Prediction of material damping of laminated polymer matrix composites

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) andhk of each lamina and then using the relations ofQij(k) in terms of the four basic engineering constantsEL,ET, GLT andvLT. Next we apply elastic and viscoelastic correspondence principle by replacingEL,ET...by the corresponding complex modulusEL*,ET*,..., 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 expressedAij′,Ay″,Bij′,Bij″, andDij″ in terms of the material damping ηL(k) and ηT(k)...of each lamina. The damping ηL(k), ηT(k)...have been derived analytically by the authors in their earlier publications. Numerical results of extensional damping lηij =Aij″/Aij′ coupling dampingcηij =Bij″/Bij′ and flexural damping Fηij =Dij″/Dij″ are presented as functions of a number of parameters such as fibre aspect ratiol/d, fibre orientation θ, and stacking sequence of the laminate.