Flexural free vibration behaviors of bimodular composite laminates with variable angle tow-steered fiber-reinforced layers

In the present work, a study on free flexural vibration characteristics of bimodular composite materials using shear flexible plate model is presented. Furthermore, laminae with curvilinear fibers which result in variable stiffness due to change in fiber path angle are introduced in the composite laminates. The composite material considered here exhibits different properties in tension and compression depending on fiber direction strain. The governing equations are obtained by Hamilton's principle and are solved numerically using shear flexible finite element in conjunction with eigenvalue analysis. As laminate neutral planes are not known in advance, their positions are found iteratively by assuming mode shape of interest and subsequently applying Newton-Raphson scheme. By evaluating laminate stiffness based on neutral planes, the natural frequencies are then obtained considering both positive and negative half response cycles of vibration. A detailed numerical investigation is conducted to obtain the variation of the fundamental frequency due to change in aspect/thickness ratio, bimodular material ratio, plate edge conditions, fiber path angle, layup, etc. Such study may be useful for the optimal design of bimodular laminate structures subjected to dynamic environment.