基于应变梯度弹性理论的铁木辛柯微梁模型.pdf

中国科技论文在线 A micro scale Timoshenko beam model based on strain gradient elasticity theory Binglei Wang, Shenjie Zhou, Junfeng Zhao School of Civil Engineering, Shandong University Jinan 250061, P. R. China zhousj@ Abstract ： A micro scale Timoshenko beam model is developed based on strain gradient elasticity theory. Governing equations, initial conditions and boundary conditions are derived simultaneously by using Hamilton’s principle. The new model incorporated with Poisson effect contains three material length scale parameters and can consequently capture the size effect. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. To illustrate the new model, the static bending and free vibration problems of a simply supported micro scale Timoshenko beam are solved respectively. Numerical results reveal that the differences in the deflection, rotation and natural frequency predicted by the present model and the other two reduced Timoshenko models are large as the beam thickness is comparable to the material length scale parameter. These differences, however, are decreasing or even diminishing with the increase of the beam thickness. In addition, Poisson effect on the beam deflection, rotation and natural frequency possesses an interesting “extreme point” phenomenon, which is quite different from that predicted by the classical Timoshenko beam model. Keywords: Micro scale; Timoshenko beam; Size effect; Strain gradient 1. Introduction Micro scal