Dynamic response of rotating beams with piezoceramic actuation

The dynamic behaviour of rotating beams with piezoceramic actuation is studied using bending (d31) and shear (d15) actuation for application to structures such as helicopter and wind turbine rotor blades. The governing equations are derived using Hamiltonʹs principle for a beam undergoing transverse bending, inplane bending, torsion and axial deformations. The effect of moderate deflections are included by retaining non-linear terms. The equations are then solved using finite element discretization in the spatial and time domain. Results are obtained for the cases with only actuation loads, with actuation loads and added periodic tip loads, and for a pretwisted beam. Numerical results show that the centrifugal stiffening effect reduces the tip transverse bending deflection and elastic twist obtained from smart actuation as the rotation speed increases. However, the effect of rotation speed on the tip elastic twist is less pronounced. The importance of non-linear terms for accurate prediction of torsion, in-plane bending and transverse bending response is also shown. It is also found that combinations of pretwist and smart actuation can be used to obtain desirable torsion response over a range of rotation speeds.