Active Vibration Control Of A Cantilever Beam On Elastic Base

The vibration of a cantilever beam on elastic support base is a common engineering problem. It is of important meaning to discuss the issue deeply for aviation, weapons, ship and many other aspects. For example, as the influence of aircraft engines vibration on the elastic supporting structure (such as beam or plate), the dynamic responses of aircraft become worsen, as well as the vibration of artillery gun barrel eliminates its accuracy of firing, etc. In order to simplify the theoretical calculation, the supporting base is assumed to be as the absolute rigid-body with infinite quality in the classical vibration theory. Because of the ignorance of the dynamic characteristics of the elastic base, it is usually happened that the desired control results can't be achieved in the engineering practice. On the base of analysis to the vibration model of the Bernoulli-Euler beam and the simplified model of the elastic supporting base, the vibration differential equation of the cantilever beam with elastic supporting base is derived. The dynamic response of the cantilever beam with elastic supporting base is obtained. Since the characteristics of the positive piezoelectric effect and inverse piezoelectric effect, the piezoelectric ceramic is used to sensor the deformation of structures, and to apply force to controlled object. The state space functions of the flexible cantilever beam with elastic supporting base, integrate the actuator equation and sensor equation together with the vibration differential equation of the cantilever beam, are formulated. The structure control energy and control signal energy is chosen as the control objective function of quadratic optimal control strategy. The active vibration control method is researched to suppress the vibration response excited by continually stimulating force from the supporting base. The simulation results show that the control method is flexible.