Letters to the Editor: Effect of Inertia Forces on the Damping of a Constrained Layer Finitely Deformed in Shearing

We analyze the e!ect of inertia forces on damping induced during large shearing deformations of an isotropic, incompressible and homogeneous viscoelastic layer constrained between two rigid circular cylinders. The layer is deformed by holding the inner solid cylinder "xed and rotating the outer one by applying to it a time-harmonic axisymmetric tangential velocity. It is assumed that the layer sticks to the cylinder walls and the length of each cylinder is very large as compared to the inner radius of the outer cylinder so that the end e!ects can be neglected. Thus, a material particle undergoes only tangential displacement which is assumed to be a function of the radial co-ordinate, r and time, t. That is,