Zhang Lang*, Gao Puyun, Li Dongxu and Wang Xue
The Journal of Mechanical Science and Technology, vol. 25, no. 7, pp.1823-1835, 2011

Abstract : The unified equations to obtain the exact solutions for piezoelectric plane beam subjected to arbitrary mechanical and electrical loads with various ends supported conditions is founded by solving functional equations. Comparing this general method with traditional trialand- error method, the most advantage is it can obtain the exact solutions directly and does not need to guess and modify the form of stress function or electric displacement function repeatedly. Firstly, the governing equation for piezoelectric plane beam is derived. The general solution for the governing equation is expressed by six unknown functions. Secondly, in terms of boundary conditions of the two longitudinal sides of the beam, six functional equations are yielded. These equations are simplified to derive the unified equations to solve the boundary value problems of piezoelectric plane beam. Finally, several examples show the correctness and generalization of this method.

Keyword : Functional equation; Piezoelectric plane beam; Exact solution; Arbitrary load; Elasticity theory