Free vibration of a type of tapered beams

Computer Methods in Applied Mechanics and Engineering

Volumn 188, Issue 1, 2000, Pages 203-216

  Zhou, D ^a   Cheung, Y K ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; BENDING (DEFORMATION); BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; VIBRATIONS (MECHANICAL);

BERNOULLI-EULER THEORY; RAYLEIGH-RITZ METHOD;

COMPUTATIONAL GEOMETRY;

EID: 0034226292     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00148-6     Document Type: Article

References (20)

1. H.D. Conway J.F. Dubil Vibration frequencies of truncated cone and wedge beams ASME J. Appl. Mech. 32 1965 923 935
2. R.P. Goel Transverse vibrations of tapered beams J. Sound Vibr. 47 1976 1 7
3. K.Y. Yang The natural frequencies of a non-uniform beam with a tip mass and with translational and rotational springs J. Sound Vibr. 137 1990 339 341
4. D.J. Sanger Transverse vibration of a class of non-uniform beams Int. J. Mech. Engrg. Sci. 16 1968 111 120
5. H.-C. Wang Generalized hypergeometric function solutions on the transverse vibration of a class of non-uniform beams ASME J. Appl. Mech. 34 1967 702 708
6. J.H. Lau Vibration frequencies of tapered bars with end mass ASME J. Appl. Mech. 51 1984 179 181
7. S. Naguleswaran A direct solution of Euler–Bernoulli wedge and cone beams J. Sound Vibr. 172 1994 289 304
8. S. Naguleswaran 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. 172 1994 305 319
9. L. Klein Transverse vibrations of non-uniform beam J. Sound Vibr. 37 1974 491 505
10. C.W.S. To Higher order tapered beam finite elements for vibration analysis J. Sound Vibr. 63 1979 33 50
11. J.R. Banerjee F.W. Williams Exact Bernoulli–Euler dynamic stiffness matrix for a range of tapered beams Int. J. Num. Methods Engrg. 21 1985 2289 2302
12. S.Y. Lee H.Y. Ke Y.H. Kuo Analysis of non-uniform beam vibration J. Sound Vibr. 142 1990 15 29
13. S.Y. Lee Y.H. Kuo Exact solution for the analysis of general elastically restrained non-uniform beams ASME J. Appl. Mech. 59 1992 S205 S212
14. K. Sato Transverse vibrations of linearly tapered beams with ends restrained elastically against rotation subjected to axial force Int. J. Mech. Sci. 22 1980 109 115
15. C.S. Kim S.M. Dickinson On the analysis of laterally vibrating slender beams subject to various complicating effects J. Sound Vibr. 122 1988 441 455
16. R.O. Grossi R.B. Bhat A note on vibrating tapered beams J. Sound Vibr. 147 1991 174 178
17. P.A.A. Laura B. Valerga de Greco J.C. Utjes R. Carnicer Numerical experiments on free and forced vibrations of beams of uniform cross-section J. Sound Vibr. 120 1988 587 596
18. F.W. Williams J.R. Banerjee Flexural vibration of axially loaded beams with linear or parabolic taper J. Sound Vibr. 99 1985 121 138
19. J.R. Banerjee F.W. Williams Further flexural vibration curves for axially loaded beams with linear or parabolic taper J. Sound Vibr. 102 1985 315 327
20. B. Downs Reference frequencies for the validation of numerical solutions of transverse vibration of non-uniform beams J. Sound Vibr. 61 1978 71 78