scholarly journals ABOUT OF THE DYNAMICS OF FORCED OSCILLATIONS IN NONLINEAR SYSTEMS

2019 ◽  
Author(s):  
A. N. Qurbanov ◽  
I. Z. Sardarova
Keyword(s):  
Nonlinear System ◽  
Harmonic Balance ◽  
Initial Conditions ◽  
Forced Oscillations ◽  
Dynamic Mode ◽  
Vibration Exciter ◽  
Balance Equations ◽  
Mechanical Part ◽  
Cyclic Mode ◽  
Electromagnetic Vibration

The article discusses the issues of determining the effectiveness indicators of an electromagnetic vibration exciter in a dynamic mode of operation. It is established that this system is whole system of electrical and mechanical circuits. In this case, the mechanical part operates in the mode of forced vibrations. The oscillation parameters of the system, such as amplitude, frequency, and phase, largely depend on the parameters of the system load. For the analysis of this system, differential equations describing an electromagnetic vibration exciter have been compiled. For this purpose, the dependence L(x) of the inductance on the displacement is used. The dynamic modes of one of the ways of asynchronous excitation of an electromagnetic vibration exciter are investigated. The accuracy analysis and the evaluation of the results were performed by the Fisher criterion for the regression model. To analysis of transients in the electromagnetic vibration exciter, were used the software packages WinFact and MatLab to simulate and optimize dynamic systems. It is established that the system, depending on the initial conditions in the simulation, goes into one of two very different modes. In this case, the initial zero conditions switch the system into a “cyclic” mode, and in other, non-zero conditions, the system goes into an approximate cyclic mode, characterized by a higher speed of movement of the anchor. The parameters of the steady state cyclic movement are determined by the method of harmonic balance. The obtained results allow us to describe autoparametric oscillations of the electric equivalent circuit. It has been established that the compilation of harmonic balance equations corresponding to a linear system helps simplify the solution of the task of determining the dynamics of forced oscillations. The expressions for determining the tractive force and the current flowing through the circuit are obtained, the wavelet spectra of vibration are constructed using the MatLab software package. As a result, for the mechanical part of a nonlinear system, in fact, it is necessary to solve only harmonic balance equation. The results show that this theoretical model allows a more qualitative and accurate assessment of the observed phenomenon. Based on this, the asymptotic conditions for solving the harmonic balance equations of a nonlinear system are determined. The expressions for the electromagnetic force acting on the anchor are obtained, the conditions for the harmonic balance of the mechanical part of the system are determined. The expressions obtained allow us to construct the amplitude-frequency characteristics of the electromagnetic vibration exciter. In conclusion, not only qualitative, but also quantitative estimates of the observed phenomena were obtained. It has been established that mechanical oscillations of a nonlinear system are insensitive to changes in the supply network and practically have a large amplitude with a constant frequency.

Generalized Harmonic Analysis of Nonlinear Ship Roll Dynamics

1996 ◽  
Vol 40 (04) ◽  
pp. 316-325
Author(s):  
J. C. Peyton Jones ◽  
I. Cankaya
Keyword(s):  
Harmonic Analysis ◽  
Harmonic Balance ◽  
Initial Conditions ◽  
Balance Equations ◽  
Validation Process ◽  
Algebraic Expressions ◽  
Resonant Modes ◽  
Ship Roll ◽  
Righting Moment ◽  
Simulation Time

Algebraic expressions are presented which enable the harmonic balance equations to be written down directly in terms of the coefficients of a general nonlinear ship roll equation, without restriction on the number of harmonics considered. The rolling response is then readily computed, as illustrated by an investigation of the resonant modes of ships with angle-dependent cubic damping, or quintic terms in the righting moment. Details are also given of the validation process, showing how simulation time can be reduced by an appropriate choice of initial conditions.

