Thermally induced vibration of an electro-statically deected functionally graded micro-beam considering thermo-elastic coupling effect

This study investigates the dynamic response of an electrostatically deected capacitive cantilever Functionally Graded (FG) micro-beam subjected to a harmonically varying thermal load, which incites vibration due to the different material properties of the beam constituents and the thermo-elastic coupling effect. The FG beam is made of a mixture of metal and ceramic, where the material properties vary continuously through the thickness according to an exponential distribution law (E-FGM). Assuming the Euler-Bernoulli beam theory and the infnite speed of heat transportation, the equation of motion and the conventional coupled energy equation are derived. Applying Galerkin formulation and then using the Rung-kutta method as an eficient numerical tool, these equations are simultaneously solved. Changing the ceramic constituent percentage of the bottom surface, five different types of FGM micro-beams are investigated and the results are presented for all types. Numerical results show the response of a cantilever FG microbeam subjected to a harmonically varying temperature input. Moreover, the inuences of the beam ceramic constituent percentage on stability, vibrational behavior and natural frequency are presented.