Abstract
The performance of a constrained layer damping treatment is greatly affected by its length, and the damping effectiveness can be optimized by choosing a damping treatment length appropriate to the geometry and material properties of the viscoelastic and constraining layers. In this paper, the equilibrium equation and boundary conditions are formulated for a constraining layer on a substrate with a linearly varying strain distribution, and an analysis is developed that allows conclusions to be drawn about the optimal length of the constraining layer. Plunkett and Lee1 analyzed this problem for the special case of uniform strain in the substrate, and they showed that a loss coefficient depends only on the viscoelastic loss factor and a stiffness parameter that is a function of the material properties and thickness of the damping layers. In this paper, the uniform strain analysis is extended for the case of linearly varying substrate strain of the form ax+b, where a and b are arbitrary constants. The corresponding loss coefficient was shown to be a function of the parameters identified in the uniform strain problem, plus an additional parameter that accounts for the degree of non-uniformity of the substrate strain. It is shown that the non-uniformity of the substrate strain increases the length at which the damping treatment is optimized.