Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Prediction of material damping of laminated polymer matrix composites

  • 198 Accesses

  • 28 Citations


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.

This is a preview of subscription content, log in to check access.


  1. 1.

    R. F. Gibson, S. K. Chaturvedi andC. T. Sun,J. Mater. Sci. 17 (1982) 3499.

  2. 2.

    C. T. Sun, S. K. Chaturvedi andR. F. Gibson,Computers and Structures 20 (1985) 391.

  3. 3.

    C. T. Sun, R. F. Gibson andS. K. Chaturvedi,J. Mater. Sci. 20 (1985) 2575.

  4. 4.

    C. T. Sun, J. K. Wu andR. F. Gibson,J. Reinforced Plastics and Composites 4 (1985) 262.

  5. 5.

    S. A. Suavez, R. F. Gibson, C. T. Sun andS. K. Chaturvedi, “The Influence of Fiber Length and Fiber Orientation of Damping and Stiffness of Polymer Composite Materials”, presented at the SESA Spring 1985 Conference, June 9–13, 1985, Las Vegas, Nevada. In “Experimental Mechanics” Vol. 26 (1986) p. 175.

  6. 6.

    H. L. Cox,Brit. J. Appl. Phys. 3 (1953) 72.

  7. 7.

    B. D. Agarwal andL. J. Broutman, “Analysis and Performance of Fiber Composites”, (John-Wiley Interscience, New York, 1979).

  8. 8.

    R. F. Gibson andR. Plunkett,J. Composite Mater. 10 (1976) 325.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation


  • Lamination
  • Constitutive Equation
  • Matrix Composite
  • Stiffness Matrix
  • Fibre Orientation