A Nonlinear Microbeam Model Based on Strain Gradient Elasticity Theory

被引：0
作者：
Farshid Rajabi
Shojaa Ramezani
机构：
[1] Islamic Azad University,Department of Mechanical Engineering
[2] University of Guilan,Department of Mechanical Engineering, Faculty of Engineering
来源：
Acta Mechanica Solida Sinica | 2013年 / 26卷
关键词：
strain gradient elasticity; microbeam; geometric nonlinearity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A micro scale nonlinear beam model based on strain gradient elasticity is developed. Governing equations of motion and boundary conditions are obtained in a variational framework. As an example, the nonlinear vibration of microbeams is analyzed. In a beam having a thickness to length parameter ratio close to unity, the strain gradient effect on increasing the natural frequency is predominant. By increasing the beam thickness, this effect decreases and geometric nonlinearity plays the main role on increasing the natural frequency. For some specific ratios, both geometric nonlinearity and size effects have a significant role on increasing the natural frequency.
引用
收藏
页码：21 / 34
页数：13
相关论文
共 85 条
[1]  
Fleck NA(1994)Strain gradient plasticity: theory and experiment Acta Metallurgical et Materialia 42 475-487
[2]  
Muller GM(2005)Role of material microstructure in plate stiffness with relevance to microcantilever sensors Journal of Micromechanics and Microengineering 15 1060-1067
[3]  
Ashby MF(2008)A microstructure-dependent Timoshenko beam model based on a modified couple stress theory Journal of the Mechanics and Physics of solids 56 3379-3391
[4]  
McFarland AW(1964)Couple stresses in the theory of elasticity, Parts I & II Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B 67 17-44
[5]  
Colton JS(2000)Effect of couple-stresses on the elastic bending of beams International Journal of Solids and Structures 37 1003-1018
[6]  
Ma HM(2006)Bernoulli-Euler beam model based on a modified couple stress theory Journal of Micromechanics and Microengineering 16 2355-2359
[7]  
Gao XL(2008)The size-dependent natural frequency of Bernoulli-Euler microbeams International Journal of Engineering Science 46 427-437
[8]  
Reddy JN(2002)Couple stress based strain gradient theory for elasticity International Journal of Solids and Structures 39 2731-2743
[9]  
Koiter WT(2010)Investigation of the size effects in Timoshenko beams based on the couple stress theory Archive of Applied Mechanics 81 863-874
[10]  
Anthoine A(2010)On the size-dependent behavior of functionally graded microbeams Materials & Design 31 2324-2329
123456789