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1
Content available remote The calculation of the eigenfrequencies of the torsional free vibrations of the bars using the method of fundamental solutions
Uściłowska A., Fraska A.
Vibrations in Physical Systems
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2012
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Vol. 25
429--434
EN
This work concerns an application of the method of fundamental solutions to the calculation of the eigenfrequencies of the torsional natural vibrations of the bars. The problem of the torsional free vibrations of the bar is an initial-boundary value problem. In the solution process of this problem, the method of variables separation is used. The boundary value problem is solved by the method of fundamental solutions. The different shapes of the bar cross-section are taken into account. The numerical calculations are performed for the rods made of the materials with the different characteristics (mass, density, shear modulus, etc.). To check the accuracy of the proposed methods the results of numerical experiment are included.
2
Content available remote Solution of plate free vibrations problem by method of fundamental solutions
Uściłowska A.
Vibrations in Physical Systems
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2008
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Vol. 23
383--388
EN
In this paper, a meshless method for solving the natural vibration of plates problem is proposed. For this particular problem the method of fundamental solutions has been implemented. due to its features, the final resolving system can be solved with the classical approaches by using standard numerical procedures. To asses the formulation, the free vibration of some plates were calculated and the results compared with those obtained using other solution techniques. The present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach.
3
Content available remote Application of the Trefftz method to nonlinear potential problems
Uściłowska A.
Computer Assisted Mechanics and Engineering Sciences
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2008
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Vol. 15, No. 3/4
377-390
EN
In this paper some types of nonlinear potential problems are discussed and some of these problems are solved by the Trefftz method. The attention is paid to Fundamental Solutions Method (FSM) supported by Radial Basis Functions (RBF) approximation. Application of FSM to nonlinear boundary problem requires certain modifications and special algorithms. In this paper two methods of treating the nonlinearity are proposed, One on them is Picard iteration. Due to some problems of application of this method the Homotopj Analysis Method (HAM) is implemented for nonlinear boundary-value problems. The results of numerical experiment arc presented and discussed. The '(inclusion is that the method based on FSM for solving nonlinear boundary-value problem gives result with demanded accuracy.
4
Content available remote Solution of the nonlinear equation for isothermal gas flows in porous medium by Trefftz method
Uściłowska A., Kołodziej J. A.
Computer Assisted Mechanics and Engineering Sciences
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2006
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Vol. 13, No. 3
445-456
EN
This paper presents numerical solution to a problem of the transient flow of gas within a two-dimensional porous medium. A method of fundamental solution for space variables and finite difference method for time variable are employed to obtain a solution of the non-linear partial differential equation describing the flow of gas. The inhomogeneous term is expressed by radial basis functions at each time steps. Picard iteration is used for treating nonlinearity.
5
Content available remote Natural convection of power-law fluid
Uściłowska A., Stręk T.
Vibrations in Physical Systems
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2004
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Vol. 21
399--402
6
Content available remote Chaotic motion of an articulated tower under wave loading - Lyapunow exponent
Uściłowska A.
Vibrations in Physical Systems
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2004
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Vol. 21
395--398
EN
This paper contains the investigation of behaviour of an articulated tower under waves loading. The tower is fixed to the bottom by hinge without friction. The regular wave loading is considered in this work. The numerical experiment in prepared. The tower is expected to move chaoticaly for some values of the wave or the tower parameters. Therefore the Lyapunow exponent will be investigated to characterize the behaviour of the tower.
7
Content available remote Chaotic motion of a multi-articulated tower immersed in waving fluid: numerical experiment
Uściłowska A., Kołodziej J. A.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2002
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Vol. 6, No 3
371-377
EN
The offshore structures, such as multi-articulated towers, manipulators working in waving fluid are more and more popular structures. Commonly they are modelled as an inverted pendulum. The motion of such tower immersed in waving fluid is under consideration. It is assumed that the tower is hinged to the seabed by the hinge with friction. The joint of tower elements is the hinge with friction, as well. Motion of tower loaded by regular wave fluid force is considered. The numerical experiment shows that the multi-potential systems may move chaotically for some parameters of the tower and the fluid.
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