scholarly journals Stability of Sliding Frictional Surfaces with Varying Normal Force

1994 ◽  
Vol 116 (2) ◽  
pp. 237-242 ◽  
Author(s):  
P. E. Dupont ◽  
D. Bapna
Keyword(s):  
Normal Force ◽  
Elastic System ◽  
Functional Dependence ◽  
Low Velocity ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
State Dependent ◽  
Velocity Motion ◽  
The Stability ◽  
Frictional Surfaces

This paper presents the stability analysis of a single degree-of-freedom elastic system following a rate-and state-dependent friction law. Normal force is assumed to depend on the displacement, velocity and acceleration of the sliding interface. The history dependence of friction on normal force is included in the analysis. It is shown that to achieve steady sliding, system stiffness must exceed a critical value which depends on the expression for normal force. A system in which normal force depends on spring displacement is analyzed in detail. These results indicate that the functional dependence of normal force on system state can have a significant effect on the stability of low-velocity motion.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

Stochastic Dynamics of a Variable Inertia System via Lyapunov Exponents

2008 ◽  
Author(s):  
S. F. Asokanthan ◽  
X. H. Wang ◽  
W. V. Wedig ◽  
S. T. Ariaratnam
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stochastic Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Excitation ◽  
The Stability

Torsional instabilities in a single-degree-of-freedom system having variable inertia are investigated by means of Lyapunov exponents. Linearised analytical model is used for the purpose of stability analysis. Numerical schemes for simulating the top Lyapunov exponent for both deterministic and stochastic systems are established. Instabilities associated with the primary and the secondary sub-harmonic resonances have been identified by studying the sign of the top Lyapunov exponent. Predictions for the deterministic and the stochastic cases are compared. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. The effects of fluctuation density as well as that of damping on the stability behaviour of the system have been examined. Predicted instability conditions are adequate for the design of a variable-inertia system so that a range of critical speeds of operation may be avoided.

Design and Stability Analysis of Delayed Resonator With Acceleration Feedback

2013 ◽  
Author(s):  
Tomáš Vyhlídal ◽  
Nejat Olgac ◽  
Vladimír Kučera
Keyword(s):  
Vibration Suppression ◽  
Dynamics Analysis ◽  
Stability Boundaries ◽  
Single Degree Of Freedom ◽  
Stability Margins ◽  
Single Degree ◽  
Active Vibration Suppression ◽  
Acceleration Feedback ◽  
Active Vibration ◽  
The Stability

This paper deals with the problem of active vibration suppression using the concept of delayed resonator with acceleration feedback. A complete dynamics analysis of the resonator and its coupling with a single degree of freedom mechanical system are performed. It is shown that due to presence of a delay in the derivative feedback, the dynamics of the resonator itself, as well as the dynamics of its coupling with the system are of neutral character. Subsequently, the spectral approach is used to obtain the stability boundaries in the space of the resonator parameters. Both, analytical and numerical methods are employed in the analysis. As the contributions, we display a methodology to determine the resonator parameters in order to guarantee desirable functioning of the resonator and to provide safe stability margins. An example is included to demonstrate these analytical results.

Effect of Third Harmonic Vibratory Force on a Linear Spring-Mass System

1963 ◽  
Vol 67 (636) ◽  
pp. 799-803
Author(s):  
C. L. Kirk
Keyword(s):  
Resonant Frequency ◽  
Elastic System ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Single Degree ◽  
Linear Spring

SummaryThe response of an elastic system having a single degree of freedom, to a vibratory force whose waveform can be varied, is examined. The variable waveform is produced by a system of two pairs of unbalanced rotors in which one pair rotates at three times the speed of the other pair. The waveform depends on the frequency of excitation, the phasing of the rotors and the ratio of their amounts of unbalance. If the rotors are run at a speed at which the faster pair rotates above resonance while the slower pair rotates below resonance, a frequency is found at which the rate of change of amplitude with respect to frequency is zero. At this point, however, the waveform is quite sensitive to small changes in the frequency of excitation. If the rotor speeds cannot be maintained constant, and if stable vibration waveforms are required, it is necessary to run the slowest rotor well above the resonant frequency where both the amplitude and waveform will be virtually independent of frequency.

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