Resonance of an imperfect joint of plates by the lowest-order symmetric Lamb mode
Resonance behavior of an imperfect joint of elastic plates subjected to the incidence of the lowest-order symmetric (S0) Lamb mode is numerically analyzed in the frequency domain by the hybrid finite element method. To this purpose, the reflection and transmission characteristics of the S0 mode are calculated for the frequency range in which the S0 mode is the only symmetric mode that can propagate in the plates. The imperfect joint is modeled as a linear spring-type interface characterized by the normal and tangential stiffnesses. As a result, it is shown that the imperfect joint of plates has two resonance frequencies at which the out-of-plane displacement amplitudes at the joint are remarkably increased. One resonance frequency depends only on the normal stiffness, and the other only on the tangential stiffness. Each resonance frequency coincides with that of a free edge of a plate, and monotonically increases with the corresponding joint stiffness. Furthermore, it is also shown that the reflection and transmission behavior of the S0 mode at the imperfect joint of the plates can be well reproduced by the one-dimensional thin-plate approximation of extensional waves when the frequency is sufficiently small compared to the resonance frequencies.