Active vibration control of piezoelectric smart beams with radial basis function generated finite difference collocation method

A local collocation method based on finite difference generated radial basis functions considering supplementary polynomials is used to solve the governing equations of cantilever piezoelectric smart beams. The natural modes of vibration of a bimorph and a three-layered smart beam with an interior aluminium core are analysed for both open-circuit and closed-circuit electrical boundary conditions. Very accurate results are obtained at a low computational cost. Subsequently, a constant gain velocity feedback active vibration control system is implemented, and the time and frequency response functions of both beams subjected to initial impulse and displacement conditions are investigated. Different values of the applied gain and varying thickness of the piezoelectric layers are analysed. The governing equations are established using equivalent-single-layer first-order-shear-deformation theory with through-the-thickness quadratic layerwise electric potential for improved accuracy.