Constrained Layer Damping

A constrained damping treatment (Fig.15.1b) is normally more effective than an unconstrained treatment. During flexural vibration of the base plate, the viscoelastic layer is subjected to large shear deformation and the shear damping is likely to exceed the extensional damping. The base layer and the constraining layer are assumed to be nondissipative.

If the extensional stiffness of the viscoelastic layer is negligible as compared to the stiffnesses of the bottom and top layers (as is usually the case in real life), then the overall loss factor, neglecting the extensional damping, is given by

where is the loss factor of the viscoelastic material in shear and the nondimensional parameters and are defined as follows:
The parameter , called the stiffness parameter is given by

(15.7)

where
_,     ,    

with , , as the thicknesses of the base, viscoelastic, constraining layers, respectively, and , as Young's moduli of the base and constraining layer, respectively.

The parameter , called the shear factor is expressed as

where

      = storage shear modulus of VEM

       = wavelength of flexural vibration