A diffusion model for a one-dimensional structure, coupled with an auxiliary system

This paper extends the concept of a local energy approach to homogeneous structures which are coupled with an auxiliary resonant system. The case of a one-dimensional homogeneous master structure (bar, beam) coupled over its length with a homogeneous auxiliary system composed of resonant arbitrary subsystems is analyzed. It is shown that under specific assumptions, the vibrational energy density of the coupled master structure can be predicted by solving a simple energetic boundary value problem that accounts for the mechanical coupling with the auxiliary subsystem. In the context of vibrational energy propagation, an important question is whether heterogeneity introduced by the auxiliary system enhances the diffusive behavior of the master structure. Numerical results for various types of auxiliary systems show that the effective diffusion coefficient of the coupled system is generally increased compared to the uncoupled master structure.