Research On Vibration Characteristics And Active Control Of Conical Shells Based On Piezoelectric Sensing And Actuation

Severe dynamic loads in the flighting vechiles may cause accuracy loss or even damage to the precision equipment inside. Therefore better dynamic environment is requied to protect the precision equipments, and vibration isolation system (VIS) can be employeed to achieve this, which mianly consists of a vibration isolator installed between the equipment and the base. Active VIS based on piezoelectric smart structure are more promising VIS, because of its better performance, light weight, rapid response and less energy cost. Therefore, based on a conical shell model and the piezoelectric sensor/actuator, the active vibration isolation of precision equipment in flighting vechiles are investigated.The vibration characteristics of the conical shell are foundations of vibration control. Generally, the conical isolator is fixed to the base at the major end, and is free to vibrate at the minor end. The bending, axial and torsional vibrations are much more important for VIS than the transverse vibration. To analyze these vibrations, a set of modal functions are presented based polynomial and sine function. Based on the thin shell assumptions, the geometric and physical equations are given, the energy equations for clamped-free conical shell are derived. Then the natural frequencies and modal functions are solved by using a Rayleigh-Ritz method. During the derivation, the axial, torsional, bending and transverse vibrations are investigated and detailed equations for each vibration type are specified.Traditional piezoelectric sensor used for thin shells are assumed not sensitive to in-plane shear strain, is not applicable for torsional vibration of conical isolator. Therefore a shear-type piezoelectric sensor is presented, the mathematical model is developed based the direct piezoelectric effect. The shear type sensor is applied to the conical shell based on the modal analysis. Then the boundary conditions are specified and the sensing signal equations are derived. For the axial, bending and transverse modes, a diagonal sensor is presented. The signal equations of diagonal sensor are derived, the total signal consists of four components related to the four strain components respectively. By using a numerical method, the distribution of sensing signal and modal signal is evaluated. Furthermore, the distributed sensing of conical shell with payload at the minor end is investigated. The sensing signals depend on the modal deformation, sensor location, sensor geometry, the piezoelectric material and so on. The amplitudes of sensing signal are usually less than the modal one because of the average effect, but the difference is very small. Therefore, the sensing signal can be used to investigate the structural vibration characteristics. The optimal locations for sensor patches can be determined according to the results.In order to actively control the axial, bending and transverse vibrations of conical shell, a diagonal piezoelectric actuator is proposed. By using the mode superposition method, the total dynamic response can be represented by the summation of all participating natural modes and their respective modal participation factors. Therefore, the vibration equations are transformed into the mode space, and a modal vibration equation is obtained. Based on the inverse effect, the mathematical model of the diagonal actuator is derived and the equation of modal control force is achieved. The modal control force consists of four component related to the active force and moment per unit length in longitudinal and circumferential direction respectively. By using an open-loop control method, the modal control characteristics of diagonal actuator segments at different locations are investigated and compared with unit control voltage. The results prove that the diagonal actuator is applicable of active control of axial, lateral and transverse vibrations of conical shell. When rigid mass is fixed to the minor end, every actuator patch generates a similar modal control force. The optimal locations of actuator segments for the control of different natural modes are also investigated.The modal vibration equation is transformed into the state space, the sensing signal of diagonal sensor is chosen as the system output vector, the modal control force of diagonal actuator is chosen as the system input vector, and the state space equation of the active vibration control equation is established. The optimal controller is obtained by minimizing the performance function. Then the optimal control force and corresponding control voltage are investigated using a numerical method.A scaled conical shell model is build, and the experimental platform is established. Principle experiments on the modal functions, the diagonal piezoelectric sensor and actuator are performed to verify proposed theory.