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 e!ect, is developed, in which a simultaneous time-and space-average energy along the structure is considered. The analytical approach highlights di!erent scale laws in the energy transmission mechanism. The parameter, related to the ratio between a characteristic space-average length and the wavelength, controls this characteristic scale. In the small-scale transmission range ( (1), a vibration conductivity principle fails for every type of considered structure. On the other hand, in the large-scale range ( 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 di!erent behaviours is proposed and two types of basic energy interactions between waves are identi"ed, leading to di!erent energy contributions: the coincident wave energy and the interference wave energy, with totally di!erent asymptotic features. In fact, the coincident wave energy asymptotically tends to satisfy the energy balance in a thermal form over the 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 scale range.