Damping of Vibrations of Layered Elastic-Viscoelastic Beams

A five-layer cantilever beam consisting of an elastic core, two symmetric viscoelastic layers, and two elastic constraining layers is considered. The viscoelastic effects are incorporated in the Euler-Bernoulli beam theory. If the contraction and extension of the constraining layers is neglecterd a fourth order differential equation of motion is received. Inclusion of contraction and extension of the constraining layers results in a more accurate sixth order differential equation. Appropriate boundary conditions are derived. Laplace transforms are used extensively. Both the analytical solution and the numerical results are presented.