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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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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