Three-layered damped beam element for forced vibration analysis of symmetric sandwich structures with a viscoelastic core

The numerical implementation of Mead and Markusʹs two sets of differential equations of motion governing the damped forced vibration of three-constrained-layer sandwich beam requires C2-basis functions or the mixed formulation. To resolve this problem, a damped beam element for three-layered symmetric straight damped sandwich structures is derived according to the virtual work principle, in which both the virtual kinetic and strain energies are expressed in terms of the lateral displacement and the transverse shear strain of a core layer. Because the forced vibration equations of three-constrained-layer damped beam are equipped with three pairs of boundary conditions, the rotation of the mid-surface which is directly derived from the lateral displacement is added for the damped beam element to have three degrees of freedom per node. The shape functions are analytically derived using the compatibility relation between the lateral displacement and the transverse shear strain. The validity of the proposed beam element is verified through the benchmark experiments, and furthermore the DOF-efficiency is justified through the comparison with Nastran 3-D solid element.