Vibration and Buckling of Microstructure-Dependent Timoshenko MicroBeams and Finite Element Implementations with R

Abstract

The free oscillatory and elastic instability behaviours of microstructure-dependent beams are considered in this chapter. The equations governing these behaviours are established in accordance with the Timoshenko beam theory within the framework of the modified couple stress theory. For the free vibration analysis, the coupled partial differential equations exhibit space-time dependency, while only space dependency exists for buckling analyses. In each case, the effect of couple stress is considered under different boundary conditions using the finite element method. The variations of the natural frequencies (in the case of a free vibration analysis) and the critical buckling loads (for the buckling analysis) with changes in the small-scale parameter are evaluated and presented.