Modelling and numerical simulations of a pendulum elastically suspended and driven by frictional contact with rotating disk.

The work concerns modelling and numerical simulations of a special kind of physical pendulum frictionally driven. The pendulum’s joint is suspended elastically in the plane of the motion resulting in the full plane motion of the pendulum and in tree degrees of freedom of the analysed mechanical system. The pendulum is driven by frictional contact with a disk with a constant angular velocity. Examples of self-excited oscillations and bifurcation dynamics of the pendulum are presented. Majority of the work focuses on efficient approximate modelling of the resultant friction force and moment occurring on the contact surface

Axially excited spatial double pendulum nonlinear dynamics.

Analysis of a 3D spatial double physical pendulum system, coupled by two universal joints is performed. External excitation of the mechanism is realized by axial periodic rotations of the first joint of the pendulum. System of ODEs is solved numerically and obtained data are analyzed by a standard approach, including time series, phase plots and Poincaré sections. Additionally, FFT (Fast Fourier Transform and the wavelet transformation algorithms have been applied. Various wavelet basic functions have been compared to find the best fit, e.g. Morlet, Mexican Hat and Gabor wavelets. The so far obtained results allowed for detection of a number of non-linear effects, including chaos, quasi-periodic and periodic dynamics, as well the numerous and different bifurcations. Scenarios of transition from regular to chaotic dynamics have been also illustrated and studied

Dynamics simulations of a rigid body lying on a vibrating table with the use of special approximations of the resulting contact forces.

The work presents simulations and dynamics of a rigid body lying on a vibrating table. An attempt of shaping and control the body dynamical behavior, by the use of manipulation of parameters of the table oscillations, is presented. This work is also an implementation of the specially prepared mathematical models of friction between table and the moving body. Those models are based on the integral model assuming the fully developed sliding on the plane contact area with the foundation of any pressure distribution. In order to simplify the calculations and reduce their computational cost, special approximations of the integral models of friction force and moment are used. They are based on Padé approximants and their generalizations

Experimental and numerical investigations of a pendulum driven by a low-powered DC motor.

The work is a continuation of numerical and experimental investigations of a system consisting of a single pendulum with the joint horizontally driven by the use of a crank-slider mechanism and DC motor. The power supplied to the DC motor is relatively small when compared with our earlier investigations, which results in clear return influence of the pendulum dynamics on the DC motor angular velocity and much more rich bifurcation dynamics of the whole system, including regions of chaotic behaviour. In the experiments, the motor is supplied by the use of different but constant in time voltages. A series of experiments allow for accurate estimation of the model parameters and, in the further step, for prediction of the real system behaviour, also for other functions representing input voltage, including the time-varying ones

On the clutch dynamics with the approximations of resulting contact forces.

The aim of the work is to present effectiveness of numerical simulations of clutch with frictional contacts, elaborated by some of the current articles in the last few years. The friction models assumes full developed sliding and the classical Coulomb friction law on each element of the contact with general shape and any pressure distribution. Then special modification of the integral model of friction force and moment are proposed. The approximants based on Padé approximants and their generalizations. In the work the clutch dynamics with contacts forces model is presented. The system was simplified to friction disk on rotating master disk. Two different configurations are investigated: coaxial and non-coaxial arrangement of the two disks. For the appropriate rotations speed, the system of non-coaxial arrangement can exhibit the ability to self-centering. The models based on generalizations of Padé approximants are compared with the simulation results obtained by the use of approximants based on Taylor’s expansion and models with exact integral expressions for friction force and torque components

Matematyczne i numeryczne metody analizy bifurkacji i dynamiki chaotycznej układów mechanicznych z tarciem i uderzeniami

Książka jest przeznaczona dla studentów, inżynierów i pracowników naukowych z obszaru zagadnień, dotyczących dynamiki układów nieliniowych niegładkich dyskretnych, bifurkacji i chaosu oraz modelowania i metod numerycznych.Książka obejmuje wprowadzenie do podstaw teoretycznych, modelowania i metod numerycznych, związanych z analizą dynamiki bifurkacyjnej i chaotycznej układów mechanicznych z tarciem i uderzeniami. Autorzy przedstawiają oryginalne metody modelowania i analizy wybranych układów mechanicznych niegładkich oraz prezentują nowe wyniki uzyskane w tym obszarze dynamiki nieliniowej układów dyskretnych.Książka została dofinansowana przez Dziekana Wydziału Mechanicznego PŁ prof. dr hab. inż. Piotra Kulę, a prezentowany w niej materiał finansowany był poprzez Ministerstwo Edukacji i Nauki (granty 4 T07A 031 28; 4 T07C 044 29)

Potrójne wahadło z przeszkodami i model mechanizmu korbowego.

A model of a flat triple pendulum with obstacles imposed on its position is used for the modelling of a piston-connecting rod-cranks haft system of a mono-cylinder four-stroke combustion engine. The introduced self-excited system can be only treated as the first step in more advanced modelling of real processes, but some examples of numerical simulations exhibit well known six stages of the piston sliding along the cylinder surface per cycle.Model płaskiego potrójnego wahadła fizycznego z przeszkodami ograniczającymi jego ruch został użyty do zamodelowania mechanizmu korbowego silnika spalinowego. Wprowadzony samowzbudny model może być traktowany jedynie jako bardzo zgrabne przybliżenie rzeczywistych zjawisk zachodzących w cylindrze silnika spalinowego. Pomimo tego, kilka zaprezentowanych przykładów symulacji numerycznych wykazuje bardzo dobrą zgodność z danymi doświadczalnymi prezentowanymi w literaturze

An Investigation of Fractional Bagley–Torvik Equation

In this article, we will solve the Bagley–Torvik equation by employing integral transform method. Caputo fractional derivative operator is used in the modeling of the equation. The obtained solution is expressed in terms of generalized G function. Further, we will compare the obtained results with other available results in the literature to validate their usefulness. Furthermore, examples are included to highlight the control of the fractional parameters on he dynamics of the model. Moreover, we use this equation in modelling of real free oscillations of a one-degree-of-freedom mechanical system composed of a cart connected with the springs to the support and moving via linear rolling bearing block along a rail