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Chaotic convection of viscoelastic fluid in porous medium under G-jitter

Bhadauria B. S., Singh A., Singh M. K.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 1

37--51

The present article aims at investigating the effect of gravity modulation on chaotic convection of a viscoelastic fluid in porous media. For this, the problem is reduced into Lorenz system (non-autonomous) by employing the truncated Galerkin expansion method. The system shows transitions from periodic to chaotic behavior on increasing the scaled Rayleigh number R. The amplitude of modulation advances the chaotic nature in the system while the frequency of modulation has a tendency to delay the chaotic behavior which is in good agreement with the results due to [1]. The behavior of the scaled relaxation and retardation parameter on the system is also studied. The phase portrait and time domain diagrams of the Lorenz system for suitable parameter values have been used to analyze the system.

The effect of nonlinear restraint on torsional buckling and post-buckling behaviour of a thin-walled column

Szymczak C.

Foundations of Civil and Environmental Engineering

2006

No. 7

333-342

Torsional buckling and post-buckling of a simply supported axially compressed thin-walled column of open bisymmetric cross-section with a central restrain has been investigated. The nonlinear behaviour of the restraint against the rotation angle of the cross-section has been assumed. The stability consideration is based upon the classical theory of beams with nondeformable cross-section. The solution of the buckling and post-buckling behaviour problem formulated has been found with the perturbation approach. The critical load and the initial post-buckling path of equilibrium for I - column for the cubic relation of the restraint reaction and the rotation angle have been determined. The results show the considerable effect of nonlinearity of the restraint behaviour on the post-buckling path of equilibrium of the column in comparison with the linear restraint.

On determination of displacements from given strains and height function in the non-linear theory of thin shells

Szwabowicz M. L., Pietraszkiewicz W.

Journal of Theoretical and Applied Mechanics

2002

Vol. 40 nr 1

259-272

The position vector of the deformed shell reference surface is expressed by its projection onto the coordinate plane and the height function over that plane. The projected position is then determined by quadratures entirely from three surface strains and the height function. The latter fields can be found as solutions to the non-linear boundary value problem of thin elastic shells, developed by Szwabowicz (1999). The corresponding displacement field is determined from the deformed position vector by simple algebraic formulae.

Wektor wodzący powierzchni podstawowej powłoki odkształconej wyrażono przez jego rzut na płaszczyznę odniesienia i funkcję wysokości ponad tę płaszczyznę. Zrzutowane składowe tego wektora wyznaczono za pomocą kwadratur zależnych od odkształceń powierzchni i funkcji wysokości, które można wyznaczyć, rozwiązując zagadnienie brzegowe nieliniowej teorii cienkich powłok sprężystych w postaci zaproponowanej przez Szwabowicza (1999). Odnośne pole przemieszczeń wyznaczono przy pomocy prostych wzorów algebraicznych.