Microlocal modelling in elastodynamic of periodically compound plates

• Autorzy: Jeleniewicz, K. , Nagórko, W.
• Konferencja: Jubilee Symposium Vibrations In Physical Systems (25 ; 15-19.05.2012 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

In the paper, we will present certain method of modelling of elastic, heterogeneous, anisotropic and periodically multicomponent plates. The method is called the microlocal homogenization or the homogenization with microlocal parameters. It differs from the currently known methods in the fact that it does not consist in solving the problem on the basic cell. The system of assumptions and set of modeling relationships is different from that in the classical method of asymptotic homogenization. There occur not only displacement and stress fields in a body, but also some new fields – microlocal parameters − that describe the behavior of a plate inside the basic cell. In the constructed model, there is 1 + n coupled equations, corresponding to three displacements and n microlocal parameters. Moreover, the model equations depend on some postulated functions called shape functions, which must be known. In the paper, we will propose such functions and carry out an analysis of free vibrations of multicomponent plates.

Słowa kluczowe

PL

elastodynamika płyt; metoda homogenizacji; płyta periodyczna

EN

elastodynamics of plates; method of homogenization; periodically compound plates

• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 185--192
• Opis fizyczny: Bibliogr. 2 poz., rys.

Twórcy

autor

Jeleniewicz, K.

• Warsaw University of Life Sciences – SGGW, ul. Nowoursynowska 159, 02-776 Warszawa,

autor

Nagórko, W.

• Warsaw University of Life Sciences – SGGW, ul. Nowoursynowska 159, 02-776 Warszawa,

Bibliografia

• 1. Mathematical modelling and analysis in continuum mechanics of microstructured media, ed. Woźniak Cz. et al., Wyd. Politechniki Śląskiej, Gliwice 2010.
• 2. Nagórko W., Microlocal modelling of periodic elastic plates, (in:) Mathematical methods in continuum mechanics, Wyd. Politechniki Łódzkiej, Łódź 2011, 317-329.