School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, Western Australia 6009, Australia.
J Acoust Soc Am. 2012 Jun;131(6):4543-9. doi: 10.1121/1.4714338.
In-plane waves in a waveguide made from a thin plate are described by a superposition of a set of orthogonal functions that satisfy the edge conditions of the waveguide. Due to the Poisson and shear effects, the displacement components of the in-plane waves along the two in-plane orthogonal coordinates are coupled and this coupling affects the propagation and spatial properties of the waveguide modes. The orthogonal functions and their associated wavenumbers represent the characteristics of the uncoupled modes of the waveguide where the above mentioned couplings are ignored. This study demonstrates that the characteristics of the waveguide modes are determined by the couplings of the uncoupled mode pairs, which become significant when the pairs satisfy the conditions of spatial coincidence. At some frequencies, certain waveguide modes can be determined by a single pair of uncoupled modes. For this case, the analytical solution for the waveguide modes exists and provides both a qualitative and quantitative interpretation of the characteristics of the waveguide mode.
平面波在由薄平板制成的波导中可以通过一组满足波导边缘条件的正交函数的叠加来描述。由于泊松和剪切效应，平面波在两个平面正交坐标上的位移分量是耦合的，这种耦合会影响波导模式的传播和空间特性。正交函数及其相关波数表示忽略上述耦合时波导的非耦合模式的特性。本研究表明，波导模式的特性由非耦合模式对的耦合决定，当模式对满足空间一致性条件时，这种耦合变得显著。在某些频率下，某些波导模式可以由一对非耦合模式确定。对于这种情况，波导模式的解析解存在，并对波导模式的特性提供了定性和定量的解释。
