| Based on the theory of piezo-elasticity, a method called SSDQM (state-space based differential quadrature method) is extended to study the free vibration of a functional gradient piezoelectric material (FGPM) beam firstly. The FGPM beam is approximated as a multi-layered model, of which the solution will gradually approach the exact one with the increase of the number of layers. The material properties are treated as piecewise constants. Then, the free vibration of a piezoelectric-elastic laminated beam is studied in this paper. The results obtained in the present paper agree very well with both the results of other references and the finite element results. Finally, the influence of some parameters and electricity boundary conditions on the natural frequency of the beam is discussed. Numerical examples demonstrate that the convergence speed of present method is fast. The method proposed in this paper is convenient for vibration analysis of FGPM beam or piezoelectric-elastic laminated beam. |
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