Coupling of plate waves at joints

For flat plates with infinite lateral extent, fundamental plate waves propagate independently without coupling. However, at a joint of two or more plate elements, these waves can couple together, and a wave incident from one element will excite other waves propagating away from the junction in each element. The propagation direction for incidence oblique to the junction, and the magnitude of each wave can be determined by the following boundary conditions: continuity of displacement at the joint, continuity of rotation about the axis of the joint, and vanishing net force and torque on the joint. These boundary conditions are derived from the approximation that the joint is massless, has rigid cross section, but offers no resistance to extension along or twisting about the axis of the joint, or to bending transverse to the axis. To satisfy the boundary conditions, it is necessary to account for the first cutoff flexural wave in addition to the three propagating waves in each plate. Numerical examples for various joints of one, two, and three plate segments are discussed. Coupling at a rib stiffened plate is also computed by treating the rib as a plate segment and accounting for the coupling between two neighboring joints. The wave coupling phenomena, distribution of power among the plate segments, and the power conservation property are examined in detail for large ranges of frequency and of the wave number along the joint, which is determined by the angle of incidence. Both propagating and evanescent waves in the direction transverse to the joint are considered. The power conservation error are examined and quantified to establish the range of validity of this approach.