A general vibration theory for constrained layer damping-treated thick sandwich structures

The vibration equations of a thick sandwich structure with a viscoelastic material core were derived. The host layer was assumed thick and the top layer could be thin or thick. This type of structures may apply to various cases and the particular application for which it fit is that of constrained layer damping treatment for vibration attenuating. The governing differential equations contained nine displacements for thick–thick surface layers. For cases of thin–thick, the number of displacement was significantly reduced to only five, which were one transverse displacement, two in-plane displacements, and two layer rotation angles, all associated with the host layer. The derived theory was general, and it could be not only specialized for many commonly seen structures such as beams, plates, and cylindrical shells but also degenerated into one- or two-layer structures. Specialization for a sandwich cylindrical shell was extensively illustrated, and numerical results of natural frequencies and damping were compared to those of thin shell theory. How each layer's thickness influenced the frequency and damping of the sandwich shell were particularly discussed.