Prediction of material damping of laminated polymer matrix composites

Abstract

In this study the material damping of laminated composites is derived analytically. The derivation is based on the classical lamination theory in which there are eighteen material constants in the constitutive equations of laminated composites. Six of them are the extensional stiffnesses designated by [A] six of them are the coupling stiffnesses designated by [B] and the remaining six are the flexural stiffnesses designated by [D]. The derivation of damping of [A], [B] and [D] is achieved by first expressing [A], [B] and [D] in terms of the stiffness matrix [Q]^(k) andh _k of each lamina and then using the relations ofQ _ij ^(k) in terms of the four basic engineering constantsE _L,E _T, G_LT andv _LT. Next we apply elastic and viscoelastic correspondence principle by replacingE _L,E _T...by the corresponding complex modulusE _L ^*,E _T ^*,..., and [A] by [A]^*, [B] by [B]^* and [D] by [D]^* and then equate the real parts and the imaginary parts respectively. Thus we have expressedA _ij ^′,A _y ^″,B _ij ^′,B _ij ^″, andD _ij ^″ in terms of the material damping η_L ^(k) and η_T ^(k)...of each lamina. The damping η_L ^(k), η_T ^(k)...have been derived analytically by the authors in their earlier publications. Numerical results of extensional damping lη _ij =A _ij ^″/A _ij ^′ coupling dampingcη _ij =B _ij ^″/B _ij ^′ and flexural damping Fη _ij =D _ij ^″/D _ij ^″ are presented as functions of a number of parameters such as fibre aspect ratiol/d, fibre orientation θ, and stacking sequence of the laminate.