Entropy in vibration: energy sharing among linear and nonlinear vibrating systems

While the principle of energy conservation is used since a long time as a fundamental tool in vibration analysis, the second principle of thermodynamics has not yet an established role in this frame. By using the concept of entropy, one of the main result of this paper consists of a strict derivation of a quantity -thermodynamic temperature- controlling the energy flow between mechanical oscillators. Following such direction of investigation, a very general theoretical approach to energy sharing among freely vibrating systems, both linear and nonlinear, is disclosed.