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In this paper, the active vibration control of conical shells is studied using velocity feedback and linear quadratic regulator methods. Up to now, many researches on the active vibration control of beams, plates and cylindrical shells have been published, however, to our knowledge, few people have studied the active vibration control of conical shells. Normally, in the equation of motion of the conical shells, some coefficients are variables, which makes the equation of motion of the conical shells very complicated and difficult to solve analytically. In order to solve this problem, Hamilton's principle with the assumed mode method is employed to derive the equation of motion of the complex electromechanical coupling system. This equation of motion for the conical shell and piezoelectric patch system can be easily solved and effectively used for the structural active vibration control. Based on the traditional theory of structural dynamics, this method is easy to understand and is verified by numerical simulations. The forced vibration responses of the conical shells with two piezoelectric patches are computed to study the active vibration control. The optimal design for the locations of the piezoelectric patches is also developed by the genetic algorithm. From the results it can be seen that the control gain has a significant effect on the vibration control of the conical shell, but the effect of the size of the piezoelectric patches on controlling the vibration amplitudes is not so obvious. The overall vibration of the conical shell can be effectively reduced by the velocity feedback control method. With the increase of the control gain, the active damping characteristics of the conical shell are improved. Moreover, the optimal placement scheme of the piezoelectric patches obtained by the genetic algorithm can significantly reduce the vibration amplitudes of the conical shell.

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The optimal active flutter control of supersonic composite laminated panels is studied using the distributed piezoelectric actuators/sensors pairs. The supersonic piston theory is used to calculate the unsteady aerodynamic pressure, and Hamilton’s principle with the assumed mode method is employed to develop the equation of motion of the structural system. The controllers are designed by the proportional feedback control method and the linear quadratic Gauss (LQG) algorithm. The optimal locations of the actuator/sensor pairs are determined by the genetic algorithm (GA). The aeroelastic properties of the structural system are mainly analyzed using the frequency-domain method. The time-domain responses of the structure are also computed using the Runge–Kutta method. The influences of ply angle on the flutter bound of the laminated panel with different length–width ratios are analyzed. The optimal design for the locations for different numbers of piezoelectric patches used in the proportional feedback control is carried out through the GA. Meanwhile, the control effects using different numbers of actuator/sensor pairs are investigated. The flutter suppression by the LQG algorithm is also carried out. The control effects using the two different controllers are compared. Numerical simulations show that the optimal locations obtained by the GA can increase the critical flutter aerodynamic pressure significantly, and the LQG algorithm is more effective in flutter suppression for supersonic structures than the proportional feedback controller.

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