Aeroelastic Flutter Analysis And Control Of Supersonic Beam And Plate

In order to enhance the aeroelastic stability of the beam and plate structures, the aeroelastic flutter analysis and active vibration control of the supersonic beam and composite laminated plate are studied.The equation of motion of the supersonic beam with the active constrained layer damping (ACLD) is established by the Hamilton's principle and the assumed mode method. The unsteady aerodynamic pressure is evaluated by the first order piston theory. The controller is designed using the negative velocity feedback control, and the active damping is obtained. By using the generalized eigenvalue methodology, the complex eigenvalues are gotten, and the natural frequencies, damping ratios and some other physical quantities are further obtained. The variations of the natural frequencies of the supersonic beams with the non-dimensional aerodynamic pressure are calculated, from which the flutter analysis of the stuctural system is developed. The results of the numerical example indicate that the passive damping provided by the viscoelastic damping material can increase the critical flutter aerodynamic pressure of the structure slightly, while the active damping produced by the piezoelectric material can significantly increase the critical aerodynamic pressure of the structural system. Based on the above analysis, it is noted that the effects of the viscoelastic material on the active constrained layer damping are small in the flutter analysis and that the influence of temperature on the property of the viscoelastic material is relatively large. So the viscoelstic damping layer should be taken off and the aeroelastic flutter analysis and active vibration control of the supersonic beams are developed only by the piezoelectric actuators and sensors. The aerodynamic load model and the methods of modeling and solving the motion equation are the same as those of the beam with the ACLD. In order to study the active vibration control of the structure at the flutter bounds, the impulse responses of the supersonic structural system under a unit pulse load are calculated using the finite differential method.On the basis of the aeroelastic flutter analysis and active vibration control of the supersonic beams, the aeroelastic characteristics of the supersonic composite laminated plate are analyzed. The equation of motion of the structure is also established by the Hamilton's principle and the assumed mode method, and the unsteady aerodynamic load is also modeled by the piston theory, in which the aerodynamic damping is considered. Two different control methods, i.e. the velocity feedback control and the proportional feedback control, are employed to analyze the active aeroelastic characteristics. The equation of motion and the impulse responses of the structural system are solved. The influences of the configurations of the laminated plate on the aeroelastic characteristic are studied, and the comparisons of the effects of the two control methods on the aeroelastic flutter analysis and active vibration control are made.The genetic algorithm is used to design the optiaml locations of the distributed piezoelectric actuator/sensor pairs on the supersonic composite laminated plate, the effects of the optiaml location design with the genetic algorithm on the flutter suppression and vibration control are also analyzed. The LQR control algorithm is applied to investigate the aeroelastic flutter characteristics and active vibtation control of the supersonic composite laminated plate. The advantages of the LQR control algorithm in stabilizing the aeroelastic flutter characteristics of the supersonic laminated plates are also analyzed.The results presented in this paper may be helpful for the active aeroelastic design of supersonic structures.