Research Of Active Vibration Control Of Simply-supported Beam Based On IMSC

The active vibration control is high-tech in the area of vibration engineering, for its remarkable advantages, it is becoming an effective mean to solve the vibration control problems of the aerospace and other fields. For its light and swift response, piezoelectric material occupies an important position of vibration engineering. In the dissertation, we set up mathematical model of simply-supported beam at first, and then make the modal analysis of the beam with ANSYS, after this we design the control method with independent modal space control, at last, we control the first stage of vibration of the beam by inputting energy into the system with piezoelectric actuator. The main content of this dissertation is as follows:1. Set up the mathematical model of simply-supported beam. The actuator and sensor are designed at first. Basing on the energy rule, the piezoelectric actuator is affixed on the midst of the beam. According to the effect of detection, the sensor is used to detect the displacement of the midst of the beam. The simply-supported beam is predigested as a 3DOF system. The mass matrix and stiffness matrix are solved, and the expression of the damping matrix is derived, and then the differential equation and state space equation are set up;2. The modal analysis of the simply-supported beam. The finite element modal is set up by ANSYS, and then we analyze the mode of the beam, get the first three natural frequencies and inherent vibration modes of the beam. The actual first three natural frequencies are got by experiment. At last, we compare the result of the analysis with the result of the experiment;3. The design of control method. This paper introduces the character and design process of the independent modal space control. The first three matrixes of inherent vibration modes are derived by matrix iterative method, and then we get the modal coordinates. We get the displacement gain and speed gain by pole placement. We determine the modal control force by the displacement gain and speed gain and then translate it into the actual control force;4. The design of control program and control panel. The relationship between control force and the equivalent voltage of piezoelectric actuator is identified by experiment. We design the control program and control panel of the control system with LabVIEW;5. The experiment of active vibration control of system. We build up the active vibration control system of the simply-supported beam. With the control system, we control the freedom vibration of the beam which is disturbed by an initial disturbance, and get the response curves which without control and with control. We compare the curves and find that the attenuation time without control is 2.76s and the attenuation time with control is0.38s. We control the vibration of the beam which is incented by continuing incentives with different frequencies, and get response curves of 10Hz,20Hz,28Hz,30Hz,40Hz,50Hz . By calculating, we find that the steady amplitude with control is decrease to 41.6%,39.9%,36.2%,37.6%,37.2%,56.4% of steady amplitude without control. These data prove that active vibration control of system we designed is efficient.