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In this paper, we cast damped Timoshenko and damped Bresse systems into ageneral framework for non-equilibrium thermodynamics, namely the GENERIC(General Equation for Non-Equilibrium Reversible-Irreversible Coupling)framework. The main ingredients of GENERIC consist of five building blocks: astate space, a Poisson operator, a dissipative operator, an energy functional,and an entropy functional. The GENERIC formulation of damped Timoshenko anddamped Bresse systems brings several benefits. First, it provides alternativeways to derive thermodynamically consistent models of these systems byconstruct- ing building blocks instead of invoking conservation laws andconstitutive relations. Second, it reveals clear physical and geometricalstructures of these systems, e.g., the role of the energy and the entropy asthe driving forces for the reversible and irreversible dynamics respectively.Third, it allows us to introduce a new GENERIC model for damped Timoshenkosystems that is not existing in the literature.

Non-equilibrium thermodynamics of damped Timoshenko and damped Bresse systems