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1

Analytical model of the two-mass above resonance system of the eccentric-pendulum type vibration table

Lanets O. S., Dmytriv V. T., Borovets V. M., Derevenko I. A., Horodetskyy I. M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 4

116--129

EN

The article deals with atwo-mass above resonant oscillatory system of an eccentric-pendulum type vibrating table. Based on the model of a vibrating oscillatory system with three masses, the system of differential equations of motion of oscillating masses with five degrees of freedom is compiled using generalized Lagrange equations of the second kind. For given values of mechanical parameters of the oscillatory system and initial conditions, the autonomous system of differential equations of motion of oscillating masses is solved by the numerical Rosenbrock method. The results of analytical modelling are verified by experimental studies. The two-mass vibration system with eccentric-pendulum drive in resonant oscillation mode is characterized by an instantaneous start and stop of the drive without prolonged transient modes. Parasitic oscillations of the working body, as a body with distributed mass, are minimal at the frequency of forced oscillations.

2

Wyznaczanie obciążeń układu kostno-stawowego z wykorzystaniem modelu dynamiki kończyny górnej

Świeczkowski-Feiz D., Pałko T., Sienkiewcz M.

Elektronika : konstrukcje, technologie, zastosowania

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2018

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Vol. 59, nr 11

47--52

PL

Zastosowanie modeli dynamiki w modelowaniu biomechanicznym pozwala na wyznaczenie obciążeń w układzie kostnym lub kostno-mięśniowym. Celem opracowania modelu dynamiki kończyny górnej jest wyznaczenie oraz analiza momentów działających na układ podczas wykonywania ruchu. Model matematyczny kończyny górnej o pięciu stopniach swobody został opisany przy pomocy równań Lagrange'a drugiego stopnia. Następnie, poprzez symulację zadanego ruchu rozwiązano zadane proste dynamiki. Opracowany model dynamiki został sparametryzowany na podstawie ogólnodostępnych danych antropometrycznych.

EN

Using dynamics models in the biomechanical modeling allows to determine the loads in the skeletal or bone-muscular systems. The aim of developing the dynamic model of the upper limb is to determine and analyze the torques, which appear in the system during motion. The mathematical model of the upper limb with five degrees of freedom has been described by Lagrange's equations. Next, the forward dynamics was solved by simulating a motion. The determined dynamics model was parameterized using anthropological data.

3

Lagrangian modelling of a synchronous step-down converter by considering the parasitic elements

Skandarnezhad A., Koochaki A., Mohammadmoradi Y., Kalteh A.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 3

6--10

EN

This paper introduces a new technique to model a synchronous buck converter in the closed loop compensated conditions by Lagrange equation. In the design process of converters it is desirable to assess as many critical design parameters and parasitic effects by simulation as possible, since the control is hard to tune after fabrication. The main advantage of this method is its versatility and simple implementation. In this work, switch conduction loss of an integrated, synchronous buck converter is identified to have significant influence on control loop dynamics. Thus, an equivalent small-signal model for the close loop frequency response accounting for switch conduction loss is developed. Finally, the model is validated against the frequency response obtained by periodic stability analysis which can account for parasitic effects and loading. Very good agreement between the extended model and the simulation results obtained.

PL

W artykule opisano modelowania z wykorzystaniem równań Lagrange synchronicznego przekształtnika typu buck. Straty przełączania są identyfikowane jako wpływające na dynamikę. Analizowano okresową stabilność z uwzględnieniem efektów pasożytniczych.

4

Modelowanie i sterowanie układu kula-belka

Burghardt A., Giergiel J.

Modelowanie Inżynierskie

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2009

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T. 6, nr 37

55-62

PL

Zaprezentowane podejście do procesu modelowania obiektu typu US z wykorzystaniem równań Lagrange'a umożliwiło otrzymanie modelu matematycznego w formie umożliwiającej jego wykorzystanie w procesie syntezy adaptacyjnego algorytmu sterowania. Ponadto otrzymany model matematyczny zastosowano do budowy emulatora obiektu kula-belka, który był wykorzystywany podczas badań symulacyjnych. Zaproponowany algorytm sterowania pozwolił na stabilizację pozycji kuli na belce, co wykazano w badaniach symulacyjnych oraz podczas weryfikacji na obiekcie rzeczywistym. Dalsze prace wykorzystujące zaproponowany model będą prowadzone w kierunku nie tylko stabilizacji pozycji kuli, ale również w kierunku sterowania nadążnego ruchem kuli po belce.

