Control of Static Shape, Dynamic Oscillation, and Thermally Induced Vibration of Nozzles

Static shape actuation and dynamic control of nozzles can improve their performance, accuracy, reliability, etc. A new curved laminated piezothermoelastic hexahedral finite element is formulated based on the layerwise constant shear angle theory and it is used for modeling and analysis of piezothermoelastic conical shell structures subjected to control voltages for static shape actuation and dynamically and thermally induced vibration controls. Free vibration characteristics of an elastic truncated conical shell nozzle with fixed-free boundary conditions are studied using the new finite element. Both frequencies and mode shapes are accurately computed and compared favorably with available experimental and other numerical data. This study is then extended to evaluate control effectiveness of the conical shell with laminated piezoelectric layers. Static shape control is achieved by an applied electric potential. Vibration sensing and control are carried out using the negative velocity control scheme. Control of thermal excitation is also investigated. Analysis data suggest that the dynamic behavior and control characteristics of conical shells are quite complicated due to the coupled membrane and bending effects participating in the responses. To improve control effectiveness, segmentation and/or shaping of sensor and actuator layers need to be further investigated.