Free Vibration of Functionally Graded Material Beams in a Uniform Electric Field

Free vibration of thermal post-buckled functionally graded material (FGM) beams in a uniform electric field subjected to both temperature rise and voltage is studied. Voltage has a great influence on the deformation of the beam, and Thermo-electric post-buckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity and the material gradient parameters are plotted. It is found that the three lowest frequencies of the pre-buckled beam decrease with an increase in the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.