Spatial Electrostrictive Modal Actuation of Conical Shells

Abstract

Horns, nozzles and load carrying structures of rockets, e.g., inter-stage joint, satellite-rocket joint, solid rocket motor case, etc., are usually made of circular conical shell sections. This study is to investigate distributed electrostrictive actuation and to evaluate spatially distributed microscopic control actions of distributed electrostrictive actuator segments bonded on conical shell surfaces. Mathematical model and open-loop control equations of a generic conical shell are defined first, followed by simplification to a free-free truncated conical shell section with segmented electrostrictive actuators. Natural mode shape functions are defined based on the Donnell-Mushtati-Vlasov approximation; independent modal control equation is derived by the modal expansion. Distributed control actions induced by the electrostrictive actuator segments are evaluated in the modal domain and the total control effect can be divided into four microscopic control actions: the longitudinal/circumferential membrane and bending control actions. Detailed parametric analyses of two mode groups indicate that 1) magnitudes of control actions comply with the quadratic increase with respect to control voltages and 2) the circumferential membrane control action is the most dominating component in the total shell control effect. Also, the spatially distributed modal actuation plots can be used to locate the most effective locations and/or regions of electrostrictive actuators placed on the shell surface.