Continuum Theory for a Laminated Medium

[+] Author and Article Information
C.-T. Sun, J. D. Achenbach, George Herrmann

Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Ill.

J. Appl. Mech 35(3), 467-475 (Sep 01, 1968) (9 pages) doi:10.1115/1.3601237 History: Received November 20, 1967; Revised January 30, 1968; Online September 14, 2011


A system of displacement equations of motion is presented, pertaining to a continuum theory to describe the dynamic behavior of a laminated composite. In deriving the equations, the displacements of the reinforcing layers and the matrix layers are expressed as two-term expansions about the mid-planes of the layers. Dynamic interaction of the layers is included through continuity relations at the interfaces. By means of a smoothing operation, representative kinetic and strain energy densities for the laminated medium are obtained. Subsequent application of Hamilton’s principle, where the continuity relations are included through the use of Lagrangian multipliers, yields the displacement equations of motion. The distinctive trails of the system of equations are uncovered by considering the propagation of plane harmonic waves. Dispersion curves for harmonic waves propagating parallel to and normal to the layering are presented, and compared with exact curves. The limiting phase velocities at vanishing wave numbers agree with the exact, limits. The lowest antisymmetric mode for waves propagating in the direction of the layering shows the strongest dispersion, which is very well described by the approximate theory over a substantial range of wave numbers.

Copyright © 1968 by ASME
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In