Coupling of plate and shell modes at joints

Abstract

For cylindrical and spherical shells without truncation or for flat plates with infinite lateral extent, fundamental shell or plate modes propagate independently without coupling. However, at a joint of two or more plate or shell elements, these modes couple together. If a mode is incident at an oblique angle from one element, it will excite other modes propagating away from the junction in each element. The propagation direction and the excitation strength of each mode 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 assumption that the joint is massless and has rigid cross section but offers no resistance to extension along and twisting about the axis of the joint, and to bending transverse to the axis. To be consistent with thin plate/shell theory, it is necessary to account for the first cutoff mode in addition to the three propagating modes in each plate or shell. Numerical examples will be discussed. [Work supported by ONR.]