Accurate analysis of functionally graded piezoelectric beams within symplectic framework

Analytical solutions of the functionally graded piezoelectric beams are investigated under symplectic framework. The material parameters vary along the length in an identical exponential form. The method of separation of variables is adopted to transform the original problem into a symplectic eigenproblem. The eigensolutions of particular eigenvalues are presented which represent the basic mechanical and electric properties, and the general eigensolutions are obtained which describe the localized behaviors which usually covered up by Saint-Venant principle. The accurate elasticity solutions are linear combinations of particular and general eigensolutions. Numerical examples are considered to verify the effectiveness and accuracy of the proposed solutions.