Characteristic orthogonal polynomials-Ritz method for vibration behavior of functionally graded piezoelectric plates using FSDT

This work focuses on the free vibration characteristics of the functionally graded piezoelectric (FGPE) plate with classical and elastic constraints. First, the analytical model is established for the FGPE plate on the basis of the first-order shear deformation theory (FSDT). Besides, different distribution profiles of the material constituent are considered for the FGPE plate model, and various external initial voltages are also considered for modeling the piezoelectric effect. The displacement functions for the FGPE plate are then given in the form of third-kind orthogonal polynomials. Ultimately, the solution of the FGPE plate model is resolved by means of the Ritz method. Convergence and accuracy of the presented model are verified, and a series of parametric investigations are given.