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| Free vibration analysis of non-uniform micro-beams based on modified couple stress theory and high order shear deformation theory |
| Received:February 25, 2016 Revised:June 14, 2016 |
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| DOI：10.7511/jslx201703005 |
| KeyWord:modified couple stress theory high order shear deformation theory non-uniform beam scale effect free vibration |
| Author | Institution |
| 贺丹 |
沈阳航空航天大学 辽宁省飞行器复合材料结构分析与仿真重点实验室, 沈阳 |
| 杨万里 |
沈阳航空航天大学 辽宁省飞行器复合材料结构分析与仿真重点实验室, 沈阳 |
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| Abstract: |
| A free vibration model of micro non-uniform Reddy beam which contains only one internal material length scale parameter is developed based on the modified couple stress theory in conjunction with the high order shear deformation theory.The scale effects in the free vibration of non-uniform micro beams and the effect of transverse shear deformation on the natural frequencies are investigated.The Hamilton’ s principle is employed to derive the equations and the boundary conditions.The differential quadrature method is employed to numerically solve the governing equations with different boundary conditions.Illustrative examples indicate that the natural frequencies predicted by the present model are always higher than that by classical theory,i.e.the scale effects are captured.Moreover,the closer the geometry size to the material scale length parameter,the more apparent the scale effects are,and the effects of transverse shear deformation are more apparent in smaller length-thickness ratios. |