Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers

In this paper, natural frequencies and vibrational mode shapes of variable stiffness composite laminate (VSCL) plates with curvilinear fibers are studied. In each ply of this rectangular VSCL, the fiber-orientation angle changes linearly with respect to the horizontal coordinate. To define the modes of vibration of the laminates, a new p-version finite element, which follows third-order shear deformation theory (TSDT), is employed. The convergence properties of this new element are investigated. Taking manufacturing restrictions regarding the fiber curvatures into account, maps of natural frequencies as functions of tow-orientation angles are determined in demonstrative examples. It is verified that the use of curvilinear fibers instead of the traditional straight fibers introduces a greater degree of flexibility, which can be used to adjust frequencies and mode shapes.