Chandiramani N., Librescu L.

A composite rotating beam having hollow cross section and carrying a tip rotor is analyzed. The beam, comprising an orthotropic (graphite-epoxy) host with surface embedded and spanwise distributed transversely isotropic (PZT-4) sensors-actuator pairs, is mounted on a rigid hub. The tip rotor and hub rotate at constant speeds. This assembly occurs in spacecraft structures. The model accounts for restrained warping, linear and parabolic pretwist variation along span, double taper, and presetting. Traction-free boundary conditions are satisfied using a parabolic variation of transverse shear strains through the wall thickness, yielding a higher-order shearable (HSDT) model. Span- and thickness- wise variation of electric field applied to actuators is considered, yielding coupled electro-mechanical governing equations wherein all six displacement field variables are coupled via the electric field variable - i.e., bending-transverse shear and extension-twist coupling occurs. Spatial discretization is performed via. the extended Galerkin method using admissible functions. Optimal control using steady-state LQR with full state feedback is employed. The resulting algebraic Ricatti system is solved via. a robust method using stable eigenvectors of the Hamiltonian matrix. Parametric studies involving ply-angle, rotation speeds of beam and rotor, pretwist, taper, rotor mass, and saturation constraint on actuator voltage, are performed. The HSDT yields lowest coupled natural frequencies -as compared to unshearable and first-order shear models- thus providing conservative data, useful for passive and active control designs. The present model, with spanwise varying electric field, yields an order-of-magnitude reduction in settling time and control voltage/power required, and lower controlled response, vis-a-vis the decoupled approach. Gyroscopic forces -due to tip rotor- have a pronounced qualitative effect on the controlled response, in that the attenuation is greater for smaller ply-angles, in contrast with the rotorless system. This underscores the importance of synergizing active control and structural tailoring.