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TECHNICAL PAPERS

The Instability and Vibration of Rotating Beams With Arbitrary Pretwist and an Elastically Restrained Root

[+] Author and Article Information
S. M. Lin

Mechanical Engineering Department, Kun Shan University of Technology, Tainan, Taiwan 710-03, Republic of China

J. Appl. Mech 68(6), 844-853 (Aug 23, 2000) (10 pages) doi:10.1115/1.1408615 History: Received December 12, 1999; Revised August 23, 2000
Copyright © 2001 by ASME
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References

Leissa,  A., 1981, “Vibrational Aspects of Rotating Turbomachinery Blades,” Appl. Mech. Rev., 34, pp. 629–635.
Ramamurti,  V., and Balasubramanian,  P., 1984, “Analysis of Turbomachine Blades: A Review,” Shock Vib. Dig., 16, pp. 13–28.
Rosen,  A., 1991, “Structural and Dynamic Behavior of Pretwisted Rods and Beams,” Appl. Mech. Rev., 44, pp. 483–515.
Lin,  S. M., 1999, “Dynamic Analysis of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root,” ASME J. Appl. Mech., 66, pp. 742–749.
Lee,  S. Y., and Kuo,  Y. H., 1992, “Bending Vibrations of a Rotating Nonuniform Beams With an Elastically Restrained Root,” ASME J. Appl. Mech., 154, pp. 441–451.
Lee,  S. Y., and Lin,  S. M., 1994, “Bending Vibrations of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root,” ASME J. Appl. Mech., 61, pp. 949–955.
Gupta,  R. S., and Rao,  J. S., 1978, “Finite Element Eigenvalue Analysis of Tapered and Twisted Timoshenko Beams,” J. Sound Vib., 56, No. 2, pp. 187–200.
Carnegie,  W., and Thomas,  J., 1972, “The Coupled Bending-Bending Vibration of Pre-twisted Tapered Blading,” ASME J. Eng. Ind., 94, pp. 255–266.
Subrahmanyam,  K. B., and Rao,  J. S., 1982, “Coupled Bending-Bending Cantilever Beams Treated by the Reissner Method,” J. Sound Vib., 82, No. 4, pp. 577–592.
Celep,  Z., and Turhan,  D., 1986, “On the Influence of Pretwisting on the Vibration of Beams Including the Shear and Rotatory Inertia Effects,” J. Sound Vib., 110, No. 3, pp. 523–528.
Rosard,  D. D., and Lester,  P. A., 1953, “Natural Frequencies of Twisted Cantilever Beams,” ASME J. Appl. Mech., 20, pp. 241–244.
Lin,  S. M., 1997, “Vibrations of Elastically Restrained Nonuniform Beams With Arbitrary Pretwist,” AIAA J., 35, No. 11, pp. 1681–1687.
Rao,  J. S., and Carnegie,  W., 1973, “A Numerical Procedure for the Determination of the Frequencies and Mode Shapes of Lateral Vibration of Blades Allowing for the Effect of Pre-twist and Rotation,” International Journal of Mechanical Engineering Education 1, No. 1, pp. 37–47.
Subrahmanyam,  K. B., and Kaza,  K. R. V., 1986, “Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects,” ASME J. Vib., Acoust., Stress, Reliab. Des. 108, pp. 140–149.
Subrahmanyam,  K. B., Kulkarni,  S. V., and Rao,  J. S., 1982, “Application of the Reissner Method to Derive the Coupled Bending-Torsion Equations of Dynamic Motion of Rotating Pretwisted Cantilever Blading With Allowance for Shear Deflection, Rotary Inertia, Warping and Thermal Effects,” J. Sound Vib., 84, No. 2, pp. 223–240.
Sisto,  F., and Chang,  A. T., 1984, “A Finite Element for Vibration Analysis of Twisted Blades Based on Beam Theory,” AIAA J. 21, No. 11, pp. 1646–1651.
Young,  T. H., and Lin,  T. M., 1998, “Stability of Rotating Pretwisted, Tapered Beams With Randomly Varying Speed,” ASME J. Vibr. Acoust., 120, pp. 784–790.
Kar,  R. C., and Neogy,  S., 1989, “Stability of a Rotating, Pretwisted, Non-uniform Cantilever Beam With Tip Mass and Thermal Gradient Subjected to a Non-conservative Force,” Comput. Struct., 33, No. 2, pp. 499–507.
Hernried,  A. G., 1991, “Forced Vibration Response of a Twisted Non-uniform Rotating Blade,” Comput. Struct., 41, No. 2, pp. 207–212.
Surace,  G., Anghel,  V., and Mares,  C., 1997, “Coupled Bending-Bending-Torsion Vibration Analysis of Rotating Pretwisted Blades: An Integral Formulation and Numerical Examples,” J. Sound Vib., 206, No. 4, pp. 473–486.
Rugh, W. J., 1996, Linear System Theory, Prentice-Hall, Englewood Cliffs, NJ, pp. 41–44.
Rao,  J. S., 1987, “Turbomachine Blade Vibration,” Shock Vib. Dig., 19, No. 5, pp. 3–10.

Figures

Grahic Jump Location
Geometry and coordinate system of a rotating pretwisted beam
Grahic Jump Location
The influence of the root spring constants on the instability of a pretwisted tapered beam [Byy=(1–0.1ξ)cos2 πξ/4+100(1–0.1ξ)3 sin2 πξ/4,Bzz=100(1–0.1ξ)3 cos2 πξ/4+(1–0.1ξ)sin2 πξ/4,Byz=[50(1–0.1ξ)3–0.5(1–0.1ξ)]sin πξ/2,α=2,θ=30 deg,r=0.1]
Grahic Jump Location
The influence of the rotating speed α on the first three natural frequencies of cantilever doubly tapered beams with uniform and nonuniform pretwists [Byy=(1–0.1ξ)4 cos2 φ+100(1–0.1ξ)4 sin2 φ,Bzz=100(1–0.1ξ)4 cos2 φ+(1–0.1ξ)4 sin2 φ,Byz=49.5(1–0.1ξ)4 sin2 φ,η=0.001,θ=π/3,r=0.2; –: φ=πξ2/2; [[dashed_line]]: φ=π/2 sin(ξπ/2); [[dashed_line]]: φ=πξ/2]
Grahic Jump Location
The influence of the total pretwist angle Φ on the first four natural frequencies of cantilever doubly tapered beams [Byy=(1–0.1ξ)4 cos2 ξΦ+IZZ(0)/IYY(0)(1–0.1ξ)4 sin2 ξΦ,BZZ=IZZ(0)/IYY(0)(1–0.1ξ)4 cos2 ξΦ+(1–0.1ξ)4 sin2 ξΦ,Byz=IZZ(0)/(2IYY(0))(1–0.1ξ)4 sin2 ξΦ,η=0.001,θ=0,r=1; –: α=4; [[dashed_line]]: α=1]

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