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Microlocal modelling in elastodynamic of periodically compound plates

Jeleniewicz K., Nagórko W.

Vibrations in Physical Systems

2012

Vol. 25

185--192

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.

Non-asymptotic modelling in elastodynamics of periodically ribbed plate

Jeleniewicz K., Nagórko W.

Vibrations in Physical Systems

2010

Vol. 24

207--212

In the paper we consider plates reinforced by ribs. Assuming a periodic distribution of the ribs in the plate, an averaged model is being constructed. The method used here is not asymptotic. In the modelling equations a microstructure parameter remains (basic cell size). To test out the model, a case of free vibrations is being analyzed.

W pracy rozważa się płyty wzmocnione żebrami. Zakładając periodyczne rozmieszczenie żeber w płycie, konstruuje się model uśredniony. Metoda jaką tu zastosowano nie jest metodą asymptotyczną. W równaniach modelujących pozostaje parametr mikrostruktury (wymiar komórki periodyczności). W celu przetestowania modelu analizuje się przypadek drgań własnych.

Homogenization applied in modelling of arteries

Lukes V., Rohan E.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

2003

nr 21

165-170

The paper deals with homogenization method applied in modelling mechanics of arterial wall. The influence of microstructure on the wave propagation is pursued. The multi-layered structure of arterial wali is considered, each layer is modelled using fibre reinforced materiał consisting of hyperelastic materiał with periodic distribution of fluid filled incompressible inclusions. The effective parameters are derived by the method of homogenization. The fluid-structure interaction problem is assumed to be axisymmetric, one dimensional flow is considered through symmetric shelł which oscillates in both radial and longitudinal directions. Various arrangements of the microstructure are examined.