Guided waves in layered media: Twin ZGV and ambiguity of dispersion spectrum

Abstract

The twin zero group velocity (ZGV) points are observed, which belong to the fundamental symmetric branch (S 0) of Lamb waves propagating in a composite traction-free layered plate containing odd number of layers with alternating physical properties. It is shown that in a vicinity of these ZGV points an ambiguity of dispersion spectrum takes place, resulting in the appearance of several waves, which (i) belong to the same fundamental mode; (ii) satisfy the same boundary conditions; and, (iii) propagate at the same frequency, however (iv) with different phase velocities. The analysis is based on a combination of Cauchy formalism and the exponential fundamental matrix method.