A model for the damping of torsional vibration in thin-walled tubes with constrained viscoelastic layers

A model for torsional vibration of slender thin-walled tubes with constrained-layer dampers is developed. Assuming that the deformation obeys the Saint-Venant hypotheses, we develop a model suitable for prediction of the complex stiffness per unit length in closed, thin-walled tubes whose walls consist of laminated elastic and viscoelastic layers, and formulate a boundary-value problem for the warping deformations arising under Saint-Venant torsion. For some basic cross-sectional shapes, we solve the warping problem and thence obtain closed-form expressions for the complex stiffness per unit length. Next, we provide some guidelines for the design of tubes with high damping in torsion. Finally, we compare the damping predicted by the model to measurements performed on a simple structure.