0
TECHNICAL PAPERS

Vibrations of Tapered Timoshenko Beams in Terms of Static Timoshenko Beam Functions

[+] Author and Article Information
D. Zhou

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210014, P. R. China

Y. K. Cheung

Department of Civil Engineering, The University of Hong Kong, Hong Kong

J. Appl. Mech 68(4), 596-602 (Aug 15, 2000) (7 pages) doi:10.1115/1.1357164 History: Received November 30, 1999; Revised August 15, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Timoshenko,  S. P., 1922, “On the Transverse Vibrations of Bars of Uniform Cross Section,” Philos. Mag., 43, (Series 6), pp. 379–384.
To,  C. W. S., 1981, “A Linearly Tapered Beam Finite Element Incorporating Shear Deformation and Rotary Inertia for Vibration Analysis,” J. Sound Vib., 78, pp. 475–484.
Cleghorn,  W. L., and Tabarrok,  B., 1992, “Finite Element Formulation of a Tapered Timoshenko Beam of Non-uniform Thickness,” J. Sound Vib., 152, pp. 461–470.
Rossi,  R. E., Laura,  P. A. A., and Gutierrez,  R. H., 1990, “A Note on Transverse Vibrations of a Timoshenko Beam of Non-uniform Thickness Clamped at One End and Carrying a Concentrated Mass at the Other,” J. Sound Vib., 143, pp. 491–502.
Irie,  T., Yamada,  G., and Takahashi,  I., 1979, “Determination of the Steady State Response of a Timoshenko Beam of Varying Cross-Section by Use of the Spline Interpolation Technique,” J. Sound Vib., 63, pp. 287–295.
Gutierrez,  R. H., Laura,  P. A. A., and Rossi,  R. E., 1991, “Fundamental Frequency of Vibration of a Timoshenko Beam of Non-uniform Thickness,” J. Sound Vib., 145, pp. 341–344.
Chehil,  D. S., and Jategaonkar,  R., 1987, “Determination of Natural Frequencies of a Beam With Varying Cross Section Properties,” J. Sound Vib., 115, pp. 423–436.
Jategaonkar,  R., and Chehil,  D. S., 1989, “Natural Frequencies of a Beam With Varying Section Properties,” J. Sound Vib., 133, pp. 303–322.
Irie,  T., Yamada,  G., and Takahashi,  I., 1980, “Vibration and Stability of a Non-uniform Timoshenko Beam Subjected to a Follower Force,” J. Sound Vib., 70, pp. 503–512.
Tong,  X., Tabarrok,  B., and Yeh,  K. Y, 1995, “Vibration Analysis of Timoshenko Beams With Non-homogeneity and Varying Cross-section,” J. Sound Vib., 186, pp. 821–835.
Lee,  S. Y., and Lin,  S. M., 1992, “Exact Vibration Solutions for Nonuniform Timoshenko Beams With Attachments,” AIAA J., 30, pp. 2930–2934.
Laura,  P. A. A., Maurizi,  M. J., and Rossi,  R. E., 1990, “A Survey of Studies Dealing With Timoshenko Beams,” Shock Vib. Dig., 22, No. 11, pp. 3–10.
Zhou,  D., and Cheung,  Y. K., 2000, “The Free Vibration of a Type of Tapered Beams,” Comput. Methods Appl. Mech. Eng., 188, pp. 203–216.
Cheung,  Y. K., and Zhou,  D., 1999, “Eigenfrequencies of Tapered Rectangular Plates With Intermediate Line Supports,” Int. J. Solids Struct., 36, pp. 143–166.
Cheung,  Y. K., and Zhou,  D., 1999, “The Free Vibrations of Tapered Rectangular Plates Using a New Set of Beam Functions with the Rayleigh-Ritz Method,” J. Sound Vib., 223, pp. 703–722.
Zhou,  D., 1996, “Natural Frequencies of Rectangular Plates Using a Set of Static Beam Functions in Rayleigh-Ritz Method,” J. Sound Vib., 189, pp. 81–97.
Naguleswaran,  S., 1994, “A Direct Solution for the Transverse Vibration of Euler-Bernoulli Wedge and Cone Beams,” J. Sound Vib., 172, pp. 289–304.

Figures

Grahic Jump Location
The sketch of beams with continuously varying cross section; (a) the variation of cross-sectional area when r>0; (b) the variation of cross-sectional moment of inertia when s>0; (c) the variation of cross-sectional area when r<0; (d) the variation of cross-sectional moment inertia when s<0
Grahic Jump Location
The first two eigenfrequencies of cantilevered sharp-ended Timoshenko beams with linearly varying thickness and/or width via the thickness-length ratio h1/l: –•– Ω1 and - -•- - Ω2 for the beams with linear varying thickness; –▴– Ω1 and - -▴- - Ω2 for the beams with linear varying width; –▪– Ω1 and - -▪- - Ω2 for the beams with linear varying both thickness and width
Grahic Jump Location
The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying thickness via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
Grahic Jump Location
The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying width via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
Grahic Jump Location
The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying both thickness and width via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
Grahic Jump Location
The fundamental eigenfrequencies of cantilevered Timoshenko beams with the same thickness and width variation via the thickness-length ratio h1/l for the truncation factor α=0.5
Grahic Jump Location
The first two eigenfrequencies of cantilevered sharp-ended Timoshenko beams via the thickness-length ratio h1/l: –•– Ω1 and - -•- - Ω2 for taper factors r=1,s=2; –▴– Ω1 and - -▴- - Ω2 for taper factors r=1/2,s=3/2; –▪– Ω1 and - -▪- - Ω2 for taper factors r=1/2,s=1/2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In