Hamiltonian System And Semi-analytical Method Approach To Bending Problem Of Piezoelectric Cantilever Beam

In this paper analytical solution for bending problem of piezoelectric cantilever beam was gived based on the Hamiltonian system method, which was introduced by reference documentation[1].The basic ideas as follow: First according to the basic equation of piezoelectric cantilever beam, principle of minimum potential energy for this problem was obtained. Then employing dual-variable and making a Legendre transformation to lead this problem into the Hamiltonian system. Finally the fundamental eigenvector of this problem were acquired by solution Hamiltonian equations. So the analytical solution for concrete problems can be obtained by linear combination of these fundamental eigenvectors. Method of separation of variables and eigenfunction which can not use in the traditional method ,can use directly in the Hamiltonian system method. This is the greatest advantage of Hamiltonian system method. According to this, analytical solution for all kinds of anisotropic materials can get by method of expanding primary function.Though there were so many advantages of Hamiltonian system method, but this method will be completed when the materials in the ins and outs. Because the key to apply it is change the Lagrange system into the Hamiltonian system. The cornerstone of Hamiltonian system method is the principle of potential energy and its variation principle. This create a favorable for finite element semi-analytical method.Follow in succession this paper gived the semi-analytical method, which was integrated analytical method of Hamiltonian system and finite element numerical method. It was enriched and perfect the solving method of piezoelectric cantilever beam. The research results will play an important role in the sensing and controlling applying of piezoelectric cantilever beam.Finally ,it was a summarize of this paper and a prospecting of the researching for the piezoelectric cantilever beam.