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5 Vibrations in Physical Systems

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Governing equations for the coupled electromagnetics and acoustics of clay and clay like porous media

100%

Drzewiecki A. , Sypniewska-Kamińska G.

tom Vol. 20

138--139

Nonlinear vibrations of rotating system near resonance

100%

Starosta R. , Sypniewska-Kamińska G.

tom Vol. 26

265--272

The paper concerns analysis of nonlinear vibration of the rotating system consisted of two disks and shaft. The analytical multiple time scale method is applied to the analysis dynamics of the system near main resonance. The transition phenomenon depending on the value of the nonlinearity parameter is discussed. All the analytical results have been confirmed numerically.

Vibration of the oscillator exchanging mass with surroundings

80%

Starosta R. , Sypniewska-Kamińska G. , Awrejcewicz J.

tom Vol. 27

333--338

Vibration of two simple open systems (namely the linear mass-sprins oscillator and the mathematical pendulum) are investigated. During the motion, the body absorbs matter through its boundary. In both cases, mechanism of mass absorption is modeled as a perfectly 'inelastic' collision and constant rate of mass change is assumed. The paper is focused on the influence of mass change on the kinematic aspects of oscillations.

Dynamic analysis of collision of beam with rough obstacle

80%

Bartkowiak T. , Kamiński H. , Sypniewska-Kamińska G.

tom Vol. 25

71--76

Beam collision with an obstacle is studied in the work. It is presumed that the conditions, under which the motion of the beam before, during and after the collision is planar, are fulfilled. Friction forces between contacting surfaces of both objects are taken into consideration. The problem is solved using the Rigid Finite Element Method. Interaction between the beam and the obstacle, taking into account the elastic properties and surface roughness of the latter one, is modelled using the elastic element. Three different models of the interaction, corresponding to various conditions governing the process, have been presented. Numerical simulations for the three possible variants of collision have been conducted. The results for the three considered cases of the collision have been compared with data obtained using Routh method.

Two approaches in the analytical investigation of the spring pendulum

80%

Sypniewska-Kamińska G. , Starosta R. , Awrejcewicz J.

tom Vol. 29

art. no. 2018005

Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.