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

CHEN Qi-yong; HU Shao-wei; ZHANG Zi-ming

doi:10.3879/j.issn.1000-0887.2014.01.004

Volume 35 Issue 1

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(1): 29-38

CHEN Qi-yong, HU Shao-wei, ZHANG Zi-ming. Research on the Vibration Property of the Beam on Elastic Foundation Based on the PCs Theory[J]. Applied Mathematics and Mechanics, 2014, 35(1): 29-38. doi: 10.3879/j.issn.1000-0887.2014.01.004

Citation:

PDF( 1278 KB)

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

doi: 10.3879/j.issn.1000-0887.2014.01.004

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

Received Date: 2013-08-26
Rev Recd Date: 2013-09-03
Publish Date: 2014-01-15

Abstract

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

FullText(HTML)

References(15)

References

[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.