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In-Plane Inextensional and Extensional Vibration Analysis of Curved Beams Using DQM
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 Title & Authors
In-Plane Inextensional and Extensional Vibration Analysis of Curved Beams Using DQM
Kang, Ki-jun;
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One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In-plane vibrations of curved beams with inextensibility and extensibility of the arch axis are analyzed by the differential quadrature method (DQM). Fundamental frequencies are calculated for the member with various end conditions and opening angles. The results are compared with exact experimental and numerical results by other methods for cases in which they are available. The DQM gives good accuracy even when only a limited number of grid points is used, and new results according to diverse variation are also suggested.
DQM;Exact Experimental;Extensional Vibration;Inextensional Vibration;In-Plane;New Result;Numerical Solution;
 Cited by
R. Hoppe, "The Bending Vibration of a Circular Ring", Crelle's J. Math., Vol. 73, pp. 158-170, 1871. DOI:

A. E. H. Love, A Treatise of the Mathematical Theory of Elasticity, 4th Ed. Dover, New York, 1944.

H. Lamb, "On the Flexure and Vibrations of a Curved Bar", Proceedings of the London Mathematical Society, Vol. 19, pp. 365-376, 1888.

J. P. Den Hartog, "The Lowest Natural Frequency of Circular Arcs", Philosophical Magazine, Series 7, Vol. 5, pp. 400-408, 1928. DOI:

E. Volterra and J. D. Morell, "Lowest Natural Frequency of Elastic Arc for Vibrations outside the Plane of Initial Curvature", J. Appl. Math., Vol. 28, pp. 624-627, 1961. DOI:

R. R. Archer, "Small Vibration of Thin Incomplete Circular Rings", Int. J. Mech. Sci., Vol. 1, pp. 45-56, 1960. DOI: crossref(new window)

F. C. Nelson, "In-Plane Vibration of a Simply Supported Circular Ring Segment" Int. J. Mech. Sci., Vol. 4, pp. 517-527, 1962. DOI: crossref(new window)

N. M. Auciello and M. A. De Rosa, "Free Vibrations of Circular Arches", J. Sound Vibr., Vol. 176, pp. 443-458, 1994. DOI:

U. Ojalvo, "Coupled Twisting-Bending Vibrations of Incomplete Elastic Rings", Int. J. Mech. Sci., Vol. 4, pp. 53-72, 1962. DOI: crossref(new window)

L. C. Rodgers and W. H. Warner, "Dynamic Stability of Out-of-Plane Motion of Curved Elastic Rods", J. Appl. Math., Vol. 24, pp. 36-43, 1973. DOI:

R. E. Bellman and J. Casti, "Differential Quadrature and Long-Term Integration", J. Math. Anal. Applic., Vol. 34, pp. 235-238, 1971. DOI: crossref(new window)

A. S. Veletsos, W. J. Austin, C. A. L. Pereira, and S. J. Wung, "Free In-plane Vibration of Circular Arches", Proceedings ASCE, Journal of the Engineering Mechanics Division, Vol. 98, pp. 311-339, 1972.

W. Flugge, Stresses in Shells, Springer- Verlag, Berlin, 1960. DOI:

S. K. Jang, C. W. Bert, and A. G. Striz, "Application of Differential Quadrature to Static Analysis of Structural Components", Int. J. Numer. Mech. Engng, Vol. 28, pp. 561-577, 1989. DOI: crossref(new window)

K. Kang and J. Han, "Analysis of a Curved beam Using Classical and Shear Deformable Beam Theories", Int. J. KSME., Vol. 12, pp. 244-256, 1998.

K. Kang and Y. Kim, "In-Plane Buckling Analysis of Curved Beams Using DQM", J. KAIS., Vol. 13, pp. 2858-2864, 2012. DOI:

K. Kang and Y. Kim, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 11, pp. 2734-2740, 2010. DOI:

K. Kang and C. Park, "In-Plane Buckling Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol.141, pp .4706-4712, 2013.