Viscoelastic damping of beams

The composite damping characteristics of a viscoelastic sandwich beam are investigated. The sandwich consists of an elastic central layer coated on both sides with a viscoelastic material and two outer layers made out of the same material as the central layer. The composite beam is investigated for damping effectiveness. As in the work of DiTaranto and Kerwin, and also Mead, the energy dissipation due to the vibratory motion of the system is assumed to take place due to the shear deformation of the viscoelastic layer only. The assumption that the outer layers do not stretch or contract during bending, further enhances the composite system\u27s ability to dissipate energy in shear. The assumptions used lead to a fourth order differential equation of motion as opposed to the customary sixth order equation derived in the literature. A closed form solution to the problem of vibration of the composite beam under no load is obtained. A set of boundary conditions are derived using the energy method. The analytical solution is also shown to reduce to that of an equivalent elastic beam under the same conditions when the viscoelastic term is removed by setting the shear modulus equal to zero. When the same process is used on the composite beam characteristic equation, the result is identical to the frequency equation of an elastic beam