The motion equation of cantilevered pipe conveying pulsating fluid on the nonlinear el-
astic foundation is constructed, and is discretized into ordinary differential equations by the Galerkin method. The effect of parameters including mean flow velocity, fluctuation amplitude, fluctuation frequency and shear stiffness on the nonlinear behavior of system is discussed by the numerical method. The results show that by mean flow velocity as the bifurcation parameter the system can present quasi periodic motion, periodic motion, and chaotic motion; by fluctuation amplitude as bifurcation parameter the system presents the period-2, period-4, period-8, and chaotic motion; by fluctuation frequency as bifurcation parameter the system firstly shows quasi-periodic motion, then chaotic motion nearby second sub harmonic. Furthermore, foundation shear stiffness can suppress the period motion and chaotic motion of system. With shear stiffness increasing, chaos state of system gradually changed into periodic motion until the stable state is obtained.
Key words
cantilevered pipe conveying fluid /
elastic foundation /
period motion /
chaotic motion
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1]Paidoussis M P. Fluid-structure interactions: slender structures and axial flow [M]. London: Academic press, 1998.
[2]Li G, Paidoussis M P. Stability, double degeneracy and chaos in cantilevered pipes conveying fluid [J]. International journal of non-linear mechanics, 1994, 29(1): 83-107.
[3]Panda L, Kar R. Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances [J]. J Sound Vibrat, 2008, 309(3): 375-406.
[4] Namachchivaya N S. Non-linear dynamics of supported pipe conveying pulsating fluid—I. Subharmonic resonance [J]. International journal of non-linear mechanics, 1989, 24(3): 185-96.
[5] Namchchivaya N S, Tien W. Non-linear dynamics of supported pipe conveying pulsating fluid—II. Combination resonance [J]. International journal of non-linear mechanics, 1989, 24(3): 197-208.\
[6] 金基铎, 杨晓东, 尹峰. 两端铰支输流管道在脉动内流作用下的稳定性和参数共振 [J]. 航空学报, 2003, 24(4): 317-22.
Jin Ji-duo,Yang Xiao-dong,Yin Feng. Stability and Parametric Resonances of a Pinned-Pinned Pipe Conveying Pulsating Fluid[J]. ACTA AERONAUTICA ET AS TRONAUTICA SINICA, 2003, 24(4): 317-22.
[7] Wang L. A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid [J]. International journal of non-linear mechanics, 2009, 44(1): 115-21.
[8]Paidoussis M P, Sundararara C. Parametric and combination resonances of a pipe conveying pulsating fluid [J]. Journal of Applied Mechanics, 1975, 42(4): 780-4.
[9]Semier C, Paidoussis M P.. Nonlinear analysis of the parametric resonances of a planar fluid-conveying cantilevered pipe [J]. Journal of fluids and structures, 1996, 10(7): 787-825.
[10]唐冶, 方勃, 张业伟. 非线性弹簧支承悬臂输液管道的分岔与混沌分析 [J]. 振动与冲击, 2011, 30(8): 269-74.
Tang Ye,Fang Bo,Zhang Ye-wei, Li Qing-fei. Bifurcation and chaos analysis of cantilever pipeline conveying fluid with nonlinear spring support[J].Journal of vibration and shock, 2011,30(8):269-274.
[11] 张紫龙, 唐敏, 倪樵. 非线性弹性地基上悬臂输流管的受迫振动 [J]. 振动与冲击, 2013, 32(10): 17-21.
Zhang Zi-long ,Tang Min,Ni Qiao. Forced vibration of a cantilever fluid-conveying pipe on nonlinear elastic foundation. Journal of vibration and shock,2013,32(10):17-20.
[12]蒲 育，滕兆春.Winkler-Pasternak弹性地基FGM梁自由振动二维弹性解[J].振动与冲击,2015,34(20):74-79.
PU Yu,TENG Zhao-chun.Two-dimensional elasticity solutions for free vibration of FGM beams resting on Winkler-Pasternak elastic foundations[J].Journal of Vibration and Shock,2015,34(20):74-79.
{{custom_fnGroup.title_en}}
Footnotes
{{custom_fn.content}}
PDF(2043 KB)
