Research Of Active Vibration Control Of Cantilever Beam

Recently, the technique of the active vibration control is a kind of new technique in the area of vibration engineering. In the area of aviation and spaceflight, for the reason of specific requirement to the structure weight, the techinique of the active vibration control, which use the light piezoelectric material, has the development superiority. The technique of the active vibration control of cantilever beam set up dynamic equation with finite element analysis, finds the way of control with the theory of quadratic optimization control and controls the first stage of vibration of cantilever beam by means of inputting the energy into the system with piezoelectric actuator. This paper discusses the following:1. This paper introduces the analysis process of beam with finite element analysis, including the structure dispersal, unit analysis and whole structure analysis. It introduces the rule of unit partition with finite element analysis and the foundation of finite element equation of beam unit, deduces the expression of quality matrix and rigidity matrix of beam unit, introduces the identifying method of damp matrix.2. This paper introduces the character of linearity quadratic optimization control and the describing way of aim function and the engineering meaning of each index in the capability index. On the base of it, it introduces infinite time condition adjuster of quadratic optimization control and gives expressions of aim function.3. Basing on the energy rule, we identify the paste position of piezoelectric actuator, basing on the theory of mode control degree, we examine the effect of the position of sensory to the control the system and identify the position of the sensory is at the end of the beam. After we have analysized beam unit with the finite element analysis, we set up quality matrix and rigidity matrix of beampasting with piezoelectric material. By using the technique of P.mario's dynamic contract, we set up the dynamic model of cantilever beam using two main freedoms. We design the control rule of cantilever beam with quadratic optimization control and deduce the expression of it.4. Through the experiments, we identify the relationship between the voltage of piezoelectric actuator and equivalent force beared at the end of cantilever beam. Using the software of LABVIEW, we design the main process and front panel of the control system. By using the control system we design, it constrains freedom vibration disturbed at the beginning of cantilever beam. We draw the response curves under the condition of control and uncontrol, compare the ratio of damp and the attenuation time under the condition of control and uncontrol. Ratio of damp increase to 8.4 multiple and the attenuation time is 2.6 seconds under the condition of control. It constrains the force vibration of the cantilever beam and the magnitude of vibration decrease to that of 48.2%. This proves that the control is efficient to the vibration. Finally, we research the effect to the control efficiency under the condition of different choice of Q and R, draw a three-dimensional curve of the relationship of Q, R and ratio of damp.