Abstract
A single-elastic beam model is being developed based on Eringens nonlocal elasticity and Timoshenko beam theory. Nonlocal parameter takes into account the small scale effects in the analysis of nano-size structures. Derived herein is a decoupled sixth-order nonlocal governing differential equations for the frequency and stability analysis of nano-scale short beams. The effect of shear deformation is thereby included in the small scale analysis. A Differential Quadrature (DQ) approach is being applied and its elaborate method of solution is illustrated. The higher order DQ approach is found to be a good numerical technique for the convenient and rapid solution of the aforementioned nonlocal problems. Frequency and buckling results for various scale-based nonlocal parameters are shown. Effect of number of interpolation points on the accuracy of the results is also investigated. It is seen that there is a significant effect of aspect ratio and nonlocal parameter on the nonlocal frequency and buckling loads of nano-scale beams. Also, the present study could open up a new approach of solution technique for the analysis of nano-scale structures based on nonlocal Timoshenko theory.