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TECHNICAL PAPERS

Dynamic Snap-Through of a Shallow Arch Under a Moving Point Load

[+] Author and Article Information
Jen-San Chen, Jian-San Lin

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617

J. Vib. Acoust 126(4), 514-519 (Dec 21, 2004) (6 pages) doi:10.1115/1.1804991 History: Received October 01, 2002; Revised March 01, 2004; Online December 21, 2004
Copyright © 2004 by ASME
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References

Timoshenko,  S. P., 1935, “Buckling of Flat Curved Bars and Slightly Curved Plates,” ASME J. Appl. Mech., 2, pp. 17–20.
Fung, Y. C., and Kaplan, A., 1952, “Buckling of Low Arches or Curved Beams of Small Curvature,” NACA Technical Note 2840.
Gjelsvik,  A., and Bonder,  S. R., 1962, “The Energy Criterion and Snap Buckling of Arches,” J. Eng. Mech. Div., 88, pp. 87–134.
Franciosi,  V., Augusti,  G., and Sparacio,  R., 1964, “Collapse of Arches Under Repeated Loading,” J. Struct. Div. ASCE, 90, pp. 165–201.
Schreyer,  H. L., and Masur,  E. F., 1966, “Buckling of Shallow Arches,” J. Eng. Mech. Div., 92, pp. 1–19.
Lee,  H. N., and Murphy,  L. M., 1968, “Inelastic Buckling of Shallow Arches,” J. Eng. Mech. Div., 94, pp. 225–239.
Simitses,  G. J., 1973, “Snapping of Low Pinned Arches on an Elastic Foundation,” ASME J. Appl. Mech., 40, pp. 741–744.
Roorda,  J., 1965, “Stability of Structures With Small Imperfections,” J. Eng. Mech. Div., 91, pp. 87–106.
Simitses, G. J., 1990, Dynamic Stability of Suddenly Loaded Structures, Springer-Verlag, New York.
Hoff,  N. J., and Bruce,  V. G., 1954, “Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches,” J. Math. Phys., 32, pp. 276–288.
Hsu,  C. S., 1967, “The Effects of Various Parameters on the Dynamic Stability of a Shallow Arch,” ASME J. Appl. Mech., 34, pp. 349–358.
Hsu,  C. S., 1968, “Stability of Shallow Arches Against Snap-Through Under Timewise Step Loads,” ASME J. Appl. Mech., 35, pp. 31–39.
Hsu,  C. S., Kuo,  C. T., and Lee,  S. S., 1968, “On the Final States of Shallow Arches on Elastic Foundations Subjected to Dynamical Loads,” ASME J. Appl. Mech., 35, pp. 713–723.
Xu,  J.-X., Huang,  H., Zhang,  P.-Z., and Zhou,  J.-Q., 2002, “Dynamic Stability of Shallow Arch With Elastic Supports—Application in the Dynamic Stability Analysis of Inner Winding of Transformer During Short Circuit,” Int. J. Non-Linear Mech., 37, pp. 909–920.
Lin,  J.-S., and Chen,  J.-S., 2003, “Dynamic Snap-Through of a Laterally Loaded Arch Under Prescribed End Motion,” Int. J. Solids Struct., 40, pp. 4769–4787.
Chen,  J.-S., and Lin,  J.-S., 2004, “Effects of Prescribed End Motion on the Dynamic Stability of a Shallow Arch on an Elastic Foundation,” J. Eng. Mech. Div., 130, pp. 359–362.
Humphreys,  J. S., 1966, “On Dynamic Snap Buckling of Shallow Arches,” AIAA J., 4, pp. 878–886.
Lock,  M. H., 1966, “The Snapping of a Shallow Sinusoidal Arch Under a Step Pressure Load,” AIAA J., 4, pp. 1249–1256.
Lo,  D. L. C., and Masur,  E. F., 1976, “Dynamic Buckling of Shallow Arches,” J. Eng. Mech. Div., 102, pp. 901–917.
Johnson,  E. R., and Mclvor,  I. K., 1978, “The Effect of Spatial Distribution on Dynamic Snap-Through,” ASME J. Appl. Mech., 45, pp. 612–618.
Johnson,  E. R., 1980, “The Effect of Damping on Dynamic Snap-Through,” ASME J. Appl. Mech., 47, pp. 601–606.
Lin, J.-S., 2002, Dynamic Stability of a Shallow Arch Under Prescribed End Motion, Master Thesis, Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York.

Figures

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Schematic diagram of a shallow arch under a moving point load
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Coordinate α1 as a function of load position e for an arch with h=8: (a) Q=18, (b) Q=20, and (c) Q=18.16
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Relation between load Q and position e when snap-through occurs: (a) h=8 and (b) h=3
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The thick lines are the dynamic responses for an arch with h=8, μ=0.001, and Q=18. The thin lines are the same quasi-static results as from Fig. 2(a).
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The thick lines are the dynamic responses for an arch with h=8,Q=25, and μ=0.001. The thin lines are the results from quasi-static analysis.
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Responses after the point load leaves the arch for the two speeds in Fig. 5: (a) c=2.4 and (b) c=2.6. The black dots signify the instant when the point load leaves the arch.
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Dangerous speed zone for an arch with h=8 and μ=0.001. The solid circle indicates that the arch will snap dynamically before settling to a stable equilibrium position. The open circle indicates that the arch will never snap.

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