Journal of Korean Association for Spatial Structures (한국공간구조학회논문집)

Korean Association for Spatial Structures (한국공간구조학회)
권호 표지
DOI QR코드

DOI QR Code

Dynamic Stability and Semi-Analytical Taylor Solution of Arch With Symmetric Mode

대칭 모드 아치의 준-해석적 테일러 해와 동적 안정성

  • Pokhrel, Bijaya P. (Dept. of Architectural Eng., Korea University of Technology and Education) ;
  • Shon, Sudeok (Dept. of Architectural Eng., Korea University of Technology and Education) ;
  • Ha, Junhong (School of Liberal Arts, Korea University of Technology and Education) ;
  • Lee, Seungjae (Dept. of Architectural Eng., Korea University of Technology and Education)
  • Received : 2018.06.29
  • Accepted : 2018.07.17
  • Published : 2018.09.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

Keywords

References

  1. Hoff, N. J., & Bruce, V. G., "Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches", Journal of Mathematics and Physics, Vol.32, No.1-4, pp.276-288, 1954
  2. Humphreys, J. S., "On Dynamic Snap Buckling of Shallow Arches", AIAA Journal, Vol.4, No.5, pp.878-886, 1966 https://doi.org/10.2514/3.3561
  3. Hsu, C. S., "Equilibrium configurations of a shallow arch of arbitrary shape and their dynamic stability character", International Journal of Non-Linear Mechanics, Vol.3, No.2, pp.113-136, 1968 https://doi.org/10.1016/0020-7462(68)90011-5
  4. Donaldson, M. T., & Plaut, R. H., "Dynamic stability boundaries for a sinusoidal shallow arch under pulse loads", AIAA Journal, Vol.21, No.3, pp.469-471, 1983 https://doi.org/10.2514/3.8097
  5. Blair, K. B., Krousgrill, C. M., & Farris, T. N., "Non-linear dynamic response of shallow arches to harmonic forcing", Journal of Sound and Vibration, Vol.194, No.3, pp.353-367, 1996 https://doi.org/10.1006/jsvi.1996.0363
  6. Levitas, J., Singer, J., & Weller, T., "Global dynamic stability of a shallow arch by poincare-like simple cell mapping", International Journal of Non-Linear Mechanics, Vol.32, No.2, pp.411-424, 1997 https://doi.org/10.1016/S0020-7462(96)00046-7
  7. Bi, Q., & Dai, H. H., "Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance", Journal of Sound and Vibration, Vol.233, No.4, pp.553-567, 2000 https://doi.org/10.1006/jsvi.1999.2813
  8. Chen, J. S., & Lin, J. S., "Stability of a shallow arch with one end moving at constant speed", International Journal of Non-Linear Mechanics, Vol.41, No.5, pp.706-715, 2006 https://doi.org/10.1016/j.ijnonlinmec.2006.04.004
  9. Ha, J. H., Gutman, S., Shon, S. D., & Lee, S. J., "Stability of shallow arches under constant load", International Journal of Non-Linear Mechanics, Vol.58, pp.120-127, 2014 https://doi.org/10.1016/j.ijnonlinmec.2013.08.004
  10. Virgin, L. N., Wiebe, R., Spottswood, S. M., & Eason, T. G., "Sensitivity in the structural behavior of shallow arches", International Journal of Non-Linear Mechanics, Vol.58, pp.212-221, 2014 https://doi.org/10.1016/j.ijnonlinmec.2013.10.003
  11. Lin, J. S., & Chen, J. S., "Dynamic snap-through of a laterally loaded arch under prescribed end motion", International Journal of Solids and Structures, Vol.40, No.18, pp.4769-4787, 2003 https://doi.org/10.1016/S0020-7683(03)00181-1
  12. Budiansky, B., & Roth, R. S., "Axisymmetric dynamic buckling of clamped shallow spherical shells", NASA TN D-1510, pp.597-606, 1962
  13. Belytschko, T., "A survey of numerical methods and computer programs for dynamic structural analysis", Nuclear Engineering and Design, Vol.37, No.1, pp.23-34, 1976 https://doi.org/10.1016/0029-5493(76)90050-9
  14. Barrio, R., Blesa, F., & Lara, M., "VSVO Formulation of the taylor method for the numerical solution of ODEs", Computers & Mathematics with Applications, Vol.50, No.1-2, pp.93-111, 2005 https://doi.org/10.1016/j.camwa.2005.02.010
  15. Dogonchi, A. S., Hatami, M., & Domairry, G., "Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow", Powder Technology, Vol.274, pp.186-192, 2015 https://doi.org/10.1016/j.powtec.2015.01.018
  16. Adomian, G., & Rach, R., "Modified Adomian Polynomials", Mathematical and Computer Modeling, Vol.24, No.11, pp.39-46, 1996
  17. He, J. H., "Homotopy perturbation method: a new nonlinear analytical technique", Applied Mathematics and Computation, Vol.135, No.1, pp.73-79, 2003 https://doi.org/10.1016/S0096-3003(01)00312-5
  18. Chowdhury, M. S. H., Hashim, I., & Momani, S., "The multistage homotopyperturbation method: A powerful scheme for handling the Lorenz system", Chaos, Solitons & Fractals, Vol.40, No.4, pp.1929-1937, 2009 https://doi.org/10.1016/j.chaos.2007.09.073
  19. Shon, S. D., Ha, J. H., Lee, S. J., & Kim, J. J., "Application of multistage homotopy perturbation method to the nonlinear space truss model", International Journal of Steel Structures, Vol.15, No.2, pp.335-346, 2015 https://doi.org/10.1007/s13296-015-6006-5
  20. Dogonchi, A. S., Alizadeh, M., & Ganji, D. D., "Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect", Advanced Powder Technology, Vol.28, No.7, pp.1815-1825, 2017 https://doi.org/10.1016/j.apt.2017.04.022
  21. Barrio, R., Rodriguez, M., Abad, A., & Blesa, F., "Breaking the limits: The Taylor series method", Applied Mathematics and Computation, Vol.217, No.20, pp.7940-7954, 2011 https://doi.org/10.1016/j.amc.2011.02.080
  22. Shon, S. D., Lee, S. J., Ha, J. H., & Cho, C. G., "Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method", Materials, Vol.8, No.5, pp.2400-2414, 2015 https://doi.org/10.3390/ma8052400