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Research Papers

Almost Sure Stability of a Moving Elastic Band

[+] Author and Article Information
Ratko Pavlović1

 Mechanical Engineering Faculty, A. Medvedeva 14, 18000 Niš, Serbiaratko@masfak.ni.ac.yu

Predrag Rajković, Ivan Pavlović

 Mechanical Engineering Faculty, A. Medvedeva 14, 18000 Niš, Serbia

1

Corresponding author.

J. Appl. Mech 75(4), 041016 (May 14, 2008) (5 pages) doi:10.1115/1.2839905 History: Received March 07, 2007; Revised November 20, 2007; Published May 14, 2008

In this paper, the stochastic stability problem of a moving elastic band subjected to action in-plane acting forces is investigated. Each force consists of a constant part and a time-dependent zero mean stochastic function. By using the direct Liapunov functional method, almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, and geometric and physical parameters of the band. Numerical calculations are performed for infinite mode and compared with known results. Almost sure stability regions are shown for infinite and first mode the two-dimensional density probability function, and for higher modes when the edge load Gaussian or harmonic process is known.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 5

Moving elastic band–second, third, and fourth modes σf versus damping coefficient β

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Figure 4

Moving elastic band–first mode σf versus σg: (—) two-dimensional probability density function 23; (---) Schwartz inequality

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Figure 3

Moving elastic band–infinite mode σf versus σg: (—) two-dimensional probability density function 23; (---) Schwartz inequality

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Figure 2

Moving elastic band–infinite mode σ(P∕To) versus σ(T∕To): (—) after relation 23; (---) Ref. 5

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Figure 1

Choosing moving band parameters

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