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


Mechanical Engineering Department, Urmia University, Urmia, Iran


This study investigates the dynamic response of an electrostatically deflected capacitive cantilever functionally graded (FG) micro-beam subjected to a harmonically varying thermal load, which is incited vibration due to different material properties of the beam constituents and thermo-elastic coupling effect. The FG beam is made of 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 infinite speed of heat transportation, the equation of motion and the conventional coupled energy equation are derived. Applying Galerkin formulation and then using Rung-kutta method as an efficient 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 results are presented for all types.Numerical results are shown the response of a cantilever FG micro-beam subjected to a harmonically varying temperature input. Moreover, the influences of the beam ceramic constituent percentage on the stability, vibrational behavior and natural frequency are presented.