Abstract: In order to improve the reliability and accuracy for beam models in predicting static and dynamic responses, vibration and buckling behaviors of functionally graded piezoelectric material(FGPM) beams in thermal environment and under the action of external electric voltage and axial mechanical load are studied based on an n-th order generalized beam theory. Various types of temperature distributions through the thickness of a beam are considered and the piezoelectric material properties are described by Voigt mixture power-law model, static and dynamic models for the system are built using Hamilton principle as a unity and Navier method is utilized to solve the dynamic response for FGPM simply supported beams. The effects of various beam theories, different cases of temperature distribution, thermal-mechanical-electrical loads, material graded index and slenderness ratio on the frequency and critical buckling load of FGPM beams are analyzed. Considering various factors, the binary relations between the coupling buckling and vibration behaviors are also illustrated. The results show that the vibration control and stability design of FGPM beams subjected to thermal-mechanical-electrical loads can be performed by changing the external voltage and polarization direction.

Key words: functionally graded piezoelectric material beams, thermal-mechanical-electrical effects, n-th order generalized beam theory, coupling vibration, coupling buckling