Nonlinear vibrations of rotating system near resonance

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

Przedziałowa metoda różnic skończonych w zagadnieniu przepływu biociepła opisanym równaniem Pennesa zależnym od nieprecyzyjnych parametrów

In this paper the transient bioheat transfer problem given by the one-dimensional Pennes equation with mixed boundary conditions is considered. The model assumes the heat transfer between the skin and its surroundings in the case of a natural and forced convection. For computations the interval finite difference method of Crank--Nicolson type together with the floating-point interval arithmetic is used. In this way, uncertain geometric and thermophysical parameters can be represented in the form of intervals as well as the resultant temperature distribution over time.W pracy rozważa się nieustalone zagadnienie przepływu biociepła w skórze opisane równaniem Pennesa z mieszanymi warunkami brzegowymi. W modelu uwzględniono wymianę ciepła między skórą a otoczeniem zarówno w przypadku konwekcji swobodnej, jak i wymuszonej. Do obliczeń wykorzystano przedziałową metodę różnic skończonych typu Cranka-Nicolsona oraz zmiennopozycyjną arytmetykę przedziałową. W ten sposób nieprecyzyjnie określone wartości parametrów geometrycznych i termofizycznych mogą być reprezentowane w postaci przedziałów, podobnie jak wynikowy rozkład temperatury w czasie

Vibration of the oscillator exchanging mass with surroundings

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

Nonlinear vibration of rotating system near resonance

The paper concerns analysis of nonlinear vibration of the rotating systems consisted of rigid disks mounted on the elastic massless shaft. The investigations are focused on their behaviour under the resonance conditions. The analytical method of multiple scales in time domain is applied to the analysis of dynamics of the system near main resonance. The transition phenomenon depending on the value of the nonlinearity parameter is discussed

Nonlinear vibration of rotating system near resonance

The paper concerns analysis of nonlinear vibration of the rotating systems consisted of rigid disks mounted on the elastic massless shaft. The investigations are focused on their behaviour under the resonance conditions. The analytical method of multiple scales in time domain is applied to the analysis of dynamics of the system near main resonance. The transition phenomenon depending on the value of the nonlinearity parameter is discussed

Two approaches in the analytical investigation of the spring pendulum

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

Evaluation of the Accuracy of the Solution to the Heat Conduction Problem with the Interval Method of Crank-Nicolson Type

The paper deals with the interval method of Crank-Nicolson type used for some initial-boundary value problem for the onedimensional heat conduction equation. The numerical experiments are directed at a short presentation of advantages of the interval solutions obtained in the floating-point interval arithmetic over the approximate ones. It is also shown how we can deal with errors that occur during computations in terms of interval analysis and interval arithmetic