@article {Carcaterra:2018:0736-2935:3854,
title = "Thermodynamics of High Frequency Nonlinear Vibrations",
journal = "INTER-NOISE and NOISE-CON Congress and Conference Proceedings",
parent_itemid = "infobike://ince/incecp",
publishercode ="ince",
year = "2018",
volume = "258",
number = "4",
publication date ="2018-12-18T00:00:00",
pages = "3854-3861",
itemtype = "ARTICLE",
issn = "0736-2935",
url = "https://ince.publisher.ingentaconnect.com/content/ince/incecp/2018/00000258/00000004/art00094",
author = "Carcaterra, Antonio and Culla, Antonio",
abstract = "One of the basis to introduce a generalized thermodynamic for vibration is the temperature concept for Hamiltonian systems to describe the energy flow between two coupled sub-systems, recently introduced by the authors. A general method to approach energy sharing between linear and
nonlinear systems is produced, with applications to both theoretical mechanics as well as engineering vibroacoustics and Statistical Energy Analysis. The chance of a strict mathematical foundation to this important physical and engineering problem, is provided by the introduction of the Khinchin's
entropy. The analysis shows that, under (i) linearity, (ii) weak coupling, and (iii) close-to-equilibrium conditions, a Fourier-like heat transmission law is obtained. The mechanical analogous of the temperature is defined, and it is shown to be proportional to the modal energy of the system,
that is the ratio of its total energy and the number of its degrees of freedom, a result reminiscent of SEA. A generalization of the temperature concept is introduced for nonlinear systems, showing in this case that the temperature depends on a series of integer and fractional powers of the
system's modal energy. Finally, a generalized statistical energy analysis of nonlinear systems is presented.",
}