Coupling of in-plane and out-of-plane waves in thick flat plate structure subjected to a transverse load.

Abstract

Using the approaches of Mindlin [J. Appl. Mech. 18, 31–38 (1951)] and Kane and Mindlin [J. Appl. Mech. 23, 277–283 (1956)] for, respectively, the in-plane and out-of-plane wave motions in thick flat plates, the equations of motion for the in-plane and out-of-plane waves are unoccupied. That is with these approaches, a transverse load will not induce in-plane motion. This is not the case if one were to use a three-dimensional elasticity solution. Also, from a physical standpoint, if a transverse load is applied on one surface of a thick flat plate structure, apart from the out-of-plane deformation, the plate will also have some in-plane deformation. The reasons behind the decoupling of the in-plane and out-of-plane waves are the simplifying assumptions of the respective approaches, where the solution is based on the midplane of the plate with symmetric or asymmetric deformation about the midplane. If a transverse load is applied on one of the plate surfaces rather than the midplane, this can be represented by two sets of load components. One set consists of two loads pointing in the same direction and represents the excitation of the out-of-plane waves and a second set that represent two ‘‘pinching’’ loads that induce the in-plane wave motion. Using this approach the problem of two coupled plates of different thickness is considered to determine the influence of the thickness discontinuity on the in-plane and out-of-plane waves. [Work sponsored by ONR.]