Generalized Hamiltonian representation of thermo-mechanical systems based on an entropic formulation |
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| Affiliation: | 1. Departamento de Ingeniería Química, Universidad de Guadalajara, Calz. Gral. Marcelino García Barragán 1451, Guadalajara, Jalisco 44430, Mexico;2. Department of Chemical Engineering, Queen''s University, Kingston, ON, Canada K7L 3N6;3. ICTEAM, Université Catholique de Louvain, Bâtiment EULER 4-6, av. Georges Lemaître, B-1348 Louvain-la-Neuve, Belgium;1. State Key Lab. of Integrated Services Networks, Xidian University, Xi?an, Shaanxi, China;2. Department of Electronic Information Engineering, Nanchang University, Nanchang, Jianxi, 330031, China;3. National Lab. of Radar Signal Processing, Xidian University, Xi?an, Shaanxi, China;4. Luoyang Institute of Electro Optical Equipment of AVIC, Luoyang, Henan, China;5. Institute of Systems Science and Control Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang, China;1. Technische Universität Chemnitz, 09107 Chemnitz, Germany;2. Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany;4. Georgia Institute of Technology, Atlanta, GA 30308, USA |
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| Abstract: | In this work, we present an approach to construct generalized Hamiltonian representations for thermo-mechanical systems. Using entropic formulation of thermodynamic systems, the construction is applied to a class of thermo-mechanical systems. The proposed approach leads to an explicit expression of the dissipation along the trajectories of the dynamics. The considered thermo-mechanical systems are, in a thermodynamical sense, systems for which the dynamics of the extensive variables are functions of the intensive variables with respect to an entropic formulation. Using the entropy as the storage function, the dissipative structures of an analogue to a port-controlled Hamiltonian (PCH) representation are identified with irreversible phenomena, while the conservative structures are identified with reversible or isentropic phenomena. Examples are presented to illustrate the application of the proposed methodology, including a reacting system. |
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| Keywords: | Thermo-mechanical systems Thermodynamics Generalized Hamiltonian dynamics Dissipative systems Entropic formulation |
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