Influence of the anisotropy on zero-group velocity Lamb modes

Abstract

Guided waves in a free isotropic plate (symmetric S(n) and antisymmetric A(n) Lamb modes) exhibit a resonant behavior at frequencies where their group velocity vanishes while their phase velocity remains finite. Previous studies of this phenomenon were limited to isotropic materials. In this paper, the optical generation and detection of these zero-group velocity (ZGV) Lamb modes in an anisotropic plate is investigated. With a circular laser source, multiple local resonances were observed on a silicon wafer. Experiments performed with a line source demonstrated that the frequency and the amplitude of these resonances depend on the line orientation. A comparison between experimental and theoretical dispersion curves for waves propagating along the [100] and [110] directions of the silicon crystal verified that these resonances occur at the minimum frequency of the S(1) and A(2) Lamb modes. Simulations indicated that it is possible to deduce the three elastic constants of the plate material with good accuracy from these measurements.