1 |
Chree, C., 'The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and application', Trans. Cambridge Philos. Soc. Math. Phys. Sci., Vol.14, 1889, pp. 250-269
|
2 |
McNiven, H.D., and Perry, D.C., 'Axially symmetric waves in finite, elastic rods', J. Acoust. Soc. Amer., Vol.34, 1962, pp.433-437
DOI
|
3 |
Hutchinson, J. R., 'Vibrations of solid cylinders', ASME J. Appl. Mech., Vol.47, 1980, pp. 901-907
DOI
|
4 |
Leissa, A. W., and So, J., 'Comparisons of vibration frequencies for rods and beams from one-dimensional and three-dimensional analyses', J. Acoust. Soc. Am., Vol.98, No.4, 1995, pp.2122-2135
DOI
ScienceOn
|
5 |
Heidebrecht, A. C., 'Vibration of non-uniform simply-supported beams', ASCE J. Engng. Mech., Vol.93, 1967, pp.1-15
DOI
|
6 |
Wang, H.-C., 'Generalized gypergeometric function solutions on the transverse vibration of a class of non-uniform beams', ASME J. Appl. Mech., Vol.34, 1967, pp.702-708
|
7 |
Goel, R. P., 'Transverse vibrations of tapered beams', J. Sound Vibr., Vol.47, 1976, pp.1-7
DOI
ScienceOn
|
8 |
Downs, B., 'Reference frequencies for the validation of numerical solutions of transverse vibration of non-uniform beams', J. Sound Vibr., Vol.61, 1978, pp.71-78
DOI
ScienceOn
|
9 |
Lau, J. H., 'Vibration frequencies of tapered bars with end mass', ASME J. Appl. Mech., Vol.51, 1984, pp.179-181
DOI
|
10 |
Williams, F. W., and Banerjee, J. R., 'Flexural vibration of axially loaded beams with linear or parabolic taper', J. Sound Vibr., Vol. 99, 1985, pp.121-138
DOI
ScienceOn
|
11 |
Mabie, H. H., and Rogers, C. B., 'Transverse vibrations of tapered cantilever beams with end support', J. Acoust. Soc. Am., Vol.44, 1968, pp.1739-1741
DOI
|
12 |
Mabie, H. H., and Rogers, C. B., 'Transverse vibrations of tapered cantilever beams with end loads', J. Acoust. Soc. Am., Vol.36, 1964, pp.463-469
DOI
|
13 |
Gladwell, G. M. L., and Vijay, D. K., 'Natural frequencies of free finite length circular cylinders', J. Sound Vib. Vol.42, 1975, pp.387-397
DOI
ScienceOn
|
14 |
To, C. W. S, 'Higher order tapered beam finite elements for vibration analysis', J. Sound Vibr., Vol.63, 1979, pp.33-50
DOI
ScienceOn
|
15 |
Gladwell, G. M. L., and Tahbildar, U. C., 'Finite element analysis of the axisymmetric vibrations of cylinders', J. Sound Vib., Vol.22, 1972, pp.143-157
DOI
ScienceOn
|
16 |
McMahon, G. W., 'Experimental study of the vibrations of solid, isotropic, elastic cylinders', J. Acoust. Soc. Amer., Vol.36, 1964, pp.85-92
DOI
|
17 |
Lee, S. Y., Ke, H. Y., and Kuo, Y. H., 'Analysis of non-uniform beam vibration', J. Sound Vibr., Vol.142, 1990, pp.15-29
DOI
ScienceOn
|
18 |
Ritz, W., 'ber eine neue Methode zur Lsung gewisser Variationsprobleme der mathematischen Physik', Journal fr die Reine und Angewandte Mathematik, Vol.135, 1909, pp.1-61
DOI
|
19 |
Sanger, D. J., 'Transverse vibration of a class of non-uniform beams', Int. J. Mech. Engrg. Sci., Vol.16, 1968, pp.111-120
DOI
|
20 |
Craver Jr., W. L., and Jampala, P., 'Transverse vibrations of a linearly tapered cantilever beam with constraining springs', J. Sound Vibr., Vol.166, 1993, pp.521-529
DOI
ScienceOn
|
21 |
Laura, P. A. A., Valerga de Greco, B., 'Utjes, J. C., and Carnicer, R., Numerical experiments on free and forced vibrations of beams of non-uniform cross-section', J. Sound Vibr., Vol.120, 1988, pp.587-596
DOI
ScienceOn
|
22 |
Banerjee, J. R., and Williams, F. W., 'Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams', Int. J. Num. Methods Engrg., Vol.21, 1985, pp.2289-2302
DOI
ScienceOn
|
23 |
Leissa, A. W., and So, J., 'Accurate vibration frequencies of circular cylinders from three- dimensional analysis', J. Acoust. Soc. Am., Vol.98, No.4, 1995, pp.2136-2141
DOI
ScienceOn
|
24 |
Lee, S. Y., and Kuo, Y. H., 'Exact solution for the analysis of general elastically restrained non-uniform beams', ASME J. Appl. Mech., Vol.59, 1992, S205-S212
DOI
|
25 |
Mabie, H. H., and Rogers, C. B., 'Transverse vibrations of double-tapered cantilever beams with end support and with end mass', J. Acoust. Soc. Am., Vol.55, 1974, pp.986-991
