Studies on the kinematic assumptions for sandwich beams

Much of the work done on active and passive constrained-layer beams is done with models using kinematic assumptions proposed by Kerwin, Mead and Markus, and others. The key assumption is that the base and constraining layers undergo identical transverse displacements, which is a reasonable assumption when the middle layer (here a viscoelastic material) is thin and the constraining layer is relatively weak. There are, however, many practical cases where an effective passive damping design requires the stiffness of the constraining layer to be on the order of that of the base layer. If the base structure is stiff to begin with, a constraining layer that will produce good damping is likely to violate the above stated assumption by refusing to follow the base layer exactly. The question arises as to how this affects predictions of damping. In this work the facesheets are treated as independently deforming Timoshenko beams, which results in a more general state of strain in the core material. Expressions for the potential and kinetic energies are developed from basic principles of continuum mechanics, and the assumed modes method is used to predict how levels of strain energy in the core are affected by the assumptions on the relative motions of the facesheets.