Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature

Based on the theory of elasticity and piezoelectricity, the method called state-space based differential quadrature method (SSDQM) is extended to study the free vibration of a functionally graded piezoelectric material (FGPM) beam under different boundary conditions. The FGPM beam is approximated as a multi-layered cantilever. The state equations in terms of state variables of every discrete point are established using the differential quadrature technique. It is found that the results obtained in the present paper agree very well with both the finite element results and the results obtained by other investigations in special cases. Furthermore, at the end of this paper, the influence of some material parameters on the natural frequency of the FGPM beam is discussed.