1 |
R. Hoppe, "The Bending Vibration of a Circular Ring", Crelle's J. Math., Vol. 73, pp. 158-170, 1871.
|
2 |
A. E. H. Love, "A Treatise of the Mathematical Theory of Elasticity", 4th ed, Dover, New York, 1944.
|
3 |
H. Lamb, "On the Flexure and Vibrations of a Curved Bar", Proceedings of the London Mathematical Society , Vol. 19, pp. 365-376, 1888.
|
4 |
J. P. Den Hartog, "The Lowest Natural Frequency of Circular Arc", Philosophical Magazine, Series 7, Vol. 5, pp. 400-408, 1928.
DOI
|
5 |
E. Volterra, 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.
|
6 |
R. R. Archer, "Small Vibration of Thin Incomplete Circular Ring", Int. J. Mech. Sci. , Vol 1, pp. 45-56, 1960.
DOI
|
7 |
F. C. Nelson, "In-Plane Vibration of a Simply Supported Circular Ring Segment" Int. J. Mech. Sci., Vol. 4, pp. 517-527, 1962.
DOI
|
8 |
N. M. Auciello, M. A. De Rosa, "Free Vibrations of Circular Arche", J. Sound Vibr., Vol. 176, pp. 443-458, 1994.
|
9 |
U. Ojalvo, "Coupled Twisting-Bending Vibrations of Incomplete Elastic Ring", Int. J. Mech. Sci., Vol. 4, pp. 53-72, 1962.
DOI
|
10 |
L. C. Rodgers, W. H. Warner, "Dynamic Stability of Out-of-Plane Motion of Curved Elastic Rod", J. Appl. Math., Vol. 24, pp. 36-43, 1973.
|
11 |
R. E. Bellman, J. Casti, "Differential Quadrature and Long-Term Integration", J. Math. Anal. Applic., Vol. 34, pp. 235-238, 1971.
DOI
|
12 |
S. K. Jang, C. W. Bert, 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
|
13 |
K. Kang, Y. Kim, "In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 11, pp. 2734-2740, 2010.
|
14 |
K. Kang , C. Park, "In-Plane Buckling Analysis of Asymmetric Curved Beams Using DQM", J. KAIS., Vol. 141, pp. 4706-4712, 2013.
|
15 |
K. Kang, C. Park, "Extensional Vibration Analysis of Curved Beams Including Rotatory Inertia and Shear Deformation Using DQM", J. KAIS., Vol. 17, pp. 284-293, 2016.
|