Dynamic Instability of Rectangular Composite Plates under Parametric Excitation

The dynamic instability of rectangular graphite/epoxy composite plates under parametric excitation was investigated analytically and experimentally. In analysis, the dynamic system of the composite plate, obtained based on the assumedmodes method, is a general form of Mathieu’s equation, including parametrically excited terms. The instability regions of the system, each separated by two transition curves, were found to be functions of the modal parameters of the composite plate and the position and the excited amplitude of the electromagnetic device on the composite plates. The fiber orientation, the aspect ratio and the layer numbers of the composite plates were varied to assess their effects on the dynamic instability behavior of the composite plates. In experiment, an electromagnetic device, acting like a spring with alternating stiffness, was used to parametrically excite the composite plates. The frequency and the amplitude of the excitation force were accurately controlled by the AC current flowing through the coil of the electromagnetic device. Since the excitation force was a transversely non-contact electromagnetic force, the disturbances induced by the eccentricity of the usual planar excitation force and by the geometric imperfection of the composite plate were effectively avoided. The experimental results, for the cases of twice the fundamental frequency, were found to agree well with the analytical ones. The excitation frequencies at tip of instability regions decrease as the fiber orientation increases for composite plates with [±θ2]s lamination at bending mode; while the excitation frequencies increase to a maximum at 45° fiber orientation for composite plates with [±θ2]sslamination at torsional mode. The excitation frequency at tip of instability regions decreases for higher aspect ratios and thinner composite plates.