Semi-analytical finite element method for modeling of lamb wave propagation

Abstract

Lamb wave propagation in plates is multi-modal, dispersive and highly dependent on the material properties. In homogeneous isotropic plates, Lamb modes can be grouped into symmetric and anti-symmetric modes, and they are decoupled from the shear modes. Due to the material isotropy, Lamb wave propagation behavior is independent from the propagation direction. This property can be used to find analytical solutions for the field of displacements in the frequency domain. However, in composite plates having anisotropic material properties, Lamb wave propagation behavior depends on the propagation direction. For this reason, the complexity of Lamb wave propagation modes increases, and no direct analytical solutions are available. Thus, numerical methods need to be used. In this paper, the semi-analytical finite element (SAFE) method is applied as it is suitable for both isotropic homogeneous plates and anisotropic composite laminated plates. Dispersion curves for these complex materials are calculated using SAFE. The effect of obstacles on the reflection and transmission of Lamb waves is considered. SAFE is also used for 2D point force response analysis. By applying the 2D point response analysis for perfectly bonded strip actuators, mode tuning behavior is calculated for general composite plates. A method to consider plate edge reflections in the 2D force response analysis is also presented.