Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory

Abstract Skew fibre-reinforced composite laminates are important structural elements in modern engineering structures, particularly in aero-space industry. Natural frequencies of these skew laminates are of primary significance to structural designers. As far as the author's knowledge is concerned the references on this topic is very limited. Within the context of the first-order shear deformation plate theory (SDPT) [Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. ASME , 12 , 69–76 (1945); Mindlin, influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. ASME , 12 (18), 1031–1036 (1951).] this paper presents a B-spline Rayleigh-Ritz method (RRM) for free vibration analysis of skew fibre-reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. In this approach the displacement field consists of the three mid-surface translational displacements u , v and w and the two through-thickness shear strains γ xz and γ yz instead of the two rotations ψ x and ψ y in order to avoid the shear locking phenomenon. Various numerical applications are presented and the method is shown to be accurate and efficient.

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