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Large Amplitude Free Vibration of a Rotating Nonhomogeneous Beam With Nonlinear Spring and Mass System

[+] Author and Article Information
A. Chakrabarti

 1A/14, Ramlal Agarwala Lane, Kolkata-700 050, India

P. C. Ray

Department of Mathematics, Government College of Engineering and Leather Technology, Block-LB, Salt Lake City, Kolkata-700 098, Indiaraypratap1@yahoo.co.in

Rasajit Kumar Bera1

Department of Mathematics, Heritage Institute of Technology, Anandapur, Kolkata-700 107, Indiarasajit@yahoo.com

1

Corresponding author.

J. Vib. Acoust 132(5), 054502 (Aug 18, 2010) (7 pages) doi:10.1115/1.3025825 History: Received December 14, 2006; Revised September 09, 2008; Published August 18, 2010; Online August 18, 2010

This paper investigates the free out of plane vibration of a rotating nonhomogeneous beam with nonlinear spring and mass system. The effect of nonhomogeneity of the beam appears both in the governing equations and in the boundary conditions, but the nonlinear spring-mass effect appears in the boundary conditions only. The solution is obtained by applying the method of multiple time scales directly to the nonlinear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in open literature. The effect of the nonhomogeneity of the stiffer beam (β=0.01) reduces the frequencies of vibration of the beam. A possible physical explanation of this reduced frequency of the nonhomogeneous beam is discussed. A subsequent nonlinear study of the nonhomogeneous beam indicates that the mass of the spring and its location also have a pronounced effect on the vibration of the beam. The effect of the nonhomogeneity of the beam on the relative stability of the nonlinear vibration of the beam with spring-mass system is also studied.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Rotating beam with spring-mass system

Grahic Jump Location
Figure 2

Variation in nonlinear frequency versus amplitude of oscillation (for third mode) with different locations of the massless spring (M=0) system, α1=103 and α2=107

Grahic Jump Location
Figure 3

Comparison of nonlinear frequency versus amplitude of oscillation for different rigidities (β=0.0,−0.01) of the massless spring (M=0) system with spring location (η=0.1), α1=103 and α2=107

Grahic Jump Location
Figure 4

Comparison of nonlinear frequency versus amplitude of oscillation for different rigidities (β=0.0,0.01) of the massless spring (M=0) system with spring location (η=0.1), α1=103 and α2=107

Grahic Jump Location
Figure 5

Comparison of nonlinear frequency versus amplitude of oscillation for different rigidities (β=0.0,0.01,−0.01) of the mass-spring (α4=0.15) system with spring location (η=0.1), α1=103 and α2=107

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