Vibration analysis of laminated composites

Abstract

This study presents a macromechanical analysis of vibration of laminated composites within the concept of the effective stiffnesses of composites. The laminated composite may possess arbitrary number of matrix and reinforcing layers, each with a distinct but uniform thickness, curvature, and mechanical properties. Starting with a linearized displacement field for each constituent layer and using an unconstrained, dynamic variational principle due to the author [J. Ship Res. 23, 115–122 (1979)], the set of two-dimensional governing equations of the prestressed laminated composite is systematically and consistently established. The continuity of tractions and displacements at the interfaces is maintained, and all the effects of transverse shear and normal strains and the rotary inertia of layers are included. The governing equations accommodate all the types of small incremental motions as well as those of initial finite motions of the laminated composite. Further, special cases of interest are pointed out, and in particular, the linearized version of the governing equations is considered. Then a theorem which enumerates the sufficient conditions for its solutions is constructed by means of the logarithmic convexity arguments. [Supported by AEK Tek: 2940-3-77.]