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The Rayleigh-Ritz method is applied for the damping analysis offlexural vibrations of a simply supported plate, partially covered with constrained viscoelastic damping treatment. The anaysis is carried out in terms of resonant frequencies and associated modal system loss factors. Single-term solutions for respective modes are assumed for the longitudinal displacements of the constraining layer and the transverse displacement of the plate. The variations of the resonant frequency and the associated modal loss factor with the coverage percentage, the coverage location, the core shear modulus and the thickness of the constrained and the constraining layers have been reported.

Governing equations of motion for a laminated plate consisting of an arbitrary number of fibre reinforced composite material layers have been derived using the variational principles. Each layer has been considered to be of a specially orthotropic material with its directional elastic properties depending on the fibre orientation. Extension, bending, inplane shear and transverse shear deformations in each layer are considered. The longitudinal translatory and the rotary inertias along with the transverse inertia are taken into account. A solution for simply supported rectangular plate is obtained in series summation form and the damping analysis is carried out by an application of the correspondence principle of linear viscoelasticity. The computer program for the determination of the resonating frequencies and the associated system loss factors for the various families of modes of vibration of a plate consisting of an arbitrary number of layers has been developed. Using the same, investigation for the optimum fibre orientation for maximizing the resonant frequencies and the system loss factors for the flexural and the extensional modes of vibration of a four layered crisscross laminated plate, has been carried out. The variation of the resonant frequencies and the system loss factors with aspect ratio, for the first flexural modes of 2,4 and 6 layered cross-ply laminated plates are also reported.

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