Experiment and Analysis on the Free Dynamics of a Shallow Arch After an Impact Load at the End

[+] Author and Article Information
Jen-San Chen, Chun-Yi Liao

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

J. Appl. Mech 72(1), 54-61 (Feb 01, 2005) (8 pages) doi:10.1115/1.1827245 History: Received July 15, 2003; Revised March 18, 2004; Online February 01, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.


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,” ASCE J. Struct. Div., 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, 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.
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.
Huang,  N. N., and Nachbar,  W., 1968, “Dynamic Snap-Through of Imperfect Viscoelastic Shallow Arches,” ASME J. Appl. Mech., 35, pp. 289–296.
Ariaratnam,  S. T., and Sankar,  T. S., 1968, “Dynamic Snap-Through of Shallow Arches Under Stochastic Loads,” AIAA J., 6, pp. 798–802.
Fulton,  R. E., and Barton,  F. W., 1971, “Dynamic Buckling of Shallow Arches,” J. Eng. Mech. Div., 97, pp. 865–877.
Sundararajan,  V., and Kumani,  D. S., 1972, “Dynamic Snap-Buckling of Shallow Arches Under Inclined Loads,” AIAA J., 10, pp. 1090–1091.
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.
Huang, K. Y., and Plaut, R. H., 1982, “Snap-Through of a Shallow Arch Under Pulsating Load,” Stability in the Mechanics of Continua, F. H. Schroeder, ed., Springer, Berlin, pp. 215–223.
Gregory,  W. E., and Plaut,  R. H., 1982, “Dynamic Stability Boundaries for Shallow Arches,” J. Eng. Mech. Div., 108, pp. 1036–1050.
Donaldson,  M. T., and Plaut,  R. H., 1983, “Dynamic Stability Boundaries for a Sinusoidal Arch Under Pulse Loads,” AIAA J., 21, pp. 469–471.
Liao, C.-Y., 2003, “Experiment and Analysis of a Flexibly Supported Arch Under Impact at the End,” Master thesis, Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan.
Rao, S. S., 1995, Mechanical Vibrations, 3rd ed., Addision-Wesley, Reading, MA.


Grahic Jump Location
Schematic diagram of a flexibly supported arch under impact at the end
Grahic Jump Location
aj curves on the kh2-a plane
Grahic Jump Location
Strain energy contours for (a) k=0.4,h=10,a=3, (b) k=0.2,h=10,a=0.6, (c) k=0.8,h=10,a=13.8
Grahic Jump Location
Effect of damping μ on the response of the assembly with h=10,k=0.4,a=3,vi=110,m=0.001. (a) μ=0.2, (b) μ=0.3, (c) μ=0.6.
Grahic Jump Location
Schematic diagram of the experimental setup
Grahic Jump Location
A photograph of the experimental setup in the laboratory
Grahic Jump Location
Measured speed history of the attached mass following the impact. Parameters of the assembly are h*=2.80 cm,k*=327 N/cm,a*=0.
Grahic Jump Location
Deflection history at the midpoint of the arch following the impact. The solid lines are the measured response while the dashed lines are the numerical results. (a) h*=3.46 cm,k*=206 N/cm,vi*=1.44 m/s. (b) h*=3.00 cm,k*=333 N/cm,vi*=1.79 m/s.
Grahic Jump Location
Critical initial speed vcr* as a function of (a) wall movement a*, (b) supporting spring constant k*, (c) initial height h* of the arch. Symbol×represents the measured data, while the solid lines are the theoretical predictions.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In