Effect of temperature on free vibration of functionally graded microbeams

Modified couple stress theory is applied to study of temperature effects on free vibration of Timoshenko functionally graded microbeams. Due to the interatomic and microstructural reactions of the structures in micro scale, the dynamic behavior of the microbeam is predicted more accurate applying the couple stress theory. Both of the simply supported and clamped boundary conditions are assumed to obtain the natural frequencies of the beam. The natural frequencies are obtained by minimization of the Lagrange function and applying the Ritz method. Finally, effects of various parameters such as; temperature change, power law index, height to length scale parameter ratio and height to length ratio on natural frequencies of the microbeam are presented and discussed in detail. The results obtained in this work is validated against numerical data given in the literature search.