On the modelling of hyperbolic heat conduction problems in periodic lattice structures

• Autorzy: Szymczyk J. , Woźniak C.
• Języki publikacji: EN

Abstrakty

EN

A new modelling approach to the hyperbolic heat conduction problems in periodic lattice structures of an arbitrary form is discussed. Taking into account the results obtained in [5] we introduce a special description of the periodic lattice geometry which leads to the heat conduction model governed by the system of finite difference equations. The continuum models are derived from the finite difference equations by using the principle of stationary action.

Słowa kluczowe

EN

periodic lattice; hyperbolic problem; heat conduction

PL

siatki periodyczne; zagadnienie hiperboliczne; przewodnictwo ciepła

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2003
• Tom: Vol. 2, nr 1
• Strony: 183--189
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Szymczyk J.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

autor

Woźniak C.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

Bibliografia

• [1] Fichera G., Is the Fourier theory of heat propagation paradoxical? Rendiconti del Circolo Matematico di Palermo 1992, Serie II, 41, 5-28.
• [2] Jikov V.V., Kozlov C.M., Oleinik O.A., Homogenization of differential operators and integral functionals, Springer Verlag, Berlin-Heidelberg 1994.
• [3] Rychlewska J., Szymczyk J., Woźniak C., A contribution to dynamics of polyatomic lattices, J. Theor. Appl. Mech. 1999, 37, 799-807.
• [4] Rychlewska J., Szymczyk J., Woźniak C., A simplicial model for dynamic problems in periodic media, J. Theor. Appl. Mech. 2000, 38, 3-13.
• [5] Rychlewska J., Szymczyk J., Woźniak C., A new model for the analysis of nonstationary processes in material systems with a periodic structure, Sympozjum Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2002.
• [6] Sanchez-Palencia E., Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127, Springer-Verlag, Berlin 1980.
• [7] Sun C.T., Achenbach J.D., Herrmann G., Continuum theory for a laminated medium, J. Appl. Mech. 1968, 35, 467-475.
• [8] Szymczyk J., Zmienne wewnętrzne w termosprężystości siatek periodycznych o złożonej strukturze (Internal variables in thermoelasticity of periodic lattice structures), Dissertation, Częstochowa University of Technology, Faculty of Mechanical Engineering and Informatics, Częstochowa 2002.
• [9] Woźniak C., Discrete elasticity, Arch. Mech. 1971, 801-816.
• [10] Woźniak C., Wierzbicki E., Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.
• [11] Woźniak C., Wierzbicki E., Woźniak M., A macroscopic model for the heat propagation in the microperiodic composite solids, Journ. of Thermal Stresses 2002, 25, 283-293.

Uwagi

EN

This is the extended version of the communication submitted to GAMM proceedings 2003.