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, GLT 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 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 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.
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Sun, C.T., Wu, J.K. & Gibson, R.F. Prediction of material damping of laminated polymer matrix composites. J Mater Sci 22, 1006–1012 (1987). https://doi.org/10.1007/BF01103543
- Constitutive Equation
- Matrix Composite
- Stiffness Matrix
- Fibre Orientation