scholarly journals Periodic Motions With Overshooting Phases of a Two-Mass Stick–Slip Oscillator

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Orbits ◽  
Dry Friction ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Contact Forces ◽  
Periodic Motions ◽  
Stick Slip ◽  
Two Degrees Of Freedom ◽  
The Masses

We investigate the dynamics of a two degrees-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs and in contact with a belt moving at a constant velocity. The contact forces between the masses and the belt are given by Coulomb's laws. Several periodic orbits including slip and stick phases are obtained. In particular, the existence of periodic orbits involving a part where one of the masses moves at a higher speed than the belt is proved.

scholarly journals Dynamics of Coupled Oscillators Excited by Dry Friction

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Dry Friction ◽  
Initial Conditions ◽  
Analytical Form ◽  
Contact Forces ◽  
Time Duration ◽  
Stick Slip ◽  
Coulomb’S Friction ◽  
The Masses ◽  
Stick Slip Motion ◽  
Two Degree Of Freedom

In this paper, we present an analytical method to investigate the behavior of a two-degree-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs. These two masses are in contact with a driving belt moving at a constant velocity. The contact forces between the masses and the belt are obtained assuming Coulomb’s friction law. Two families of periodic motions are found in closed form. The first one includes stick-slip oscillations with two switches per period, the second one is also composed of stick-slip motion, but includes three switches per period. In both cases, the initial conditions and the time duration of each kind of motions (stick or slip phases) are obtained in analytical form.

scholarly journals Analytical Investigation of Periodic Solutions for a Coupled Oscillator With Dry Friction

2009 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Solutions ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Analytical Investigation ◽  
Contact Forces ◽  
Coulomb’S Friction ◽  
Friction Laws ◽  
The Masses ◽  
Close Form ◽  
Form Stability

In this paper, we present an analytical method to investigate the behavior of a two degrees of freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs. These two masses are in contact with a driving belt moving at a constant velocity. The contact forces between the masses and the belt are obtained from Coulomb’s friction laws. A set of periodic solutions involving a global sticking phase followed by several other phases where one or both masses are slipping, are found in close form. Stability conditions related to these solutions are obtained.

Inertially Coupled Galloping of Iced Conductors

1992 ◽  
Vol 59 (1) ◽  
pp. 140-145 ◽  
Author(s):  
P. Yu ◽  
A. H. Shah ◽  
N. Popplewell
Keyword(s):  
Periodic Solutions ◽  
Cross Section ◽  
Mixed Mode ◽  
Bifurcation Theory ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Asymptotic Solutions ◽  
Periodic Motions ◽  
Two Degrees Of Freedom ◽  
First Time

This paper is concerned with the galloping of iced conductors modeled as a two-degrees-of-freedom system. It is assumed that a realistic cross-section of a conductor has eccentricity; that is, its center of mass and elastic axis do not coincide. Bifurcation theory leads to explicit asymptotic solutions not only for the periodic solutions but also for the nonresonant, quasi-periodic motions. Critical boundaries, where bifurcations occur, are described explicitly for the first time. It is shown that an interesting mixed-mode phenomenon, which cannot happen in cocentric cases, may exist even for nonresonance.

CONNECTING SYMMETRIC AND ASYMMETRIC FAMILIES OF PERIODIC ORBITS IN SQUARED SYMMETRIC HAMILTONIANS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250014 ◽  
Author(s):  
FERNANDO BLESA ◽  
SŁAWOMIR PIASECKI ◽  
ÁNGELES DENA ◽  
ROBERTO BARRIO
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Search Algorithm ◽  
Grid Search ◽  
Numerical Techniques ◽  
Two Degrees Of Freedom ◽  
Multiplicity One ◽  
Families Of Periodic Orbits ◽  
Grid Search Algorithm

In this work, we study a generic squared symmetric Hamiltonian of two degrees of freedom. Our aim is to show a global methodology to analyze the evolution of the families of periodic orbits and their bifurcations. To achieve it, we use several numerical techniques such as a systematic grid search algorithm in sequential and parallel, a fast chaos indicator and a tool for the continuation of periodic orbits. Using them, we are able to study the special and generic bifurcations of multiplicity one that allow us to understand the dynamics of the system and we show in detail the evolution of some symmetric breaking periodic orbits.

scholarly journals ANALYTICAL STUDY OF FRICTIONAL AUTO-VIBRATIONS IN SYSTEMS WITH TWO DEGREES OF FREEDOM

2021 ◽  
Author(s):  
E. Kalinin ◽  
◽  
S. Lebedev ◽  
Yu. Kozlov
Keyword(s):  
Degrees Of Freedom ◽  
System Analysis ◽  
Single Frequency ◽  
Uniform Rotation ◽  
Systems Methodology ◽  
Two Degrees Of Freedom ◽  
Resonance Modes ◽  
The Difference ◽  
Friction Function ◽  
The Masses

Abstract Purpose of the study is to study the properties of frictional self-oscillations in systems with two degrees of freedom. As a research method, the asymptotic method of N.N. Bogolyubov and Y.A. Metropolitan. Research methods. The methodological basis of the work is the generalization and analysis of the known scientific results of the dynamics of systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, goal and formulation of research objectives. When developing empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of functions were used. The results of the study. A system with two degrees of freedom is considered, assuming that the friction function is approximated by a cubic polynomial in the sliding velocity, and friction is applied only to one of the masses. The exclusion of uniform rotation, corresponding to the third degree of freedom, leads to consideration not of the frictional moment, but the difference between the frictional moment and the moment of the moving forces. From the analysis of the results of the solutions of the equation, we can conclude that, with an accuracy up to the first approximation, inclusive, self-oscillations occur with constant frequencies equal to the natural frequencies of the system. This is consistent with the conclusions of other authors obtained using other methods. Stationary values of the amplitudes are found. The following four cases are possible: trivial solution corresponding to uniform rotation of the system without oscillations; single frequency oscillations with the first frequency; single frequency oscillations with a second frequency; two-frequency oscillatory mode. Conclusions. G. Boyadzhiev's method can be applied to study multi-mass self-oscillating systems and gives their general solution in the form of asymptotic expansions to any degree of accuracy. The obtained conditions for the stability of stationary regimes confirm the experimental results that in multi-mass systems, self-oscillations are possible only in the falling sections of the friction characteristics. The nature of the developing vibrations - their frequency and the ratio of the amplitudes of the constituent harmonics - is completely determined by the structure of the system, its elastic and inertial properties.

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