Research On Kinetic Model Reduction And Active Vibration Control Of Flexible Structures With Dense Frequency

When the large flexible structure in space is subjected to arbitrary impacts such as space junk and aircraft wreckage,due to its structural characteristics such as large flexibility,weak damping,low modal frequency and denseness,and extremely weak environmental damping in space environment,once the vibration is generated,it is very difficult to attenuate.It is difficult to achieve the purpose of eliminating vibration by ordinary passive control.Because of the flexibility of the structure and the large model obtained by modeling,with regard to these questions,this paper studies by following steps,modeling of coupling model,model reduction,optimal configuration of piezoelectric structure and active vibration control,which provides a complete and clear solution for vibration control of such structures.This paper focuses on the modeling and reduction of dense frequencies structures.According to the thin plate assumption,the differential equation of thin plate vibration has been derived and the research object's natural frequency is expressed.The electromechanical coupling relationship of the piezoelectric material is analyzed.Based on the mechanical and electrical properties of the piezoelectric ceramic,the related theory of the finite element 4-node rectangular plate element and the Hamilton principle,the dynamic model of the piezoelectric-structural coupling unit is preliminarily established.Combined with the cantilever boundary conditions of the structure and the position of the piezoelectric structure on the structure,grouping the mass matrix and adding the stiffness matrix of the element and Rayleigh damping,the dynamic model of the coupled structure is established.On the basement of the model,obtaining the mass,stiffness and damping matrix of the whole structure,after finishing the numerical calculation to get the inherent frequency of the structure,compared results with the simulation results,thus the correctness of the established model is verified by experiments.For the system dynamics model has the property of very large dimensionality,the internal equilibrium reduction method and the modal value criterion are used to reduce the order.The two reduction methods are compared according to the reduction degree of the system at each point.Getting the trend of the effect of model reduction on the flexible board,selecting the nodes to compare the response,the amplitude frequency and the phase-frequency performance curve of the system before and after the process of reduction,the system of the flexible structure after model reduction is obtained.For the model of the flexible plate without piezoelectric structure,the point is to use the controlling energy minimization optimization criterion and the particle swarm optimization algorithm to optimize the position of the piezoelectric structure on the plate.After location optimization of the piezoelectric structure,by comparing the inherent frequency of the flexible plate before and after the piezoelectric piece installed,the comparison of inherent frequency characteristics of the plate are finished.The system obtained by reducing the order,combined with the result of optimal positioning of the piezoelectric structure on the flexible board,is controlled by linear quadratic optimal control and PID control method,besides the relevant parameters are adjusted to get relevant parameters with better control response.