EN

The ball-and-beam problem is a benchmark for testing control algorithms. This paper we presents analysis and implementation adaptive control schemes on ball and beam system. Dynamic model for the system was derived using Lagrange equations. Control algorithm solves a stabilization under-actuated ball and beam system was created by using Lyapunov theory. The controllers designed for the system have been simulated by Matlab/Simulink.

5

Torsional and transverse vibrations of an unbalanced circular disc

Matyka K., Buśkiewicz J.

Vibrations in Physical Systems

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2006

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Vol. 22

273--278

6

The influence of linearization of nonlinear dynamic equations of motion concerning the impact phenomenon on the impulse load of working machines

Towarek Z., Zakrzewski S.

Vibrations in Physical Systems

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2006

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Vol. 22

355--360

7

The change in the hyperbolic orbital elements due to application of a small impulse

Kamel O. M., Soliman A. S., Ammar M. K.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 2

107-119

EN

The differential variations in the hyperbolic orbital classical element s due to a small impulse in the direction of the velocity vector are computed. We applied the method of Gauss for secular perturbations using the Lagrangian form of planetary equations.

8

Methodology of the stepper motor rotational motion investigations

Wawszczak W., Towarek Z., Jagiełło B.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 1

87-95

EN

Advantages and disadvantages of separate studies on dynamic systems using either theoretical or experimental methods have been emphasized, and a stand point has been expressed that both methods must definitely be combined. Measurements of vibration in the rotational motion by means of an RWJ instrument served as the methodology of experimental studies, while Lagrange quadratic equations were used for theoretical analysis. The combined experimental-theoretical methodology was adopted for the nonstationary motion of a stepper motor. The analysis and reduction of the system of equations of dynamics for an inverse issue have been presented and selected experimental solutions for the motion of the drive system of a stepper motor has been quoted.

9

Uwagi na temat dynamiki mechanizmów

Skalmierski B.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2001

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z. 17

195-200

PL

Analiza dynamiki mechanizmów wymaga rozwiązywania nieliniowych równań różniczkowych. Są nimi równania Lagrange ’a , które są równaniami drugiego rzędu. Są nimi równania Lagrange ’a , które są równaniami drugiego rzędu. W postaci tensorowej zapiszemy je następująco [wzór] W szczególnym przypadku, układów o jednym stopniu swobody redukują się one do postaci [2, 3]: [wzór]

EN

Mechanism dynamics analysis demands the solution of the complicated non-linear differential equations. These equations are derived on the basis of Lagrange equations of the second order and they are the tensor equations in the form: [formula] For the systems of single degree of freedom the system of equations (A) is reduced to a single equation in the form: [formula]

10

Strong discontinuity waves in extended phenomenological electrodynamics

Hoffmann T., Niechciałkowska B.

Journal of Technical Physics

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2000

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Vol. 41, no 4

387-394

EN

In the paper the description of discontinuity of the electromagnetic field in the continuum medium in terms of the extended electrodynamics in considered. The classical field theory based on the analytical Lagrange - Hamilton methods has been used as a formal apparatus. The classical theory of discontinuity waves is applied to the description of the discontinuity of the field. Dynamics of the electromagnetic field is expressed in terms of the Lagrange equations of motion in the linear approximation.

11

A reactedness model for local extinction and reignition phenomena in turbulent jet diffusion flames

Koutmos P., Mavridis C

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 1

115-130

EN

An approach for modeling finite-rate chemistry effects such as local extinction and reignition in piloted diffusion flames of CO/H2/N2 or CH4 and air is presented. A partial equilibrium/two-scalar exponential PDF combustion model is combined with a 2D Large Eddy Simulation procedure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of tge PDF scalars is avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local Damkohler number against a 'critical' local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable that follows a linear deterministic relaxation to its mean value (IEM). Comparisons between simulations and measurements suggested the ability of the method to calculate adequately the partal extinction and reignition phenomena observed in the experiments.