Bending of Circular Sandwich Plates

The governing differential equations for the nonrotationally symmetrical bending of isotropic circular sandwich plates are developed by means of a variational theorem. The face layers are considered as membranes but made of different materials and unequal thickness; however, for simplicity, Poisson's ratio is assumed to be the same. In the present case, two fundamental differential equations are obtained. One corresponds to the well-known equation, Δ4 w = q/D, in the bending of homogeneous plates and the other appears in the form of a second order differential equation which, after transformation, becomes Bessel equation of order one. Using two differential equations, one of the fourth order and the other of the second order, three conditions are satisfied on the edge of the plate instead of only two. To illustrate the use of these equations, a simply-supported circular sandwich plate under linearly varying load, is presented as an example.