Thermal effect on free vibration and buckling of size-dependent microbeams

Based on the modified couple stress theory, free vibration and buckling of the microbeams with the effect of the temperature change are investigated. The non-classical Timoshenko beam model, which contains a material length scale parameter, is developed to interpret the size effect in microscale structures. The higher-order governing equations and boundary conditions are derived by using the Hamilton principle. The differential quadrature method is employed to determine the natural frequency and the critical buckling load of the microbeams with different boundary conditions. The effects of the temperature change, length scale parameter, slenderness ratio and end supported conditions on the free vibration and buckling of the microbeams are discussed in detail. Results show that the thermal effect on the fundamental frequency and critical buckling load is slight when the thickness of the microbeam has a similar value to the material length scale parameter, but it becomes significant when the thickness of the microbeams becomes larger.