Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

In-plane free vibrations of catenary arches with unsymmetric axes

  • Wilson, James F. (Department of Civil Engineering, Duke University) ;
  • Lee, Byoung Koo (Department of Civil Engineering, Wonkwang University)
  • Published : 1995.09.25
⟨ Previous Next ⟩

Abstract

The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.

Keywords

References

  1. Austin, W.J. and Veletsos, A.S. (1973), "Free vibration of arches flexible in shear", Journal of the Engineering Mechanics Division, 99(EM4), 735-753.
  2. Borg, S.F.;Gennaro, J.J. (1959), Advanced structural analysis, Van Nostrand, Princeton, New Jersey.
  3. Davis, R.,Henshell, R.D. and Warburton, G.B. (1972), "Constant curvature beam finite elements for in-plane vibration", Journal of Sound and Vibration, 25, 561-576. https://doi.org/10.1016/0022-460X(72)90478-6
  4. Ewins, D.J. (1985), Modal testing: theory and practice, John Wiley, New York.
  5. Irie, T., Yamada, G. and Tanaka, K. (1983), "Natural frequencies of in-plane vibration of arcs", Journal of Applied Mechanics, 50, 449-452. https://doi.org/10.1115/1.3167058
  6. Laura, P. A. A. and Maurizi, M.J. (1987), "Recent research in the vibration of arch-type structures", Shock and Vibration Digest, 19(1), 6-9.
  7. Lee, B.K. and Wilson, J.F. (1989), "Free vibrations of arches with variable curvature", Journal of Sound and Vibration, 136(1), 75-89.
  8. Leonard, J.W. (1988), Tension structures, McGraw-Hill Book Company, 300-304.
  9. Perkins, N.C. (1990), "Planar vibration of an elastica arch: theory and experiment", Journal of Vibration and Acoustics, 112, 374-379. https://doi.org/10.1115/1.2930518
  10. Romanelli, E. and Laura, P. A. A. (1972), "Fundamental frequencies of non-circular, elastic, hinged arcs", Journal of Sound and Vibration, 24(1), 17-22. https://doi.org/10.1016/0022-460X(72)90118-6
  11. Veletsos, A.S. and Austin, W.J., Pereira, C. A. L. and Wung, S.J. (1972), "Free in-plane vibration of circular arches", Journal of the Engineering Mechanics Division, 98(EM2), 311-329.
  12. Volterra, E. and Morell, J.D. (1961), "Lowest natural frequencies of elastic hinged arcs", Journal of the Acoustical Society of America, 33, 1787-1790. https://doi.org/10.1121/1.1908576
  13. Wang, T.M. (1972), "Lowest natural frequency of clamped parabolic arcs", Journal of the Structural Division, 98(ST1), 407-411.
  14. Wang, T.M. and Moore, J.A. (1973), "Lowest natural extensional frequency of clamped elliptic arcs", Journal of Sound and Vibration, 30, 1-7. https://doi.org/10.1016/S0022-460X(73)80046-X
  15. Wung, S.J. (1967), "Vibration of hinged circular arches", Master's Thesis, Rice University, Houston, Texas.

Cited by

  1. Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations vol.40, pp.3, 2016, https://doi.org/10.1016/j.apm.2015.09.024
  2. Free Vibration Analysis of Parabolic Arches in Cartesian Coordinates vol.03, pp.03, 2003, https://doi.org/10.1142/S021945540300094X
  3. Free vibrations of non-circular arches with non-uniform cross-section vol.37, pp.36, 2000, https://doi.org/10.1016/S0020-7683(99)00194-8
  4. Free vibrations of arches with general boundary condition vol.6, pp.4, 2002, https://doi.org/10.1007/BF02842001
  5. Thin-walled curved beam theory based on centroid-shear center formulation vol.19, pp.2, 2005, https://doi.org/10.1007/BF02916181
  6. Free vibration and elastic analysis of shear-deformable non-symmetric thin-walled curved beams: A centroid-shear center formulation vol.21, pp.1, 2005, https://doi.org/10.12989/sem.2005.21.1.019
  7. In-plane Free Vibrations of Horseshoe Circular Arch vol.34, pp.4, 2014, https://doi.org/10.12652/Ksce.2014.34.4.1043
  8. Planar free vibrations of horseshoe elliptic arch vol.20, pp.4, 2016, https://doi.org/10.1007/s12205-015-0582-y
  9. Free vibrations of arches with inclusion of axial extension, shear deformation and rotatory inertia in Cartesian coordinates vol.8, pp.1, 2004, https://doi.org/10.1007/BF02829079
  10. Free vibrations of inclined arches using finite elements vol.13, pp.6, 2002, https://doi.org/10.12989/sem.2002.13.6.713
  11. Application of Numerical Differentiation Using Differential Quadrature (DQ) to Curved Member-like Structural Analysis vol.17, pp.2, 2007, https://doi.org/10.5050/ksnvn.2007.17.2.185
  12. 중공단면을 갖는 포물선형 아치의 면내 자유진동 해석 vol.18, pp.2, 1995, https://doi.org/10.5050/ksnvn.2008.18.2.215
  13. Series solutions for spatially coupled buckling anlaysis of thin-walled Timoshenko curved beam on elastic foundation vol.33, pp.4, 1995, https://doi.org/10.12989/sem.2009.33.4.447
  14. Free Vibrations of Tapered Horseshoe Circular Arch with Constant Volume vol.10, pp.16, 1995, https://doi.org/10.3390/app10165431