0
TECHNICAL PAPERS

Exact Solutions for Out-of-Plane Vibration of Curved Nonuniform Beams

[+] Author and Article Information
S. Y. Lee, J. C. Chao

Mechanical Engineering Department, National Cheng Kung University, Tainan, Taiwan 701, R. O. C.

J. Appl. Mech 68(2), 186-191 (May 16, 2000) (6 pages) doi:10.1115/1.1346679 History: Received October 20, 1999; Revised May 16, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Michell,  J. H., 1890, “The Small Deformation of Curves and Surfaces With Application to the Vibrations of a Helix and a Circular Ring,” Messenger Math., 19, pp. 68–76.
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, 4th Ed., Dover, New York.
Markus,  S., and Nanasi,  T., 1981, “Vibrations of Curved Beams,” Shock Vib. Digest, 7, pp. 3–14.
Laura,  P. A. A., and Maurizi,  M. J., 1987, “Recent Research on Vibrations of Arch-Type Structures,” Shock Vib. Digest, 7, pp. 3–14.
Childamparam,  P., and Leissa,  A. W., 1993, “Vibrations of Planar Curved Beams, Rings and Arches,” Appl. Mech. Rev., 46, pp. 467–483.
Auciello,  N. M., and De Rosa,  M. A., 1994, “Free Vibrations of Circular Arches: A Review,” J. Sound Vib., 174, No. 4, pp. 433–458.
Ojalvo,  I. U., 1962, “Coupled Twist-Bending Vibrations of Incomplete Elastic Rings,” Int. J. Mech. Sci., 4, pp. 53–72.
Nelson,  F. C., 1963, “Out-of-Plane Vibration of a Clamped Circular Ring Segment,” J. Acoust. Soc. Am., 35, No. 6, pp. 933–934.
Suzuki,  K., Kosawada,  T., and Takahashi,  S., 1983, “Out-of-Plane Vibrations of Curved Bars With Varying Cross-Section,” Bull. JSME, 26, No. 212, pp. 268–275.
Royster,  L. H., 1966, “Effect of Linear Taper on the Lowest Natural Extensional Frequency of Elastic Arcs,” ASME J. Appl. Mech., 33, pp. 211–212.
Reddy,  M. N., 1968, “Lateral Vibrations of Plane Curved Bars,” J. Struct. Div. ASCE, 94, No. 10, pp. 2197–2211.
Bickford,  F. C., and Strom,  B. T., 1975, “Vibration of Plane Curved Beams,” J. Sound Vib., 39, No. 2, pp. 135–146.
Kawakami,  M., Sakiyama,  T., Matsuda,  H., and Morita,  C., 1995, “In-Plane and Out-of-Plane Free Vibrations of Curved Beams With Variable Sections,” J. Sound Vib., 187, No. 3, pp. 381–401.
Fung, Y. C., 1965, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
Timoshenko, S., 1955, Strength of Materials: Part I, 3rd Ed., D. Van Nostrand, Princeton.
Lee,  L. S. S., 1975, “Vibrations of an Intermediately Supported U-Bend Tube,” ASME J. Eng. Ind., 97, pp. 23–32.
Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan, New York.
Lee,  S. Y., and Kuo,  Y. H., 1992, “Exact Solutions for the Analysis of General Elastically Restrained Non-uniform Beams,” ASME J. Appl. Mech., 59, Part 2, pp. S189–S196.
Rao, J. S., 1992, Advanced Theory of Vibration, Wiley Eastern Limited, New Delhi.
Volterra,  E., and Morell,  J. D., 1961, “Lowest Natural Frequency of Elastic Arc for Vibrations Outside the Plane of Initial Curvature,” ASME J. Appl. Mech., 28, pp. 624–627.

Figures

Grahic Jump Location
Geometry and coordinate system of a curved nonuniform beam of constant radius
Grahic Jump Location
The influence of taper ratio on the first dimensionless natural frequencies Λθ of clamped-free beams with various center angle θ0 (Lθ=30,b(0)=1.5; –: θ0=0 deg; [[dot_dash_line]]: θ0=20 deg; [[dashed_line]]: θ0=40 deg; [[dotted_line]]: θ0=60 deg)
Grahic Jump Location
The influence of taper ratio on the second dimensionless natural frequencies Λθ of clamped-free beams with various center angle θ0 (Lθ=30,b(0)=1.5; –: θ0=0 deg; [[dot_dash_line]]: θ0=20 deg; [[dashed_line]]: θ0=40 deg; [[dotted_line]]: θ0=60 deg)
Grahic Jump Location
The influence of dimensionless arc length on the first dimensionless natural frequencies Λθ of clamped-free beams with various taper ratio (b(0)=1.5,θ0=60 deg; –: η=0; [[dashed_line]]: η=0.2; [[dotted_line]]: η=0.4; [[dot_dash_line]]: η=0.6)
Grahic Jump Location
The influence of dimensionless arc length on the second dimensionless natural frequencies of clamped-free beams with various taper ratio (b(0)=1.5,θ0=60 deg; –: η=0; [[dashed_line]]: η=0.2; [[dotted_line]]: η=0.4; [[dot_dash_line]]: η=0.6)

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