1 |
Seely, F. B. and Smith, J. O., 1952, 'Advanced Mechanics of Materials', 2nd Ed., John Wiley and Sons, New York
|
2 |
Cowper, G. R., 1966, 'The Shear Coefficient in Timoshenko's Beam Theory', Journal Applied Mechanics, Vol. 33, pp, 335-340
DOI
|
3 |
Leissa, A. W. and So, J., 1995, 'Comparisons of Vibration Frequencies for Rods and Beams from One-dimensional and Three-dimensional Analysis', Journal of the Acoustical Society of America , Vol. 98, pp. 2122-2135
DOI
ScienceOn
|
4 |
Lincoln, J. W. and Volterra, E., 1967, 'Experimental and Theoretical Determination of Frequencies of Elastic Toroids'', Experimental Mechanics, Vol. 24, pp. 211-217
|
5 |
Volterra, E., 1967, 'Vibrations of Circular Elastic Rings' , Israel Journal of Technology, Vol. 5, No. 4, pp. 225-233
|
6 |
Kang, J.-H. and Leissa, A. W., 2001, 'Three-dimensional Field Equations of Motion, and Energy Functionals for Thick Shells of Revolution with Arbitrary Curvature and Variable Thickness' , Journal of Applied Mechanics, Vol. 68 pp. 953-954
DOI
ScienceOn
|
7 |
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, Second Edition, McGraw-Hill Book Co., New York, p. 184
|
8 |
Kantorovich, L. V. and Krylov, V. I., 1958, Approximate Methods in Higher Analysis, Noordhoff, Gronigen, The Netherlands, pp, 266-268
|
9 |
Kirkhope, J., 1977, 'In-plane Vibration of a Thick Circular Ring' , Journal of Sound and Vibration, Vol. 50, No.2, pp. 219-227
DOI
ScienceOn
|
10 |
Kirkhope, J., 1976, 'Out-of-plane Vibration of Thick Circular Ring', Journal of Engineering Mechainics, Vol. 102, pp. 239-247
|
11 |
McGee, O. G. and Leissa, A. W., 1991, 'Three-dimensional Free Vibrations of Thick Skewed Cantilever Plates' , Journal of Sound and Vibration, Vol. 144, pp. 305-322; Errata Vol. 149, pp. 539-542
DOI
ScienceOn
|
12 |
Kang, J. H., Lee, E. T. and Yang, K. H., 2001, 'Three-dimensional Field Equations, Equations of Motion, and energy Functionals for Thick Shells of Revolution with Arbitrary Curvature and Variable Thickness' Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 11, No. 1, pp, 156-166
|
13 |
So, J. and Leissa, A. W., 1997, 'Free Vibrations of Thick Hollow Circular Cylinders from Three-dimensional Analysis', Journal of Vibration and Acoustics, Vol. 119, pp. 89-95
DOI
ScienceOn
|
14 |
Kang, J.-H. and Leissa, A. W., 2000, 'Three-dimensional Vibrations of Thick, Circular Rings with Isosceles Trapezoidal and Triangular Cross-sections' , Journal of Vibration and Acoustics, Vol. 122, pp. 132-139
DOI
ScienceOn
|
15 |
Zhou, D., Au, F. T. K, Lo, S. H. and Cheung, Y. K, 2002, 'Three-dimensional Vibration Analysis of a Toms with Circular Cross Section' , Journal of the Acoustical Society of America, Vol. 12, No.6, pp. 2831-2839
|
16 |
Endo, M., 1972, 'Flexural Vibrations of a Ring with Arbitrary Cross-section', Bull. JSME, Vol. 15, pp. 446-544
DOI
|
17 |
Singal, R. K. and Williams, K., 1988, 'A Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shells and Rings', Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, pp. 533-537
DOI
ScienceOn
|
18 |
Love, A. E. H., 1934, 'Treatise on the Mathematical Theory of Elasticity' , Cambridge University Press' , Cambridge, England
|
19 |
Hoppe, R., 1871, 'Vibration in eines Ringes in seiner Ebene', J. Reine Angew, Math. (Crelle's J.), Vol. 73, pp. 415-432
|
20 |
Ritz, W., 1909, 'Uber eine neue Methode zur Losung Gewisser Variationsprobleme der Mathematischen Physik', Journal fur die Reine und Angewandte Mathematik, Vol. 135, pp, 1-61
|