Complex eigensolutions of rectangular plates with damping patches

A new analytical, energy based approach that predicts the vibration characteristics of a rectangular plate with multiple viscoelastic patches is presented. This paper extends the method presented earlier by the authors that was applied to the determination of the eigensolutions of viscoelastically damped beams. The method first relates all motion variables of a sandwich plate in terms of the flexural displacement of the base structure. Then the flexural shape function sets are incorporated in the Rayleigh-Ritz minimization scheme to obtain a complex eigenvalue problem. This method allows for the visualization of complex modes of all deformation variables including shear deformations of the viscoelastic core that are the major contributors to the overall energy dissipation. Comparison with the work of three prior investigators on a simply supported plate validates the model for the Limiting case of full coverage. Benchmark experimental measurements are made on a plate with free edges, and five damping cases are considered. Analytical predictions of natural frequencies, modal loss factors and complex modes for all cases are in excellent agreement with modal measurements. A normalization scheme for complex mode shapes has also been developed. Finally, simplified loss factor estimation procedures are presented to illustrate the additive effect of two damping patches. (C) 1998 Academic Press.