Lamb waves in sandwich orthotropic elastic plates

In this paper, the propagation of Lamb waves in an orthotropic elastic sandwich plate is investigated. The surface layers and the core layer may be compressible or incompressible. The main aim of the paper is to derive explicit dispersion equations. First, the dispersion equations of symmetric modes and asymmetric modes are derived for compressible sandwich plates by using the effective boundary condition method along with the transfer matrices for orthotropic elastic layers. These dispersion equations recover the dispersion equations of Lamb waves propagating in compressible isotropic sandwich plates. The dispersion equations for incompressible sandwich plates are obtained by using the incompressible limit method. It is shown numerically that the thickness ratio and the stiff contrast affect strongly higher modes and the incompressibility has strong influence on symmetric modes. Remarkably, the obtained dispersion equations can be used to analyze the dispersion characteristic of Lamb waves propagating in sandwich plates with honeycomb core layers because the honeycomb core layers can be replaced effectively by transversely isotropic elastic layers by mean of homogenization.