Nonlinear Vibration Analysis of Piezoelectric Functionally Graded Porous Timoshenko Beams

In this paper, nonlinear vibration analysis of functionally graded piezoelectric (fgp) beam with porous materials is investigated based on the timoshenko beam theory. material properties of fg porous beam are described according to the rule of mixture which is modified to approximate material properties with porosity phases. ritz method is used to obtain the governing equation which is then solved by a direct iterative method to determine the nonlinear vibration frequencies of fgp porous beam subjected to different boundary conditions.the effects of external electric voltage, material distribution profile, porosity volume fraction, slenderness ratios and boundary conditions on the nonlinear vibration characteristics of the fgp porous beam are discussed in detail. the results indicate that piezoelectric layers have a significant effect on the nonlinear frequencies. also, it is found that porosity has a considerable influence on the nonlinear frequency, especially when the electric voltage is applied.