Thermodynamics of high frequency nonlinear vibrations

In the field of vibrations of complex structures, energy methods like SEA and a series of mid-frequency methods, represent an important resource for computational analysis. All these methods are based in general on a linear formulation of the elastic problem. However, when nonlinearities are present, for example related to clearance or stiffening of joints, these methods, in principle, cannot be applied. This paper, on the basis of a theory presented recently by one of the authors, proposes a foundation of a new energy method able to deal with nonlinearities when studying the energy exchange between subsystems. The idea relies on the concept of a thermodynamic vibroacoustic temperature, that can be directly defined when introducing the entropy of a vibrating structure. The theory is introduced in general, and examples of calculation of the power flow between nonlinear resonators are presented introducing stiffening and clearences for systems with many degrees of freedom.