Active Control Of Vibration About Piezoelectric Material Based On Hamilton Theory

Piezoelectric material is the main composition of control and sensing units in the real application, and it is very important for the structures of aeronautical and aerospace. Hence,the study on the piezoelectric material is one important aspect for the design and manufacture of the intellectual structure. In terms of the structure that requires excellent property and accuracy, the functionally gradient piezoelectric material is a kind of material that is more excellent and the more stringent requirements. The main work of this paper includes three parts:Firstly, the finite element dynamic equation of piezoelectric laminate is given based upon the Hamilton theory.Secondly, based on the finite element dynamic equation, the APDL language in ANSYS is applied to program for the analysis of the change about the property of the functionally gradient piezoelectric material. The APDL program is to lay the groundwork for the dynamic characteristics of the functionally gradient piezoelectric material. The concrete example analysis is presented for some of the standards modal of graphics. From the numerical results,for different thickness of piezoelectric functionally gradient plate, with the increase of the first-order gradient power, main frequency shows a rising trend. As the order increase, when the gradient power increases, the frequency of the growth rate is also higher.Lastly, on the basis of Hamilton system, for the problem in vibration control of laminated plates, the optimal control method(LQR method) is used to design the vibration control system. For the selection of core LQR in Q, R matrix, the control system is completed by using the energy principle of control. And then, the Simulink function in Matlab is used to simulate the system and some of the pictures of effect control are obtained. The results are compared with the pole placement method and the modal control method. Numerical results shows the effect of the energy control method is more superiority and the effect is excellent.in this paper. For instance, the effect of energy control method is 75%, the effect of other two kinds of methods is 57% and 28%, respectively.Some of case and guidance is obtained by using of the theoretical research and examples study. Some of results can provide reference for the actual engineering application, and leads to the need to continue the future research work in this paper.