Damping analysis of laminated composite plates by finite-element method

Abstract

1. Because of their favorable relation of weight to strength, fibre reinforced laminated plates have been used increasingly in the last few years. Methods of reliable prediction of the dynamic properties of transverse vibration of the composite plates have received much attention. Authors of [1-3] used the classical plate theory (CPT) for damping analysis of laminated plates. This theory can provide reasonably accurate predictions only for relatively thin plates. The CPT which uses the Kirchhoff hypothesis overestimates the natural frequencies of the plates since it neglects the effect of the trans- verse shear deformation. The well-known Timoshenko (Mindlin), first-order shear deformation theory (FOSDT) has been used in many papers on dynamic analysis of laminated plates. Authors of [4-6] introduced FOSDT for damping analysis of laminated plates. However, FOSDT does not satisfy the zero shear stress conditions on the top and bottom surfaces of plates. Considering the effect of transverse shear deformation, a higher order shear deformation theory which satisfies these conditions was introduced by author of [7]. The modal damping factor (MDF) or loss factor r/ is a measure of the strain energy dissipated per radian of vibration in the mode of interest defined as ~/ = AU/2rUma “ where AU is the strain energy dissipated during one cycle of vibration, Urea x is total strain energy of the entire laminate at maximum displacement during the same cycle. In the present investigation we have analyzed the natural frequencies and modes, and MDF of laminated plates using the finite-element model based on the FOSDT described in [8] and the damped element model presented in [1]. Here the finite element model [8] has been used with some improvements. At first, a shear correction factor is introduced to take into account the fact that the transverse shear strain distribution is not uniform through the plate thickness. It allows to use the finite element method for analysis of both multilayered composite plates and sandwich plates. At second, selective integration procedure [9] has been developed. It allows to analyze both thick and thin plates. 2.2.1. Strain Energy of the Laminate. In the typical Timoshenko (Mindlin) theory, the plate displacements can be expressed as [8]