Free Vibration Analysis of a Functionally Graded Piezoelectric Beam Based on Higher-order Beam Theory Using the Finite Fourier Transformation Method

This paper presents the free vibration characteristics of a laminated functionally graded piezoelectric material (FGPM) beam using the higher-order shear deformation beam theory. The beam consists of three layers; the top and bottom homogeneous layers are divided by a non-homogeneous FGPM transit interlayer. The material properties of the FGPM interlayer are assumed to vary through the thickness direction following a power law distribution. The beam is simply supported and grounded in its two ends. The governing equations are derived using Hamilton's principle. The resulting system of differential equations of vibration is solved using the analytical hybrid Fourier method. Initially, the convergence of the present solution is examined and the obtained results are compared with previous studies and Finite Element Method (FEM). The effects of parameters, such as the material composition, beam's geometry and shear deformation on natural frequencies are investigated. In addition, by changing the thickness of the FGPM interlayer the present model is compared with the traditional bimorph actuators.

کلیدواژه ها:

Functionally graded piezoelectric material (FGPM) ، higher-order shear deformationbeam theory ، hybrid Fourier method ، free vibration ، Hamilton's principal