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 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.

Analytical study of the structural-dynamics and sound radiation of anisotropic multilayered fibre-reinforced composites

“…Here, the free standing displacement fieldsûðx; y; z; tÞ are approximated for the stationary vibration state as timeharmonic displacementsû n x; y; z; t ð Þ¼u x; y; z ð Þe iωt ; ω ¼ 2π T P : angular frequency (19) and satisfy the chosen boundary conditions. Considering the Lagrange variation and assuming harmonic time dependence forû, the following variational equation can be derived:…”

A procedure for the evaluation of damping effects in composite laminated structures

“…Several works are found in the literature implementing the correspondence principle. Simply supported plates were studied by Alam and Asnani [4] by means of a semi-analytical procedure based on trigonometric expansion of the three displacement components. The formulation was applied to the analysis of plates with cross-and angle-ply lay-ups, and the effects of the material properties, the number of layers and the angles of orientation were investigated.…”

High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams

“…Gibson and Plunkett, 1976;Ni and Adams, 1984;Saravanos and Chamis, 1990;Wren and Kinra, 1992;Alam and Asnani, 1986). Saravanos (1994) reported a linear fully layerwise damping plate theory for laminated composite plates together with semi-analytical solutions, as well as, a finite element (1993) capable of predicting the damping of thick composite plates, and the damping of composite sandwich plates with interlaminar damping layers (Saravanos and Pereira, 1992); whereas, Taylor and Nayfeh (1997) presented an analytical solution for the damped vibrational characteristics of thick composite plates.…”