The frequency response and damping effect of three-layer thin shell with viscoelastic core

General differential equations of motion for a three-layer sandwich structure with viscoelastic core are derived. The Hamiltonʹs principle and Donnell–Mushtari–Vlasov simplification are employed in the derivation. The differential equations, unlike the existing models with five displacements, contain only three displacements, which are one transverse displacement and two in-plane displacements of the host structure. The proposed theory is very general and can be specialized to account for many other commonly occurring geometry, such as spherical shells, cylindrical shells, plates, cones, beams, etc. The derived theory can be directly applied to the studies of structures with constrained layer damping (CLD). The theory can also degenerate into one single layer or two-layer structures. Specialization of the theory to a cylindrical shell, to a rectangular plate and to a beam is demonstrated in a sequel as some of the possible applications.