Group velocity and characteristic wave curves of Lamb waves in composites: Modeling and experiments

Abstract

The propagation characteristics of Lamb waves in composites, with emphasis on group velocity and characteristic wave curves, are investigated theoretically and experimentally. In particular, the experimental study focuses on the existence of multiple higher-order Lamb wave modes that can be observed from piezoelectric sensors by the excitation of ultrasonic frequencies. Using three-dimensional (3-D) elasticity theory, the exact dispersion relations governed by transcendental equations are numerically solved for an infinite number of possible wave modes. For symmetric laminates, a robust method by imposing boundary conditions on the mid-plane and top surface is proposed to separate symmetric and anti-symmetric wave modes. A new semi-exact method is developed to calculate group velocities of Lamb waves in composites. Meanwhile, three characteristic wave curves: velocity, slowness, and wave curves are adopted to analyze the angular dependency of Lamb wave propagation. The dispersive and anisotropic behavior of Lamb waves in a two different types of symmetric laminates is studied in detail theoretically. In the experimental study, two surface-mounted piezoelectric actuators are excited either symmetric or anti-symmetric wave modes with narrowband signals, and a Gabor wavelet transform is used to extract group velocities from arrival times of Lamb wave received by a piezoelectric sensor. In comparison with the results from the theory and experiment, it is confirmed that multiple higher-order Lamb waves can be excited from piezoelectric actuators and the measured group velocities agree well with those from 3-D elasticity theory.