基于声子晶体理论的弹性地基梁的振动特性研究

陈启勇; 胡少伟; 张子明

doi:10.3879/j.issn.1000-0887.2014.01.004

基于声子晶体理论的弹性地基梁的振动特性研究

doi: 10.3879/j.issn.1000-0887.2014.01.004

¹河海大学力学与材料学院, 南京 210098;²南京水利科学研究院材料结构所, 南京 210029

详细信息

作者简介:
陈启勇(1986—)，男，南京人，博士生(E-mail: chenqiyong@outlook.com);

中图分类号: O422.6
计量
- 文章访问数: 1590
- HTML全文浏览量: 216
- PDF下载量: 1100
- 被引次数: 0
出版历程
- 收稿日期: 2013-08-26
- 修回日期: 2013-09-03
- 刊出日期: 2014-01-15

Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory

¹ College of Mechanics & Materials, Hohai University,Nanjing 210098, P.R. China;²Department of Materials & Structure Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, P.R. China

摘要

摘要: 荷载影响结构的振动特性，引起抗振性能的变化．借助声子晶体理论，研究弹性地基梁的带隙特性，建立了轴向力作用时Winkler地基上声子晶体Euler梁弯曲振动模型，采用改进的传递矩阵法，计算出梁的能带结构，判断出能带结构的变化趋势．研究表明，轴力改变能带结构，带隙范围发生变化．拉力提升带隙，但地基带隙保持不变；压力降低带隙频率，地基带隙随着压力的增加而减小．同时，进行Euler模型的数值模拟，仿真的结果与理论值基本吻合．通过轴力可以调节带隙的频率范围，达到抗振、减振的效果.
- 声子晶体 /
- 弹性地基梁 /
- 带隙
Abstract: Axial loads imposed on the structure influence the vibration properties and cause the change of vibration resistance functions. Theory about the band gap properties of phononic crystals (PCs) were used to study the flexural vibration band gaps of an Euler beam on elastic foundation. A flexural vibration model of the infinite periodic PCs Euler beam was established, which was under the actions of axial force and Winkler foundation. A modified transfer matrix (MTM) method was applied to calculate the band structure of the beam. The change tendency of the band structure were estimated on the basis of the band structure. Results show that axial loads influence the band gaps and band frequency ranges. Axial tensile loads elevate the band gap frequencies, but the base band gaps remain unchanged; axial compressive loads lower the band gap frequencies, and the base band gap frequencies drop when the amplitudes of the compressive loads increase. Meanwhile, the Euler beam model was numerically simulated, and the results were matched with the analytical ones. Through adjusting the magnitude of the axial loads, different band frequency ranges and effects of vibration reduction could be achieved.
- phononic crystal /
- beam on elastic foundation /
- band gap

HTML全文

参考文献(15)

[1]	McLean D J. Solar Radiophysics [M]. London: Cambridge University Press, 1985.
[2]	HUANG Guang-li. Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares[J]. Astrophysics and Space Science,2009, 321(2): 79-89.
[3]	Aschwanden M J. Particle Acceleration and Kinematics in Solar Flares [M]. Netherlands: Springer, 2002: 187-227.
[4]	Sakai J I, Kitamoto T, Saito S. Simulation of solar type III radio bursts from a magnetic reconnection[J]. The Astrophysical Journal Letters,2005, 622(2): 157-160.
[5]	Grechnev V V, White S M, Kundu M R. Quasi-periodic pulsations in a solar microwave burst[J]. Astrophysical Journal,2003, 588(2): 1163-1175.
[6]	HUANG Guang-li, JI Hai-sheng. Radio, hard X-ray, EUV and optical study of september 9, 2002 solar flare[J]. Astrophysics and Space Science,2006, 301(1/4): 65-71.
[7]	MO Jia-qi, LIN Su-rong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J]. Chin Phys B,2009, 18(9): 3628-3631.
[8]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J].Commun Theor Phys,2011, 55(3): 387-390.
[9]	MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chin Phys B,2010, 19(10): 100203.
[10]	MO Jia-qi, LIN Wan-tao, WANG Hui. A class of homotopic solving method for ENSO model[J]. Acta Math Sci,2009, 29(1): 101-110.
[11]	姚静荪, 欧阳成, 陈丽华, 莫嘉琪. 非线性扰动耦合Schrodinger系统激波的近似解法[J]. 应用数学和力学, 2012, 33(12): 1477-1486.(YAO Jing-sun, OUYANG Cheng, CHEN Li-hua, MO Jia-qi. Approximate solving method of shock for nonlinear disturbed coupled Schrdinger system[J]. Applied Mathematics and Mechanics,2012, 33(12): 1477-1486.(in Chinese))
[12]	李晓静. 厄尔尼诺大气物理机制的周期解[J]. 物理学报, 2008, 57(9): 5366-5368.(LI Xiao-jing. The periodic solutions of EI Nio mechanism of atmospheric physics[J]. Acta Physica Sinica,2008, 57(9): 5366-5368.(in Chinese))
[13]	Tang X H, LI Xiao. Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential[J]. Nonlinear Analysis: Theory, Methods & Applications,2009, 71(3/4): 1124-1132.
[14]	Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations [M]. Berlin: Springer, 1977.
[15]	Kivelson M G, Russell C T. Introduction to Space Physics [M]. Cambridge, New York: Cambridge University Press, 1995.