Research On Active Vibration Control Of Flexible Structure Based On Energy Flow Element Method

Forecast and control of structural vibration and noise is important in many fields. For the past few years, flexible components have been widely used in the field of aerospace industry, shipping industry, civil engineering and medicine enquipment industry. The vibration of flexible structures during using will cause the adverse influence in enquipment characteristic and safety. Therefore the forecast and control of flexible structures vibration is an important subject in the vibration control field.The most widely used forecast methods of structural vibration are Finte Element Method, Statistical Energy Analysis and Energy Finte Element Method. The last method as a new numerical analysis method is applicable in whole frequency range while Finte Element Method can he used only in low frequency. This method can also be predicting the internal vibrating information of structures. In Statistical Energy Analysis can only be obtained total crude results.Theory and its application research work have been carried out as follows:Firstly, as the basis of Energy Finte Element Method, the energy density and power flow expression of bars and beams are derived, then deduce the differential energy density equations through energy-balance equation. The differential equations are analogous to the Helmholtz equation. Furthermore, the proportion of farfield and nearfield energy density in the total energy density is compared.Secondly, the differential energy density equation of beam is dispersed by Galerkin weighted residual method. Considering the energy density is discontinuous at the coupling point, a special coupled matrix is needed. The energy-balance equation of beams is developed to the coupling relationships at the coupling point, and the energy transmission and reflection coefficients are deduced for coupling beams. Then, apply the Energy Finte Element Method to uniform and coupled beams under various boundary conditions. The results indicate that the exact energy density solution is good agreement with the Energy Finte Element Method results.Thirdly, derive the output equation of the piezoelectric sensor and actuator by using the equation of the piezoelectric materials. Then establish the dynamics equation of the flexural piezoelectric cantilever control system based on wave theory. The influences of feedback gain, location of piezoelectric elements and structure damping to the distribution of energy density in beams are analyzed. Finally, based on above work, we use Energy Finte Element Method to establish the Energy Finte Element equation of the flexural piezoelectric cantilever control system. Then compare the results of the influences of feedback gain, location of piezoelectric elements and structure damping to the distribution of energy density in beams with exact solution which based on wave theory. It is shown that Energy Finte Element Method is a simple and effective method for analyzing structure vibration.