Axisymmetric Vibration of Circular Sandwich Plates

Nomenclature p, pc = mass density of the face and core materials, respectively G, Gc = modulus of rigidity of the face sheet and core, respectively E, v = modulus of elasticity and Poisson's ratio of the face sheet h, 2c = thickness of face sheet and core, respectively u = radial displacement of midsurface of face sheet w = displacement in transverse direction pr = rotation of the normal to the middle surface of the face sheet in the radial direction a = radius of the sandwich plate r = radial polar coordinate a) = circular frequency of the sandwich plate t = time u,r = partial differentiation of u with respect to r V =d/dx+(l/x)d/dx