Minimum-variance-response and irreversible energy confinement

  • A. Carcaterra
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 27)


This paper discusses the question of the energy confinement in mechanical structures in the light of the uncertainties affecting the natural frequencies of the system. More precisely, recent studies have shown that energy can be introduced to a linear system with near irreversibility, or energy within a system can migrate to a subsystem nearly irreversibly, even in the absence of dissipation, provided that the system has a particular natural frequency distribution. In this paper the case of uncertainty in the system’s natural frequency is discussed and a remarkable statistical property of the natural frequency is derived for a permanent energy confinement within a part of the system. The results demonstrate the existence of a special class of linear non-dissipative dynamic systems that exhibit nearly-irreversible energy confinement-IEC if they satisfy a minimum-variance-response-MIVAR property. In this case, if the probability density function of the natural frequencies has a special shape, the conservative system shows an unexpected decaying impulse response.


Probability Density Function Impulse Response Acoustical Society Frequency Response Function Energy Confinement 
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  1. 1.
    A.D. Pierce, V.W. Sparrow, D.A. Russel, ‘Foundamental structural-acoustic idealization for structure with fuzzy internals’, Journal of Vibration and Acoustics, vol. 117, 339–348 (1995). CrossRefGoogle Scholar
  2. 2.
    M. Strasberg, D. Feit, ‘Vibration damping of large structures induced by attached small resonant structures’, Journal of Acoustical Society of America, vol. 99, 335–344 (1996). CrossRefGoogle Scholar
  3. 3.
    R.J. Nagem, I. Veljkovic, G. Sandri, ‘Vibration damping by a continuous distribution of undamped oscillators’, Journal of Sound and Vibration, vol. 207, 429–434 (1997). CrossRefGoogle Scholar
  4. 4.
    R.L. Weaver, ‘The effect of an undamped finite degree of freedom ‘fuzzy’ substructure: numerical solution and theoretical discussion’, Journal of Acoustical Society of America, vol. 101, 3159–3164 (1996). CrossRefGoogle Scholar
  5. 5.
    A. Carcaterra, A. Akay, ‘Transient energy exchange between a primary structure and a set of oscillators: return time and apparent damping’, Journal of Acoustical Society of America, vol. 115, 683–696 (2004). CrossRefGoogle Scholar
  6. 6.
    I. Murat Koç, A. Carcaterra, Zhaoshun Xu, Adnan Akay, ‘Energy sinks: vibration absorption by an optimal set of undamped oscillators’, Journal of Acoustical Society of America, vol. 118(5), 3031–3042 (2005). CrossRefGoogle Scholar
  7. 7.
    A. Carcaterra, A. Akay, ‘Theoretical foundation of apparent damping and energy irreversible energy exchange in linear conservative dynamical systems’, Journal of Acoustical Society of America, vol. 121, 1971–1982 (2007). CrossRefGoogle Scholar
  8. 8.
    A. Akay, Z. Xu, A. Carcaterra, and I.M. Koc, ‘Experiments on vibration absorption using energy sinks’, J. Acoust. Soc. Amer., vol. 118, 3043–3049 (2005) CrossRefGoogle Scholar
  9. 9.
    A. Carcaterra and A. Akay, “Damping device”, 2006, International Patent Number: WO 2006/103291 A1. Google Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • A. Carcaterra
    • 1
  1. 1.Department of Mechanics and AeronauticsUniversity of RomeRomeItaly

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