Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems

Journal of the Acoustical Society of America

Volumn 121, Issue 4, 2007, Pages 1971-1982

  Carcaterra, A ^a,b   Akay, A ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; DYNAMICAL SYSTEMS; ENERGY TRANSFER; HARMONIC ANALYSIS; NATURAL FREQUENCIES; PROBABILITY DISTRIBUTIONS;

HARMONIC SERIES; IRREVERSIBILITY; LINEAR CONSERVATIVE SYSTEMS;

LINEAR SYSTEMS;

ACOUSTICS; ARTICLE; ENERGY TRANSFER; ENGINEERING; FREQUENCY MODULATION; LINEAR ENERGY TRANSFER; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; NONLINEAR SYSTEM; PRIORITY JOURNAL; PROBABILITY; THEORETICAL STUDY;

EID: 34047251476     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2697030     Document Type: Article

References (20)

1. A. D. Pierce, V. W. Sparrow, and D. A. Russel, "Fundamental structuralacoustic idealization for structure with fuzzy internals," J. Vibr. Acoust. 117, 339-348 (1995).
2. M. Strasberg and D. Feit, "Vibration damping of large structures induced by attached small resonant structures," J. Acoust. Soc. Am. 99, 335-344 (1996).
3. G. Maidanik, "Induced damping by a nearly continuous distribution of nearly undamped oscillators: Linear analysis," J. Sound Vib. 240, 717-731 (2001).
4. R. L. Weaver, "The effect of an undamped finite degree of freedom 'fuzzy' substructure: Numerical solution and theoretical discussion," J. Acoust. Soc. Am. 101, 3159-3164 (1996).
5. R. J. Nagem, I. Veljkovic, and G. Sandri, "Vibration damping by a continuous distribution of undamped oscillators," J. Sound Vib. 207, 429-434 (1997).
6. C. E. Celik and A. Akay, "Dissipation in solids: Thermal oscillations of atoms," J. Acoust. Soc. Am. 108, 184-191 (2000).
7. R. L. Weaver, "Equipartition and mean square response in large undamped structures," J. Acoust. Soc. Am. 110, 894-903 (2001).
8. A. Carcaterra and A. Akay, "Transient energy exchange between a primary structure and a set of oscillators: Return time and apparent damping," J. Acoust. Soc. Am. 115, 683-696 (2004).
9. I. Murat Koç, A. Carcaterra, Zhaoshun Xu, and A. Akay, "Energy sinks: Vibration absorption by an optimal set of undamped oscillators," to appear, J. Acoust. Soc. Am. 118(5), 3031-3042 (2005).
10. A. Carcaterra, A. Akay, and I. M. Koc, "Near-Irreversibility and damped response of a conservative linear structure with singularity points in its modal density," J. Acoust. Soc. Am. 119(4), 2141-2149 (2006).
11. A. Akay, Z. Xu, A. Carcaterra, and I. Murat Koç, "Experiments on vibration absorption using energy sinks," J. Acoust. Soc. Am. 118(5), 3043-3049 (2005).
12. A. Carcaterra, "An entropy formulation for the analysis of energy flow between mechanical resonators," Mech. Syst. Signal Process. 16(5), 905-920 (2002).
13. A. Carcaterra, "Ensemble energy average and energy flow relationships for nonstationary vibrating systems," J. Sound Vib. Special Issue, Uncertainty in Structural Dynamics, 288(3), 751-790 (2005).
14. T. Y. Petrosky, "Chaos and irreversibility in a conservative nonlinear dynamical system with a few degrees of freedom," Phys. Rev. A 29(4), 2078-2091 (1984).
15. P. K. Datta and K. Kundu, "Energy transport in one-dimensional harmonic chains," Phys. Rev. B 51(10), 6287-6295 (1995).
16. R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione, and A. Vulpiani, "Equipartition threshold in nonlinear large Hamiltonian systems: The Fermi-Pasta-Ulam model," Phys. Rev. A 31(2), 1039-1045 (1985).
17. R. R. Nigmatullin and A. Le Mehaute, "To the nature of irreversibility in linear systems," Magn. Reson. Solids 6(1), 165-179 (2004).
18. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics (Charles Griffin Limited, London, 1961).
19. E. J. G. Pitman, "Sufficient statistics and intrinsic accuracy," Proc. Cambridge Philos. Soc. 32, 576 (1936).
20. B. O. Koopman, "On distributions admitting a sufficient statistics," Trans. Am. Math. Soc. 39, 399 (1936).