Vibration control of toroidal shells with parallel and diagonal piezoelectric actuators

Effective control of toroidal shells, e.g., cooling tubes, space colonies, inflatable space structures, etc., enhances their operational precision, accuracy, and reliability. Dynamics and control effectiveness of toroidal shell panels laminated with distributed piezoelectric sensor/actuator layers are investigated in this study. Mathematical model and finite element formulations of piezo(electric)-elastic shell structures are presented. Element and,system matrix equations of the piezoelastic shell structronic (sensor/actuator/structure/control) system are defined and the system equations reveal the coupling of mechanical and electric (or control) fields. Free vibration analyses of two toroidal shells are investigated and compared favorably with published data. Two sensor/actuator configurations based on identical sensorlactuator sizes, namely the parallel configuration and the diagonal configuration, laminated on the toroidal shell are investigated and analysis data suggest that the diagonal configuration provides better control affects, as compared with the parallel configuration. The parallel configuration is ineffective to anti-symmetrical modes; the diagonal configuration is effective to most natural modes and ineffective to quad-anti-symmetrical modes with respect to the panel center.