Reflection and transmission of Lamb waves at an imperfect joint of plates

The reflection and transmission of Lamb waves at an imperfect joint of plates are analyzed numerically by the modal decomposition method and the hybrid finite element method. The joint is modeled as a spring-type interface characterized by distributed normal and tangential stiffnesses. The analysis is focused on a low-frequency range where the lowest-order symmetric and antisymmetric Lamb waves are the only propagating modes. The frequency-dependent reflection and transmission characteristics of these Lamb modes are computed for different interfacial stiffnesses, together with the generation behavior of localized, non-propagating higher-order Lamb modes. As a result, S0-mode Lamb wave is shown to exhibit the reflection and transmission characteristics which are monotonically frequency-dependent. On the other hand, A0-mode Lamb wave shows complicated and non-monotonic frequency dependence in the reflection and transmission characteristics. The obtained Lamb wave characteristics are discussed in the light of approximate one-dimensional models constructed based on classical plate theories. As a result, the reflection and transmission coefficients of S0-mode Lamb wave are accurately reproduced by a simple model of longitudinal wave in thin plates, while those of A0-mode Lamb wave are well described by the Mindlin plate model of flexural wave. It is also shown that stiffness reduction at the corners of the contacting edges of plates has only minor influence on the reflection and transmission characteristics.