Vibration and Damping Analysis of Fibre Reinforced Composite Material Plates

Abstract

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 criss cross 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.