Coupling of velocity dispersion curves of leaky Lamb waves on a fluid-loaded plate

Abstract

The coupling of velocity dispersion curves of leaky Lamb waves is studied based on analytical calculations to clarify the problem of repulsion and crossing of the curves. Two curves, corresponding to the 4th and 5th modes, are closely observed while artificially varying the properties of virtual materials, in the combination of piezoelectric ceramic and glass. The imaginary part of the Lamb-wave velocity is essential for distinguishing the coupling phenomena. The behaviors of the velocity values as functions of two variables, material property and the product of frequency and thickness of the plate, are analogous to the Riemann sphere defined by a mathematical function of ω=z(1/2) (both z and ω are complex) inside the domain containing the point z=0 on the complex plane.