Chapter 5 - Plates

Abstract

This chapter discusses fundamental equations of thick and thin plates. There are some fundamental differences in the equations of laminated plates, as they are compared with those obtained for homogeneous plates. The most important fundamental difference is that for generally laminated plates, the bending is coupled with stretching. This is of great importance, as the equations will be of order eight, just like shells, instead of the fourth order equations, which describe thin homogeneous plates. The equations will reduce to order four only if the lamination sequence is symmetric with respect to the plate's middle surface. The inplane modes are then totally decoupled from the out-of-plane ones and often ignored in the analysis because they usually are of higher frequencies. The theory described here is referred to as classical plate theory (CPT). Thicker plates are ones with a thickness smaller by approximately one order of magnitude when compared with other plate parameters, particularly its vibration mode shape wavelength (thickness is smaller than (1/10)th of the smallest of the wave lengths). Thick plate theories, also known as shear deformation plate theories (SDPT), require the inclusion of shear deformation and rotary inertia factors when compared with thin or CPT.