DOI
ScienceOn
|
26 |
Klein, L., 'Transverse vibrations of non-uniform beam', J. Sound Vibr., Vol.37, 1974, pp. 491-505
DOI
ScienceOn
|
27 |
Rosa, M. A., and Auciello, N. M., 'Free vibrations of tapered beams with flexible ends', Computers & Structures, Vol.60, No.2, 1996, pp.197-202
DOI
ScienceOn
|
28 |
Hutchinson, J. R., 'Axisymmetric vibrations of a free finite length rod', J. Acoust. Soc. Amer., Vol.51, 1972, pp.233-240
DOI
|
29 |
Sokolnikoff, I. S., Mathematical theory of elasticity, Second Edition, McGraw-Hill Book Co., New York, 1956
DOI
|
30 |
Pickett, G., 'Flexural vibration of unrestrained cylinders and disks', J. Appl. Phys., Vol.16, 1935, pp.820-831
DOI
|
31 |
Grossi, R. O., and Bhat, R. B., 'A note on vibrating tapered beams', J. Sound Vibr., Vol. 147, 1991, pp.174-178
DOI
ScienceOn
|
32 |
McMahon, G. W., 'Finite difference analysis of the vibrations of solid cylinders', J. Acoust. Soc. Amer., Vol.48, 1970, pp.307-312
DOI
|
33 |
Tefft, W. E., 'Numerical solution of the frequency equations for the flexural vibrations of cylindrical rods', J. Res., (NBS) 64B, 1969, pp. 237-242
|
34 |
Alvares, S. I., Ficcadenti de Iglesias, G. M., and Laura, P. A. A., 'Vibrations of an elastically restrained, non-uniform beam with translational and rotational springs, and with a tip mass', J. Sound Vibr., Vol.120, 1991, pp. 465-471
DOI
|
35 |
Kantorovich, L. V., and Krylov, V. I., Approximate methods in higher analysis. Noordhoff, Gronigen, The Netherlands, 1958, pp.266-268
DOI
|
36 |
Conway, H. D., and Dubil, J. F., 'Vibration frequencies of truncated cone and wedge beams', ASME J. Appl. Mech., Vol.32, 1965, pp.923-935
|
37 |
McGee, O. G. and Leissa, A. W., 'Three-dimensional free vibrations of thick skewed cantilever plates', Journal of Sound and Vibration, Vol.144, 1991, pp.305-322; Errata Vol.149, 1991, pp.539-542
|
38 |
Yang, K. Y., 'The natural frequencies of a non-uniform beam with a tip mass and with translational and rotational springs', J. Sound Vibr., Vol.137, 1990, pp.339-341
DOI
ScienceOn
|
39 |
Mabie, H. H., and Rogers, C. B., 'Transverse vibrations of double-tapered cantilever beams', J. Acoust. Soc. Am., Vol.51, 1972, pp.1771-1774
DOI
|
40 |
Sato, K., 'Transverse vibrations of linearly tapered beams with ends restrained elastically against rotation subjected to axial force', Int. J. Mech. Sci., Vol.22, 1980, pp.109-115
DOI
ScienceOn
|
41 |
Zhou, D., and Cheung, Y. K., 'The free vibration of a type of tapered beams', Comput. Methods Appl. Mech. Engrg, Vol.188, 2000, pp.203-216
DOI
ScienceOn
|
42 |
Hutchinson, J. R, 'Transverse vibrations of beams, exact versus approximate solutions', ASME J. Appl. Mech., Vol.48, 1981, pp.923-928
DOI
|
43 |
Chree, C., 'Longitudinal waves of a solid bar', Quart. J. Math., Vol.21, 1886, p.287
|
44 |
Banerjee, J. R., and Williams, F. W., 'Further flexural vibration curves for axially loaded beams with linear or parabolic taper', J. Sound Vibr., Vol.102, 1985, pp.315-327
DOI
ScienceOn
|
45 |
Naguleswaran, S., 'A direct solution of Euler- Bernoulli wedge and cone beams', J. Sound Vibr., Vol.172, 1994, pp.289-304
DOI
ScienceOn
|
46 |
Rumerman, M., and Raynor, S., 'Natural frequencies of finite circular cylinders in axially symmetric longitudinal vibration', J. Sound Vib., Vol.15, 1971, pp.529-543
DOI
ScienceOn
|
47 |
Pochhammer, L., 'ber die Fortpflanzungsgeschwingdigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiszylinder', J. Reine Angew. Math., Vol.81, 1876, pp.324-326
|
48 |
Kim, C. S., and Dickinson, S. M., 'On the analysis of laterally vibrating slender beams subject to various complicating effects', J. Sound Vibr., Vol.122, 1988, pp.441-455
DOI
ScienceOn
|
49 |
Naguleswaran, S., 'Vibration in the two principal planes of a non-uniform beam of rectangular cross-section, one side of which varies as the square root of the axial co-ordinate', J. Sound Vibr., Vol.172, 1994, pp.305-319
DOI
ScienceOn
|