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The present work examines the analytical solutions of the mathematical fractional Maxwell fluid model near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimensional form. For the sake of better rheology of rate type fluid, developed a fractional model by applying the new definition of Constant Proportional Caputo (CPC) fractional derivative operator that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler functions for velocity and temperature, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, some limiting models such as ordinary Newtonian model had been recovered from fractional model. It is also analyzed that for Newtonian heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity and energy distribution. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models. [ABSTRACT FROM AUTHOR]

In this article, a simple prototype and control system of a lower limb exoskeleton driven by stepper motors was proposed. To study kinematic parameters of the device, a general, three-dimensional simulation model of the exoskeleton was developed. Moreover, a gait pattern was modeled for hip, knee, and ankle joints. It represents sagittal plane angular positions of joints during normal gait and consists of three piecewise-defined sine-square-based functions. It is based on the experimental gait data recorded with an optoelectronic motion capture system for a healthy subject walking on a treadmill. Although the developed pattern is intended to be implemented in a control system of a lower limb exoskeleton for gait rehabilitation, it can be used to control bipedal robots as well. Last but not least, the control approach was tested with the exoskeleton prototype. [ABSTRACT FROM AUTHOR]

This article contains theoretical analysis and experimental study of the original mechatronics system with flexible characteristics which we can adapt to changing needs and external interference. The main purpose of our research is to find a solution that allows tailoring the desired characteristics of systems regardless of changing conditions without their mechanical interference. The system consists of the guide endowed with mass suspended in the air by the linear aerostatic bearing. Linear mechanical spring is attached to the one side of the guide whereas the neodymium magnet is fixed to the other side. Magnet-magnet and magnet-coil interactions have been investigated. The magnet-magnet interaction plays the role of the nonlinear magnetic spring while the magnet-coil interaction plays the role of the electromagnetic spring or electromagnetic damper in terms of the coil current signal. Static and dynamic characteristics of mechanical, magnetic and electromagnetic springs have been analyzed. A new physical model of the magnet-magnet interaction has been presented, the validity of which is confirmed experimentally. In addition, modern IT (information technology) techniques have been used to control the system behavior. The reliable results of the entire system and its springs are obtained by conducting tests on specially constructed laboratory setup. The main benefit of the fabricated setup concerns an elimination of dry friction effects though the frictions is viscous with identifiable movement resistance. [ABSTRACT FROM AUTHOR]

We consider a mathematical model of two-layer beams coupled by boundary conditions in a stationary temperature field taking into account geometric nonlinearity. The stationary temperature field is defined by a 2D heat transfer equation with boundary conditions of the first kind. The geometric nonlinearity is introduced via von Kármán's relations for both beams. Equations of beam deflection are derived due to the Euler–Bernoulli hypothesis. The contact interaction is described using Winkler's model. Scenarios of a transition from regular to chaotic regimes are studied. Phase synchronization of beam vibrations versus both character and intensity of the applied temperature field is investigated. [ABSTRACT FROM AUTHOR]

In this work a new one-dimensional model of thermoelastic inertial contact of a braking pad and a rotating inertial shaft, in the braking or accelerating process, is presented and analyzed. Besides dry friction, frictional heat is generated between the two given bodies in contact. The dynamics of the considered system is governed by two non-linear differential equations and one non-linear integral equation. The stability of static solutions, as well as the behavior of contact characteristics in braking and acceleration are analysed. [ABSTRACT FROM AUTHOR]

The derived differential equations govern a coupled linear thermoelastic behaviour in the frame of the Kirchhoff-Love model with the neglected effect of shell element rotary inertia. Then an abstract Cauchy problem for a coupled system by two differential equations in the Hilbert space is defined. It generalizes a series of coupled thermoelastic problems including those considered previously (Kirchhoff-Love and Timoshenko-type shells). All considerations are valid for a wide class of initial and boundary value problems. [ABSTRACT FROM AUTHOR]

Introduction of small parameters to the real physical problems very often is a delicate and non-trivial problem and may be produced in the various ways. Here we analyze non-linear dynamical equation for n → ∞. We propose new formula in the following form and this approach is compared with the usual one. We also obtained asymptotic solutions for Eq. ( 1 ) for γ = ω 2 = 0, n → ∞; γ = 0, n → ∞. We show that cases ω 2 = 0, n → ∞ and γ ≪ 1, n → ∞ may be reduced to the previous ones. [ABSTRACT FROM AUTHOR]

Presents information on the 5th Conference on Dynamical Systems, Theory and Applications, held in December 1999 in Lódz, Poland. Event organizers; Members of the International Scientific Committee; Invited lecturers.