Helicopter vibration reduction in forward flight with induced-shear based piezoceramic actuation

Governing equations are obtained for helicopter rotor blades with surface bonded piezoceramic actuators using Hamilton's principle. The equations are then solved for dynamic response using finite element discretization in the spatial and time domains. A time domain unsteady aerodynamic model is used to obtain the airloads. The nonlinear relationship between the piezoelectric shear coefficient and applied ac field is represented as a polynomial curve fit. The nonlinear effects are investigated by applying a sinusoidal voltage to the helicopter rotor blade. The rotor blade is modeled as a two-cell box section with piezoelectric layers surface bonded to the top and bottom of the box beam. Comparison of results with linear and nonlinear shear coefficients is presented. Use of a nonlinear relationship (compared to linear) to achieve targeted reductions in strains or displacements results in a reduction in the requirement of applied amplitude of the sinusoidal field. A rate feedback control law is implemented which feeds back the higher harmonics of the time rate of change of strain in the azimuthal direction. The sensed voltage is then applied to the rotor blade, resulting in a vibration reduction of approximately 43% for a four-bladed, soft-in-plane hingeless rotor in forward flight