程获得了板的导波带结构,并与将波纹高度设置为零的广义形式进行比较。然后通过与从严格的有限元模拟获得的结果进行比较来验证解析解。最后,研究了波纹高度和周期性对传播和渐逝波模式的影响,以备将来参考。
更新日期:2020-10-01
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