Dynamic instability of composite beams under parametric excitation

The dynamic instability of graphite/epoxy composite beams under parametric excitation was investigated experimentally and analytically. In experiment an electromagnetic device, acting like a spring with alternating stiffness, was designed to parametrically excite the composite beam. The dynamic system of the composite beam was analyzed based on the assumed-modes method and the Lagrangeʹs equation. The derived dynamic equation, which contains parametrically excited terms, is a general form of Mathieuʹs equation. An analytical method, different from the traditional perturbation method, to determine the instability regions of the composite beam was applied to obtain the transition curves. The instability regions of the system were found to be functions of the modal parameters of the composite beam and the position, the stiffness of the electromagnetic device for the cantilevered composite beams. The fiber orientation, the length, the width and the thickness of the composite beams were varied to assess their effects on the dynamic instability behavior of the composite beams. The experimental results were found to agree well with the analytical ones.