Thermal analogy in wave energy transfer: Theoretical and experimental analysis

In this paper a theoretical and experimental analysis of the wave energy transmission in structures is proposed, aimed at introducing a new point of view about energy exchange in dynamical systems. A systematic asymptotic analysis, based on the concept of wavelength scale effect, is developed, in which a simultaneous time- and space-average energy along the structure is considered. The analytical approach highlights different scale laws in the energy transmission mechanism. The mu parameter, related to the ratio between a characteristic space-average length and the wavelength, controls this characteristic scale. In the small-scale transmission range (mu < 1), a vibration conductivity principle fails for every type of considered structure. On the other hand, in the large-scale range (mu much greater than 1), an asymptotic thermal energy behaviour is found for one-dimensional systems. The plate energy does not indeed obey a thermal law. A physical explanation of these different behaviours is proposed and two types of basic energy interactions between waves are identified, leading to different energy contributions: the coincident wave energy and the interference wave energy, with totally different asymptotic features. In fact, the coincident wave energy asymptotically tends to satisfy the energy balance in a thermal form over the mu large-scale range. The interference energy indeed exhibits a complex behaviour: only part of its non-thermal contribution asymptotically vanishes, but another persists even in the large mu scale range. (C) 1999 Academic Press.