Optimal control of a pretwisted shearable smart composite rotating beam

Summary

The optimal vibration control of a rotating, composite, pretwisted, single-celled box beam, exhibiting transverse shear flexibility and restrained warping, is analyzed. A higher-order shear deformation theory (HSDT) enabling satisfaction of traction-free boundary conditions is employed. An orthotropic host with Circumferentially Uniform Stiffness ply angle configuration and transversely isotropic sensors-actuator pairs that are surface embedded along the span are considered. The total output from sensors is fed to a controller and then uniformly applied to actuators. The extended Galerkin method, along with either instantaneous or classical LQR methods, is used. Instantaneous LQR provides greater response attenuation in case of sustained external forcing. Results are obtained for a linear spanwise variation of pretwist. Compared to the unshearable and first-order shearable (FSDT) models, the HSDT appears most sensitive to pretwist and – when a saturation constraint is considered – it predicts the lowest settling time. The HSDT predicts significant attenuation in response and power required as compared to the FSDT, the differences being especially pronounced for constrained input control. Parametric studies involving the ply angle, pretwist, and patch length are performed. An optimum pretwist that yields lowest response, power, and settling time is obtained. Its value differs when the saturation constraint is used. Tailoring provides greater attenuation at the expense of an increase in settling time. Using constrained input control, an order-of-magnitude reduction in power requirement is possible via tailoring. The results underscore the importance of shear strain variation across the beam wall, and also of synthesizing active control with tailoring, for achieving efficient control.