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Research Papers

Entropy for Strongly Coupled Oscillators

[+] Author and Article Information
Dante A. Tufano

M.A.N.E. Department,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: tufand@rpi.edu

Zahra Sotoudeh

Department of Aerospace Engineering,
California State Polytechnic Institute,
Pomona, CA 91768
e-mail: zahra.vpi@gmail.com

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 22, 2017; final manuscript received May 24, 2017; published online August 17, 2017. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 140(1), 011003 (Aug 17, 2017) (8 pages) Paper No: VIB-17-1170; doi: 10.1115/1.4037142 History: Received April 22, 2017; Revised May 24, 2017

This paper examines an approach for determining the entropy of coupled oscillators that does not rely on the assumption of weak coupling. The results of this approach are compared to the results for a weakly coupled system. It is shown that the results from each methodology agree in the case of weak coupling, and that a correction term is required for moderate to strong coupling. The correction term is shown to be related to the mixed energy term from the coupling spring as well as the geometry and stiffness of the system. Numerical simulations are performed for a symmetric system of identical coupled oscillators and an asymmetric system of nonidentical oscillators to demonstrate these findings.

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Topics: Entropy
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References

Figures

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Fig. 1

System composed of two coupled oscillators with spring stiffnesses k1, k2 and masses m1, m2, coupled by a spring of stiffness kc

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Fig. 2

Correction term, h(E,Ê), plotted over time for the normalized coupling stiffnesses ε=0.01,ε=0.1,ε=0.5, and ε=1.0

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Fig. 3

The exact system entropy, H(d), compared to the composite method estimate, H(c), and the correction term, h, for ε=0.1

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Fig. 4

The exact system entropy, H(d), compared to the composite method estimate, H(c), and the correction term, h, for ε = 1

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Fig. 5

hE plotted over time for ε=0.01,ε=0.1,ε=0.5, and ε=1.0

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Fig. 6

hs plotted against ε

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Fig. 7

System composed of two nonidentical-coupled oscillators with spring stiffnesses k1≠0,k2=0, and masses m1, m2, coupled by a spring of stiffness kc

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Fig. 8

Correction term, h(E,Ê) plotted over time for the normalized coupling stiffnesses ε=0.01,ε=0.1,ε=0.5, and ε=1.0

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Fig. 9

The exact system entropy, H(d), compared to the composite method estimate, H(c), and the correction term, h, for ε=0.01

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Fig. 10

The exact system entropy, H(d), compared to the composite method estimate, H(c), and the correction term, h, for ε=0.1

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Fig. 11

hE, the component of the correction term relating to the energies E and Ê, over time for ε=0.01,ε=0.1,ε=0.5, and ε=1.0

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Fig. 12

hs, the component of the correction term relating to the system parameters, plotted against ε

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