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In this paper, for the first time, the complete set of Tangens hyperbolicus approximations of model of dry friction coupled with rolling resistance for circular contact area between interacting bodies is proposed. The developed approximations are compared with corresponding Padé approximants of the first and second order well known from the literature and with the numerical solution of the exact integral model as well. It is shown that Tangens hyperbolicus approximants are closest to the exact solution. Then the approximated models are applied to the celtic stone dynamics, however with the significant simplifying assumption of circular contact between stone and the table, presenting differences between them again. Certain specific approximations and regularizations of the friction and rolling resistance models enabling and facilitating their application to the real problem are shown. The analysis of the response dependence on initial conditions is performed by the use of a special kind of diagram. [ABSTRACT FROM AUTHOR]

No abstract received. [ABSTRACT FROM AUTHOR]

A weakly nonlinear 2-DOF system, parametrically and externally excited, is studied. An intensive energy transfer between modes of vibrations is discovered. Multiple scales method is used for recognizing resonances occurring in the system. The amplitude response functions for some chosen cases of resonances are obtained and studied. Many of the engineering systems can be investigated in the presented way. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other. [ABSTRACT FROM AUTHOR]

The triple physical pendulum with barriers is used to model a piston — connecting rod — crankshaft system of a mono-cylinder combustion engine. Among other results, a peculiar motion of the piston — connecting rod — crankshaft model is reported, i.e. six sliding stages of the piston along the cylinder per one engine cycle are illustrated. In spite of its simplicity, the introduced model can serve as the first step in a more advanced modeling taking into account various technological details. In particular, the proposed model can be considerably useful for the investigations of impacts between the piston and the cylinder aiming at the reduction or total elimination of this source of harmful noise. [ABSTRACT FROM AUTHOR]

A self-excited friction pair is modeled by a mechanical system of two degrees-of-freedom with a normal force varying during the block displacement. Two different friction coefficients are used, and a normal force pressing the sliding body to a belt depending on an angle bar motion of the analyzed system is applied. In addition, the numerical analysis is supported by the investigation of a real laboratory object modeling the feedback reinforcement of friction forces acting on the block. Both numerical and experimental results are compared showing good agreement. [ABSTRACT FROM AUTHOR]

In this work a triple pendulum with damping, external forcing and impacts is investigated. We integrate the obtained system of governing equations between two successive impacts, and the discontinuity points are detected (by halving time step until the required precision is obtained). For each impact time, the state of the system is transformed using the extended restitution coefficient rule. The theory of Aizerman and Gantmakher is used to calculate the fundamental solution matrices in the analyzed system exhibiting discontinuities. Fundamental matrices are used during calculation of Lyapunov exponents, in stability analysis of periodic solution (Floquet multipliers) and in shooting method of finding periodic orbits. Then some examples for three coupled identical rods with horizontal barrier are shown. [ABSTRACT FROM AUTHOR]

Introduces the articles published in the June 2005 issue of the "International Journal of Bifurcation and Chaos."