Model Validation Research On Cantilever Beam Active Vibration Control System Based On Electromagnetic Actuator

Active vibration control is one of the important research directions in the field of vibrationcontrol, whose design starts from the modeling. For the loss caused by the vibration of flexiblestructure, this article focus on related modeling research of the cantilever beam active vibrationcontrol system based on electromagnetic actuator.The cantilever beam active vibration control system and its working principle are introduced andthe transfer functions of controller, sensors, power amplifier and design size of the electromagneticactuator are given. Establish finite element models of the free board and the cantilever beam, thencalculate the vibration mode matched-degree between modal experiment and simulation. The resultsprove that the finite element model of the cantilever beam has a very high credibility.Split the cantilever beam into two beam elements and obtain the polycondensation mass matrixand stiffness matrix by finite element method and static condensation method. Then the cantileverbeam is simplified to the under-damped second-order linear system, in which proportional dampingmatrix is obtained through the free oscillation test and theoretical calculation. Choosing state variables,cantilever beam’s state space matrixes are obtained without control and with control, which aresimulated by Simulink. The method to establish state space matrix is feasible.The theory of finite element model updating based on response surface is introduced. For therubber-cantilever structure, establish response surfaces based on D-optimal experimental designmethod. Regard the simulation value and experiment value as the goals to identify stiffness anddamping. Comparing identified stiffness with tested stiffness by rubber extrusion experiment, itproves that this model updating method has high accuracy in identification of stiffness.It briefly introduces the basic theory of model validation. Based on the confirmation experimentof the cantilever beam active vibration control system, the electromagnetic actuator’s averages ofstiffness and damping are identified by response averages. It considers the uncertainty of parametersand response, cantilever beam-electromagnetic actuator subsystem’s simulation research and exampleanalysis prove the credibility of the stiffness distribution identified by model validation is higher.