Investigation of Non-axisymmetric Lamb Wave in an Elastic Plate with Free Boundaries

Purpose Lamb wave is widely used in damage detection and structural health monitoring of plate-like structures. In the current stage, the propagation of non-axisymmetric circular crested Lamb has not been theoretically solved. Therefore, it is essential to find its exact solutions. Methods The displacement expressions and frequency equations are derived through three-dimensional elastic theory using Helmholtz conversion. Numerical simulations and experiments are conducted on plates for verification of theoretical results. Results Both axisymmetric and non-axisymmetric waves are obtained from the governing equation with free boundary conditions. Lamb wave travels along the radial direction and holds as a standing wave in circumferential and longitudinal directions. The displacement field is expressed with Bessel functions in the radial direction and trigonometric functions in circumferential and longitudinal directions. Two families of Lamb wave modes are generated, which are identified by radial wavenumber and circumferential order. The amplitudes of displacements decrease with the propagation distance increases, and the circumferential distributions of displacements are affected by the circumferential order. Results obtained from simulation and experiment provide good verification for theoretical predictions. Conclusions The analytic solutions are presented in non-axisymmetric problems for circular crested Lamb wave in this paper, which provides a theoretical foundation for further investigation of Lamb wave propagation in plates.