全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
力学学报  2015 

基于应变梯度中厚板单元的石墨烯振动研究

DOI: 10.6052/0459-1879-15-074, PP. 751-761

Keywords: 应变梯度,有限元,明德林板,振动,尺度效应

Full-Text   Cite this paper   Add to My Lib

Abstract:

基于应变梯度理论建立了单层石墨烯等效明德林(Mindlin)板动力学方程,推导了四边简支明德林中厚板自由振动固有频率的解析解.提出了一种考虑应变梯度的4节点36自由度明德林板单元,利用虚功原理建立了单层石墨烯的等效非局部板有限元模型.通过对石墨烯振动问题的研究,验证了应变梯度有限元计算结果的收敛性.运用该有限元法研究了尺寸、振动模态阶数以及非局部参数对石墨烯振动特性的影响.研究表明,这种单元能够较好地适用于研究考虑复杂边界条件石墨烯的尺度效应问题.基于应变梯度理论的明德林板所获得石墨烯的固有频率小于基于经典明德林板理论得到的结果.尺寸较小、模态阶数较高的石墨烯振动尺度效应更加明显.无论采用应变梯度理论还是经典弹性本构关系,考虑一阶剪切变形的明德林板模型预测的固有频率低于基尔霍夫(Kirchho)板所预测的固有频率.

References

[1]  Novoselov KS, Geim AK, Morozov SV, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696): 666-669
[2]  Stelmashenko NA, Walls MG, Brown LM, et al. Microindentations on W and Mo oriented single crystals: an STM study. Acta Metallurgica et Materials, 1993, 41(10): 2855-2865
[3]  Fleck NA, Muller GM, Ashby MF, et al. Strain gradient plasticity: theory and experiment. Acta Metallurgica et Materials, 1994, 42: 475-487
[4]  Stolken JS, Evans AG. A microbend test method for measuring the plasticity length scale. Acta Metallurgica et Materials, 1998, 46: 5109-5115
[5]  Wang LF, Hu HY. Flexural wave propagation in single-walled carbon nanotubes. Physical Review B, 2005, 71: 195412
[6]  冯秀艳, 郭香华, 方岱宁等. 微薄梁三点弯曲的尺度效应研究. 力学学报,2007,39(4): 479-485 (Feng Xiuyan, Guo Xianghua, Fang Daining, et al. Three-point microbend size effects for pure Ni foils. Chinese Journal of Theoretical and Applied Mechanics, 2007,39(4): 479-485 (in Chinese))
[7]  Bazant ZP, Jirasek M. Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics, 2002, 128(11): 1119-1149
[8]  Papargyri-Beskou S, Beskos DE. Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates. Archive of Applied Mechanics, 2008, 78(8): 625-635
[9]  Lazopoulos KA. On the gradient strain elasticity theory of plates. European Journal of Mechanics, 2004, 23(5): 843-852
[10]  Lazopoulos KA. On bending of strain gradient elastic micro-plates. Mechanics Research Communications, 2009, 36(7): 777-783
[11]  徐巍, 王立峰, 蒋经农. 基于应变梯度有限元的单层石墨烯振动研究. 固体力学学报,2014,35(5): 441-450 (Xu Wei, Wang Lifeng, Jiang Jingnong. Finite element analysis of strain gradient on the vibration of single-layered graphene sheets. Chinese Journal of Solid Mechanics, 2014, 35(5): 441-450 (in Chinese))
[12]  Pradhan SC, Phadikar JK. Nonlocal elasticity theory for vibration of nanoplates. Journal of Sound and Vibration, 2009, 325: 206-223
[13]  Ma HM, Gao XL, Reddy JN. A non-classical mindlin plate model based on a modified couple stress theory. Acta Mechanica, 2011, 220: 217-235
[14]  Zhang B, He YM, Liu DB, et al. A non-classical mindlin plate finite element based on a modified couple stress theory. European Journal of Mechanics A/Solids, 2013, 42: 63-80
[15]  Shi JX, Ni QQ, Lei XW, et al. Study on wave propagation characteristics of double-layer graphene sheets via nonlocal Mindlin-Reissner plate theory. International Journal of Mechanical Sciences, 2014, 84: 25-30
[16]  Arash B, Wang Q, Liew KM. Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation. Computer Methods in Applied Mechanics and Engineering, 2012, 223: 1-9
[17]  Soh A, Chen WJ. Finite element formulations of strain gradient theory for microstructures and the C^0-1 patch test. International Journal for Numerical Methods in Engineering, 2004, 61(3): 433-454
[18]  Ansari R, Rajabiehfard R, Arash B. Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Computational Materials Science, 2010, 49(4):831-838
[19]  Askes H, Suiker ASJ, Sluys LJ. A classification of higher-order strain-gradient models - linear analysis. Archive of Applied Mechanics, 2002, 72: 171-188
[20]  赵杰, 陈万吉, 冀宾. 关于两种二阶应变梯度理论. 力学学报,2010,42(1): 138-145 (Zhao Jie, Chen Wanji, Ji Bin. A study on the two second-order strain gradient theories. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 138-145 (in Chinese))
[21]  Liu RM, Wang LF. Thermal vibrations of single-layered graphene sheets by molecular dynamics. Journal of Nanoscience and Nanotechnology, 2013, 13(2): 1059-1062

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133