Identification of a non-linear damping coefficient characteristics in the free decay test of a single pendulum with friction.

A pendulum in form of an equal arms angle body being a part of a two degrees-of-freedom mechanical system with friction is identified with respect to the observed in uence of some resistance of its rotational motion in ball bearings. It is damped in a much more complex manner, what could be considered as a non-linear damping. There is supposed between others, that the effective non-linear damping characteristics depends on a few effects such as fluid friction caused by vibrations of the pendulum with two springs in the air, as well as unknown kinds of a frictional resistance existing in ball bearings. The model under investigation finds its real realization on a laboratory rig designed for experimental investigations of viscous and structural frictional effects. A transient response oscillations of the pendulum are described by the explicitly state-dependent free decay. A free decay test of the pendulum with the state dependent non-linear parameters of damping and stiffness has been performed in this paper. It provided interesting observations that led to elaboration of a method of the overall damping coefficient identification. Effects of application of the proposed semi-empirical method of identification of the overall damping and stiffness coefficients have been illustrated and discussed

Resonances and Synchronization in Two Coupled Oscillators with Stick-Slip Vibrations and Spring Pendulums

We study the dynamical behavior of a system of two coupled mechanical oscillators with spring pendulums and driven by a stick-slip induced vibrations. Each of the oscillator consists of the body placed onto a moving belt/foundation, mechanical coupling associated with the body load pressed the belt depending on the body movement as well as suspended spring pendulum. In addition, the influence of the presence of additional electric/electromagnetic forces acting on the pendulums are analyzed. Different kinds of resonance behavior can be found in the studied system, even if it is simplified to a single degree-of-freedom system. As a result, due to many degrees-of-freedom and strong nonlinearity and discontinuity of the considered system, novel nonlinear dynamical phenomena occur, both near and beyond to the resonance. The motion analysis for different cases is carried out by employing standard numerical methods dedicated for nonlinear systems, including both qualitative and quantitative methods, as well as original animations of the system dynamics created in Mathematica. Understanding the role of coupling, transition between fixed points and energy transition in the considered system can be potentially applied in other similar systems, especially in real electro-mechanical systems, power system or in structural engineering

Simulating the damped vibrations of a fractional oscillator with fuzzy initial conditions.

A Picard-like scheme using quadrature and differential quadrature rules, formerly introduced to solve integro-differential equations, is herein adapted to solve the problem of an oscillator with damping defined by the Riemann- Liouville fractional derivative and with fuzzy initial conditions. Considering fuzzy initial conditions has the meaning of a fuzzification of the problem via the Zadeh’s extension principle. Following Zadeh, fuzziness is a way to take into account an uncertainty which cannot be identified as randomness. In the crisp domain, the proposed approach is able to approximate the reference analytical solutions with high accuracy and a relatively low computational cost. In the linear regime, the technique proposed becomes a non-recursive scheme, providing semi-analytical solutions by means of operational matrices and vectors of known quantities. In this sense, an example of application is given by the free damped vibrations of a linear oscillator in a medium with small viscosity, usually solved by using the method of multiple scales (in the crisp domain)

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

On the Controlling of Multi-Legged Walking Robots on Stable and Unstable Ground

In this chapter, we developed and investigated numerically a general kinematic model of a multi-legged hybrid robot equipped with a crab-like and/or mammal-like legs. To drive the robot’s limbs, a novel generator of gait was employed and tested. The simulation model developed in Mathematica is suitable for virtual study and visualization of the locomotion process. In contrast to our previous papers, in this study we focused especially on precise control of the position of the robot during walking in different directions. In our study we were able to simultaneously control all six spatial degrees of freedom of the robot’s body, as well as all the robot’s legs. Therefore, the investigated robot can be considered and used as a fully controlled walking Stewart platform. What is more, the used algorithm can also be successfully employed to coordinate and control all limbs of the robot on unstable or vibrating ground. As an example, it can be used to stabilize spatial position of the robot when the supporting ground becomes vibrating or unstable, and it will keep the robot stable and prevent it from falling over. Eventually, the developed simulation algorithms can be relatively simply adopted to control real constructions of different multi-legged robots

Лингвистические способы реализации наложений речи в ходе устного дискурса (на материале американских и российских теле- и радиоинтервью)

Рассмотрены типы наложений, встречающиеся в рамках американских и российских радио- и телеинтервью, определены способы их лингвистической и паралингвистической реализации, а также проведен их контрастивный прагматический анализ

Study of dynamic forces in human upper limb in forward fall.

Knowledge of dynamic forces acting on the upper limb is useful, and sometimes even necessary, in its treatment and rehabilitation after injuries, during prostheses designing, as well as in optimization of the sports training process. In this work an attempt to determine the quantity of the inertia forces generated in forward fall has been undertaken. For this purpose a simplified mechanical model of the human body biokinematic chain has been prepared. Geometric data and mass of each element have been taken from anthropometric atlas for the Polish population. Kinematic data necessary to perform the analysis was calculated using fundamental laws of Mechanics. In this way accelerations of the selected points necessary for the determination of inertia forces acting on the individual links of the model were yielded. For validation of the obtained results a numerical model was constructed using SimMechanic module of the Matlab Simulink software. It made possible to compare the results obtained in both simulation methods. To make joints model more realistic a values of the viscous friction were assumed

Investigation of the parametric vibration of the orthotropic plates subjected to periodic in plane forces by multi-modal approximation and R-functions method

The original method of studying parametric vibrations of orthotropic plate with complex shape is proposed. Suggested approach is based on combined application of variational methods and the R-functions theory. Using the proposed method and developed software the regular and chaotic regimes of T-shaped plate are analyzed