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TECHNICAL PAPERS

Vibro-Impact Dynamics of a Periodically Forced Beam

[+] Author and Article Information
Jakob Knudsen

Malmö University, SE 205 06 Malmö, Sweden

Ali R. Massih

Luleå University of Technology, SE 971 87 Luleå, SwedenABB Atom AB, SE 721 63 Västerås, Sweden

J. Pressure Vessel Technol 122(2), 210-221 (Jan 27, 2000) (12 pages) doi:10.1115/1.556175 History: Received June 14, 1999; Revised January 27, 2000
Copyright © 2000 by ASME
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References

Moon, F. C., 1992, Chaotic and Fractal Dynamics: an Introduction for Applied Scientists and Engineers, Wiley, New York, NY.
Shaw,  S. W., and Holmes,  P. J., 1983, “A Periodically Forced Piecewise Linear Oscillator,” J. Sound Vib., 90, pp. 129–155.
Axisa,  F., Antunes,  I., and Villard,  B., 1988, “Overview of Numerical Methods for Predicting Flow-Induced Vibration,” ASME J. Pressure Vessel Technol., 110, pp. 6–14.
de Langre, E., Doveil, F., Porcher, G., and Axisa, F., 1990, “Chaotic and Periodic Motion of a Non-Linear Oscillator in Relation with Flow-Induced Vibration of Loosely Supported Tubes,” ASME PVP-Vol. 189, pp. 119–125.
Rogers,  R. J., and Pick,  R. J., 1976, “On the Dynamic Spatial Response of a Heat Exchanger Tube with Intermittent Baffle Contacts,” Nucl. Eng. Des., 36, No. 1, pp. 81–90.
Axisa,  F.Dessaux,  A.Gilbert  R. J., 1984, “Experimental Study of Tube/Support Impact Forces in Multi-Span PWR Steam Generator Tubes,” ASME Symp. Flow-Induced Vibr., 3, pp. 139–148.
Axisa,  F.Izquiedero,  P., 1992, “Experiments on Vibro-Impact Dynamics of Loosely Supported Tubes Under Harmonic Excitation,” ASME PVP-Vol. 242, Symp. Flow-Induced Vibr. Noise, 2, pp. 281–299.
Sauvé,  R. G., and Teper,  W. W., 1987, “Impact Simulation of Process Equipment and Support Plates—A Numerical Algorithm,” ASME J. Pressure Vessel Technol., 109, pp. 70–79.
Johansson,  L., 1997, “Beam Motion with Unilateral Contact Constraints and Wear of Contact Sites,” ASME J. Pressure Vessel Technol., 119, pp. 1–6.
Knudsen, J., Massih, A. R., and Johansson, L., 1997, “Calculation of Vibro-Impact Dynamics of Loosely Supported Rods,” ASME AD-Vol. 53-1, Fluid-Structure Interaction, Aeroelasticity, Flow-Induced Vibration and Noise, I , pp. 229–237.
Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
de Langre, E., and Phallipou, C, 1996, personal communication.
Knudsen, J., and Massih, A. R., 1999, “Analysis of Loosely Supported Beam Under Harmonic Excitation,” ASME PVP-Vol. 389, Flow-Induced Vibration, pp. 265–272.
Archard,  J. F., 1953, “Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24, pp. 981–988.
Frick, T. M., Sobek, E., and Reavis, J. R., 1984, “Overview on the Development and Implementation of Methodologies to Compute Vibration and Wear of Steam Generator Tubes,” ASME Special Publication, Symposium on Flow-Induced Vibrations in Heat Exchangers, eds., M. P. Paidoussis, J. M. Chenoweth, and M. D. Bernstein, New Orleans, LA, December 9–14.
Antunes, J., Axisa, F., Beaufils, B., and Guilbaud, D., 1988, “Coulomb Friction Modelling in Numerical Simulations of Vibration and Wear Work Rate of Multispan Tube Bundles,” ASME Symposium on Flow-Induced Vibration and Noise, Flow-Induced Vibration in Heat Transfer Equipment, 5 , pp. 157–176.
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Figures

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Contact point geometry and definitions
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Sketch of the cantilever beam with loose supports at one end subject to a time-varying force
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Schematic view of the rod-support cell system, showing also the deformed support cell with gaps
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FE representation of portion of beam crossing the support cell, where S identifies a soft spring and B1 and B2 identify the arches
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Vibro-impact dynamic behavior of a loosely supported rod under harmonic excitations with a clearance of 0.25 mm and 0.20 mm in x and y directions, respectively. The driving frequency is 20 Hz. Computations utilize the simple contact algorithm, neglecting friction. (a) Impact force in x direction; (b) force in y direction; (c) Lissajous plots for displacements; (d) phase plane trajectories. The solid line shows measured values while the broken line indicates calculated values.
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Vibro-impact dynamic behavior of a loosely supported rod under harmonic excitations with full Coulomb friction contact algorithm, with μ=0.27. Other input parameters are described in the caption of Fig. 5. (a) Impact force in x direction; (b) force in y direction; (c) Lissajous plots for displacements; (d) phase plane trajectories. The solid line shows measured values while the broken line shows calculated values.
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WWR versus friction coefficient μ. Other input parameters are described in the caption of Fig. 5.
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WWR versus gap size in y direction 2gy with a friction coefficient of μ=0.27 and a clearance in the x direction of 0.25 mm. The forcing frequency is 20 Hz.
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Extreme deflections versus gap size in the y direction. See caption of Fig. 8 for a description of other input parameters. Solid and broken lines denote measurements at 0.492±0.05 m from the supported end, respectively.
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WWR versus the support stiffness proportionality coefficient α. The clearances are set to 0.25 and 0.20 mm for the x and y directions, respectively. The forcing frequency is 20 Hz.
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Single-degree-of-freedom oscillator with two-sided constraints subjected to a harmonic load
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Nondimensional contact velocities of the single-degree-of-freedom harmonic forced two-sided impact oscillator versus frequencies ω∊{1,2,[[ellipsis]]10}
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Nondimensional contact velocity of the simplified cantilever beam with constrained two-sided open supports subjected to harmonic excitation in the nondimensional frequency range ω∊[1,10]
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Nondimensional time evolution of contact velocity for an applied frequency of ω=10, other input parameters are described in Section 5. The symbol ‘−’ stands for the SDOF oscillator, and ‘+’ for the beam.

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