The effect of an external harmonic force on a self-excited oscillating system with a variable parameter

1971 ◽  
Vol 7 (10) ◽  
pp. 1061-1068 ◽  
Author(s):  
V. C. Kononenko ◽  
P. S. Koval'chuk
Keyword(s):  
Variable Parameter ◽  
Harmonic Force ◽  
External Harmonic Force

scholarly journals Manipulating Single Enzymes by an External Harmonic Force

2007 ◽  
Vol 98 (16) ◽  
Author(s):  
Michael A. Lomholt ◽  
Michael Urbakh ◽  
Ralf Metzler ◽  
Joseph Klafter
Keyword(s):  
Harmonic Force ◽  
External Harmonic Force

Nonlinear argumental oscillators: A few examples of modulation via spatial position

2016 ◽  
Vol 23 (18) ◽  
pp. 2888-2911 ◽  
Author(s):  
Daniel Cintra ◽  
Pierre Argoul
Keyword(s):  
Magnetic Field ◽  
Spatial Localization ◽  
Spatial Position ◽  
Experimental Results ◽  
Harmonic Force ◽  
Van Der Pol ◽  
Stable Regime ◽  
Van Der Pol Representation ◽  
Localized Magnetic Field ◽  
External Harmonic Force

Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called “argumental oscillation”. In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.

scholarly journals REACTANCES AND SUSCEPTANCES OF MECHANICAL SYSTEMS

2021 ◽  
pp. 64-75
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Harmonic Force ◽  
Parallel Connection ◽  
Electrical Circuits ◽  
Major Interest ◽  
Inert Body ◽  
Complex Mechanical Systems ◽  
External Harmonic Force

The classical solution to the problems associated with calculating the velocities and reactions of elements of complex mechanical systems under harmonic force consists in the compilation and integration of systems of differential equations and is rather cumbersome and time-consuming. In most cases, a steady state is of major interest. The purpose of this study is to develop essentially compact methods for calculating systems under steady-state conditions. The problem is solved by the methods which are typically used to calculate electrical circuits. Representation of harmonic quantities as rotating vectors in a complex plane and the operations with their complex amplitudes can greatly facilitate the calculation of arbitrarily complex mechanical systems under harmonic effects in the steady state. In the proposed method, a key role is played by mechanical reactance, resistance, and impedance for the parallel connection of consumers of mechanical power, as well as susceptance, conductance, and admittance for the serial one. At force resonance, the total reactance of the mechanical system is zero. This means that the system does not exhibit reactive resistance to the external harmonic force. At velocity resonance, the total susceptibility of the mechanical system is zero. This means that the system has infinitely high resistance to the external harmonic force. As a result, the stock of the source of harmonic force is stationary, although the inert body and the elastic element oscillate.

Screw Theory Applied to a Rigid Cylinder Moving on a Plane

2011 ◽  
Author(s):  
James Di´az-Gonza´lez ◽  
Lourdes Rosario
Keyword(s):  
Coulomb Friction ◽  
Screw Theory ◽  
Cylindrical Part ◽  
Rolling Motion ◽  
Harmonic Force ◽  
Friction Forces ◽  
Dimensionless Variable ◽  
Static Plane ◽  
Vibration Parameters ◽  
External Harmonic Force

In this work a mathematical model of the motion of a cylinder moving on a plane is deduced using screw theory. The linear Coulomb friction equations are applicable for the maximum static and kinetic friction forces. In the case of the rolling motion of a cylinder, the friction forces are not necessarily maxima. This paper describes the dynamic states of motion of a cylindrical part moving in three separate scenarios by the Euler dual equation. The first scenario is when the cylinder is moving on a horizontal static plane due to an external harmonic force proportional to the mass of the part. For this case, the sliding conditions are expressed as a function of the vibration parameters and generalized based on a harmonic dimensionless variable. The second and third scenarios are when the cylinder is moving by translational displacements on a horizontal and inclined plane.

Stochastic Models for Chladni Figures

2015 ◽  
Vol 59 (2) ◽  
pp. 287-300 ◽  
Author(s):  
Jaime Arango ◽  
Carlos Reyes
Keyword(s):  
Stochastic Stability ◽  
Stochastic Models ◽  
Natural Frequencies ◽  
Vibrational Mode ◽  
Equilibrium Solutions ◽  
Harmonic Force ◽  
Plausible Model ◽  
Nodal Set ◽  
Chladni Figures ◽  
External Harmonic Force

AbstractChladni figures are formed when particles scattered across a plate move due to an external harmonic force resonating with one of the natural frequencies of the plate. Chladni figures are precisely the nodal set of the vibrational mode corresponding to the frequency resonating with the external force. We propose a plausible model for the movement of the particles that explains the formation of Chladni figures in terms of the stochastic stability of the equilibrium solutions of stochastic differential equations.

Some Aspects of the Dynamical Behavior of the Impact Damper

2005 ◽  
Vol 11 (4) ◽  
pp. 459-479 ◽  
Author(s):  
F. Peterka ◽  
B. Blazejczyk-Okolewska
Keyword(s):  
Vibration Amplitude ◽  
Degrees Of Freedom ◽  
Dynamical Behavior ◽  
Coefficient Of Restitution ◽  
Harmonic Force ◽  
Impact Damper ◽  
Motion Trajectories ◽  
The Impact ◽  
Impact Motion ◽  
External Harmonic Force

In this paper we show some aspects of the dynamical behavior of a two-degrees-of-freedom system forced with an external harmonic force, which impacts cause a reduction of the vibration amplitude of the basic system. The purpose of the presented investigations is to determine the coefficient of restitution and the damping coefficient of the fender that ensure the required degree of a reduction in these vibrations. The regions of existence bifurcation diagrams and motion trajectories of different kinds of impact motion are presented and analyzed. The impact damper of vibrations is compared with a linear damper. The investigations have been conducted by means of numerical simulations.

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