Abstract
The Hopf bifurcation and chaotic motions of a tubular cantilever impacting on loose support is studied using an analytic model that involves delay differential equations. By using the damping-controlled mechanism, a single flexible cantilever in an otherwise rigid square array of cylinders is analyzed. The analytical model, after Galerkin discretization to five d.o.f., exhibits interesting dynamical behavior. Numerical solutions show that, with increasing flow beyond the critical, the amplitude of motion grows until impacting with the loose support placed at the tip end of the cylinder occurs; more complex motions then arise, leading to chaos and quasi-periodic motions for a sufficiently high flow velocity. The effect of location of the loose support on the global dynamics of the system is also investigated.
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References
Paidoussis, M.P.: Flow-induced vibration in nuclear reactors and heat exchangers: practical experiences and state of knowledge. In: Naudascher, E., Rockwell, D. (eds.) Practical Experiences in Flow-Induced Vibrations, pp. 1–81. Springer, Berlin (1980)
Lever, J.H., Weaver, D.S.: A theoretical model for the fluidelastic instability in heat exchanger tube bundles. J. Press. Vessel Technol. 104, 147–158 (1982)
Price, S.J., Paidoussis, M.P.: A single-flexible-cylinder analysis for the fluidelastic instability of an array of flexible cylinders in cross-flow. J. Fluids Eng. 108, 193–199 (1986)
Price, S.J., Paidoussis, M.P.: An improved mathematical model for the instability of cylinder rows subject to cross-flow. J. Sound Vib. 97, 615–640 (1984)
Chen, S.S.: Instability mechanics and stability criteria of a group of circular cylinders subject to cross-flow. J. Vib. Acoust., Stress Reliab. Des. 105, 51–58 (1983)
Lever, J.H., Weaver, D.S.: On the stability of heat exchanger tube bundles, parts I and II. J. Sound Vib. 107, 375–392, 393–410 (1986)
Paidoussis, M.P.: Flow-induced instabilities of cylindrical structures. Appl. Mech. Rev. 40, 163–175 (1987)
Chen, S.S.: A general theory for dynamic instability of tube arrays in cross-flow. J. Fluids Struct. 1, 35–53 (1987)
Price, S.J.: A review of theoretical models for fluidelastic instability of cylinder arrays in cross-flow. J. Fluids Struct. 9, 463–518 (1995)
Price, S.J., Valerio, N.R.: A non-linear investigation of single-degree-of-freedom instability in cylinder arrays subject to cross flow. J. Sound Vib. 137, 419–432 (1990)
Paidoussis, M.P., Li, G.X.: Cross-flow-induced chaotic vibrations of heat-exchanger tubes impacting on loose supports. J. Sound Vib. 152, 305–326 (1992)
de Bedout, J.M., Franchek, M.A., Bajaj, A.K.: Robust control of chaotic vibrations for impacting heat exchanger tubes in crossflow. J. Sound Vib. 227, 183–204 (1999)
Cai, Y., Chen, S.S.: Chaotic vibrations of nonlinearly supported tubes in crossflow. ASME J. Press. Vessel Technol. 115, 128–134 (1993)
Hassan, M., Hayder, M.: Modelling of fluidelastic vibrations of heat exchanger tubes with loose supports. Nucl. Eng. Des. 238, 2507–2520 (2008)
Hassan, M., Weaver, D., Dokainish, M.: A simulation of the turbulence response of heat exchanger tubes in lattice-bar supports. J. Fluids Struct. 16(8), 1145–1176 (2002)
Paidoussis, M.P., Li, G.X., Moon, F.C.: Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. J. Sound Vib. 135, 1–19 (1989)
Paidoussis, M.P., Li, G.X., Rand, R.H.: Chaotic motions of a constrained pipe conveying fluid: comparison between simulation, analysis and experiment. J. Appl. Mech. 58, 559–565 (1991)
Wang, L.: A further study on the nonlinear dynamics of simply supported pipes conveying pulsating fluid. Int. J. Non-Linear Mech. 44, 115–121 (2009)
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Wang, L., Ni, Q. Hopf bifurcation and chaotic motions of a tubular cantilever subject to cross flow and loose support. Nonlinear Dyn 59, 329–338 (2010). https://doi.org/10.1007/s11071-009-9542-8
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DOI: https://doi.org/10.1007/s11071-009-9542-8