Zero-group velocity modes in plates with continuous material variation through the thickness.

Lamb modes with zero group velocity at nonzero wave numbers correspond to local and stationary resonances in isotropic plates. Lamb modes can be utilized for nondestructive evaluation of the elastic properties and thickness. One example of an application is the testing of plate-like concrete structures. In this example, continuous variation in the material velocity through the thickness may occur. This is usually not accounted for in analyses, and with this as starting point, two inhomogeneous and nonsymmetric cases with continuous material variations are investigated using a semi-analytical finite element technique and a simulated measurement application. In a numerical study limited to the lowest zero-group velocity mode, results show that these modes for the inhomogeneous cases are generated with similar behavior and the same detectability as in the case of an isotropic plate. However, a complex relationship between mode frequency and material velocity exists for the inhomogeneous cases. This hinders the evaluation and interpretation of representative estimations such as those for a cross-sectional mean value of the plate properties. This may lead to errors or uncertainties in practical applications.