A Resonant Electromagnetic Vibration Exciter of Oscillations with a Feedback

Vestnik MEI ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 62-66
Author(s):  
Mukhtorkhan Ibadullaev ◽  
◽  
Almikhan K. Nuraliev ◽  
Azamat Zh. Esenbekov ◽  
Alisher Zh. Nazarov ◽  
...  
Keyword(s):  
Vibration Exciter ◽  
Electromagnetic Vibration

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

Schwingungsanalyse an Industrierobotern*/Vibration analysis of industrial robots

2019 ◽  
Vol 109 (09) ◽  
pp. 656-661
Author(s):  
A. Karim ◽  
C. Michalkowski ◽  
A. Lechler ◽  
A. Verl
Keyword(s):  
Modal Analysis ◽  
Active Control ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Industrial Robots ◽  
Vibration Exciter ◽  
Dynamic Vibration ◽  
Vibration Behavior ◽  
Working Space ◽  
Electromagnetic Vibration

Dieser Beitrag untersucht experimentell das dynamische Schwingverhalten eines „KR-500–3 MT“ von Kuka mittels eines elektromagnetischen Schwingerregers (Shaker) an insgesamt 28 Messposen im Arbeitsraum. Diese Untersuchungsmethode ist neuartig, da die Ergebnisse mit einer Modalanalyse mit Impulshammeranregung verglichen werden. Ab der vierten Eigenmode entstehen Unterschiede aufgrund der Anregungsform. Zudem wird an jeder Pose eine Messung mit angezogener Motorbremse und eine mit aktiver Regelung durchgeführt und miteinander verglichen.   This paper explores experimentally the dynamic vibration behavior of a Kuka KR-500 MT, using an electromagnetic vibration exciter (shaker) on a total of 28 measuring poses in the working space. As such studies are not known, the results are compared to a modal analysis with impulse hammer excitation. Starting from the fourth normal mode, differences arise due to the form of excitation. Both measurements are performed and compared with each other on each pose with brakes applied as well as with active control.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

scholarly journals Mathematical Modeling of Linear Fractional Oscillators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1879 ◽  
Author(s):  
Roman Parovik
Keyword(s):  
Cauchy Problem ◽  
Fractional Derivatives ◽  
Model Equation ◽  
Initial Conditions ◽  
Memory Function ◽  
Analytical Formula ◽  
Forced Oscillations ◽  
Caputo Fractional Derivatives ◽  
Specific Test ◽  
The Cauchy Problem

In this work, based on Newton’s second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov–Caputo fractional derivatives is carried out. For the resulting model equation, local initial conditions are set (the Cauchy problem). Numerical methods for solving the Cauchy problem using an explicit non-local finite-difference scheme (ENFDS) and the Adams–Bashforth–Moulton (ABM) method are considered. An analysis of the errors of the methods is carried out on specific test examples. It is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method. Forced oscillations of linear fractional oscillators (LFO) are investigated. Using the ABM method, the amplitude–frequency characteristics (AFC) were constructed, which were compared with the AFC obtained by the analytical formula. The Q-factor of the LFO is investigated. It is shown that the orders of fractional derivatives are responsible for the intensity of energy dissipation in fractional vibrational systems. Specific mathematical models of LFOs are considered: a fractional analogue of the harmonic oscillator, fractional oscillators of Mathieu and Airy. Oscillograms and phase trajectories were constructed using the ABM method for various values of the parameters included in the model equation. The interpretation of the simulation results is carried out.

Parameters estimation of HIV infection model of CD4+T-cells by applying orthonormal Bernstein collocation method

2018 ◽  
Vol 11 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Farshid Mirzaee ◽  
Nasrin Samadyar
Keyword(s):  
T Cells ◽  
Nonlinear System ◽  
Hiv Infection ◽  
Initial Conditions ◽  
Bernstein Polynomials ◽  
Nonlinear Ordinary Differential Equation ◽  
Parameters Estimation ◽  
Infection Model ◽  
Algebraic Equations ◽  
Hiv Infection Model

The HIV infection model of CD4[Formula: see text][Formula: see text]T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.

Sign in / Sign up

Export Citation Format

Share Document