Chaotic Response of a Hard Duffing Type Vibration Isolator With Combined Coulomb and Viscous Damping

1995 ◽  
Author(s):  
A. Y. T. Leung ◽  
B. Ravindra ◽  
A. K. Mallik ◽  
C. W. Chan
Keyword(s):  
Chaotic Motion ◽  
Viscous Damping ◽  
Vibration Isolator ◽  
Bifurcation Structure ◽  
Restoring Force ◽  
Coulomb Damping ◽  
Secondary Resonances ◽  
Excited System ◽  
Subharmonic Resonances

Abstract Numerical simulations of the response of a harmonically excited mass on an isolator with a cubic, hard, non-linear restoring force and combined Coulomb and viscous damping are presented. For a base-excited system, the inclusion of a Coulomb damper with a suitable break-loose frequency can suppress the secondary resonances and chaotic motion. However, for a force-excited system, the introduction of Coulomb damping does not alter the bifurcation structure. Transmissibility indices have been defined for the solution obtained by numerical integration and the role of the subharmonic resonances and chaotic motion on the performance of the system is pointed out.

On the Role of Marangoni Effects on the Critical Heat Flux for Pool Boiling of Binary Mixtures

1996 ◽  
Vol 118 (1) ◽  
pp. 103-109 ◽  
Author(s):  
W. R. McGillis ◽  
V. P. Carey
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Binary Mixtures ◽  
Critical Heat Flux ◽  
Full Range ◽  
Pool Boiling ◽  
Marangoni Effect ◽  
Restoring Force ◽  
Marangoni Effects

The Marangoni effect on the critical heat flux (CHF) condition in pool boiling of binary mixtures has been identified and its effect has been quantitatively estimated with a modified model derived from hydrodynamics. The physical process of CHF in binary mixtures, and models used to describe it, are examined in the light of recent experimental evidence, accurate mixture properties, and phase equilibrium revealing a correlation to surface tension gradients and volatility. A correlation is developed from a heuristic model including the additional liquid restoring force caused by surface tension gradients. The CHF condition was determined experimentally for saturated methanol/water, 2-propanol/water, and ethylene glycol/water mixtures, over the full range of concentrations, and compared to the model. The evidence in this study demonstrates that in a mixture with large differences in surface tension, there is an additional hydrodynamic restoring force affecting the CHF condition.

Dynamic Motion Analysis of Plane Mechanisms With Coulomb and Viscous Damping via the Joint Force Analysis

1975 ◽  
Vol 97 (2) ◽  
pp. 551-560 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Dynamic Equilibrium ◽  
Viscous Damping ◽  
Force Analysis ◽  
Initial Value ◽  
Damping Force ◽  
Joint Force ◽  
Coulomb Damping ◽  
Dynamic Motion ◽  
Joint Forces ◽  
Input Torque

Analysis of response of determinate plane mechanisms to known driving input force, or input torque, via the joint force analysis is presented. Coulomb damping and viscous damping forces in the pair bearings are included. Equations of dynamic equilibrium are solved for the components of the normal joint forces and for the motion of the mechanism as initial-value problems. The rotation of the resultant joint force, due to the fact that the pair member on a link is the inner member or the outer member of the pair, is considered by defining a generalized Coulomb damping force. Links of the mechanisms are considered rigid. The plane 4R and slider-crank switch mechanisms are investigated. Explicit solutions and numerical examples are given.

On the Effects of Mistuning a Force-Excited System Containing a Quasi-Zero-Stiffness Vibration Isolator

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Ali Abolfathi ◽  
M. J. Brennan ◽  
T. P. Waters ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Zero Dynamic ◽  
Low Frequency Vibration ◽  
Excited System ◽  
Better Than

Nonlinear isolators with high-static-low-dynamic-stiffness have received considerable attention in the recent literature due to their performance benefits compared to linear vibration isolators. A quasi-zero-stiffness (QZS) isolator is a particular case of this type of isolator, which has a zero dynamic stiffness at the static equilibrium position. These types of isolators can be used to achieve very low frequency vibration isolation, but a drawback is that they have purely hardening stiffness behavior. If something occurs to destroy the symmetry of the system, for example, by an additional static load being applied to the isolator during operation, or by the incorrect mass being suspended on the isolator, then the isolator behavior will change dramatically. The question is whether this will be detrimental to the performance of the isolator and this is addressed in this paper. The analysis in this paper shows that although the asymmetry will degrade the performance of the isolator compared to the perfectly tuned case, it will still perform better than the corresponding linear isolator provided that the amplitude of excitation is not too large.

Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model: The Role of the Extended Nonlinear Feedback Loop

2018 ◽  
Vol 28 (06) ◽  
pp. 1850072 ◽  
Author(s):  
Sara Faghih-Naini ◽  
Bo-Wen Shen
Keyword(s):  
Periodic Solution ◽  
Feedback Loop ◽  
Three Dimensional ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Restoring Force ◽  
Oscillatory Solutions ◽  
Nonlinear Temperature

A recent study suggested that the nonlinear feedback loop (NFL) of the three-dimensional nondissipative Lorenz model (3D-NLM) serves as a nonlinear restoring force by producing nonlinear oscillatory solutions as well as linear periodic solutions near a nontrivial critical point. This study discusses the role of the extension of the NFL in producing quasi-periodic trajectories using a five-dimensional nondissipative Lorenz model (5D-NLM). An analytical solution to the locally linear 5D-NLM is first obtained to illustrate the association of the extended NFL and two incommensurate frequencies whose ratio is irrational, yielding a quasi-periodic solution. The quasi-periodic solution trajectory moves endlessly on a torus but never intersects itself. While the NFL of the 3D-NLM consists of a pair of downscaling and upscaling processes, the extended NFL within the 5D-NLM additionally introduces two new pairs of downscaling and upscaling processes that are enabled by two high wavenumber modes. One pair of downscaling and upscaling processes provides a two-way interaction between the original (primary) Fourier modes of the 3D-NLM and the newly-added (secondary) Fourier modes of the 5D-NLM. The other pair of downscaling and upscaling processes involves interactions amongst the secondary modes. By comparing the numerical simulations using one- and two-way interactions, we illustrate that the two-way interaction is crucial for producing the quasi-periodic solution. A follow-up study using a 7D nondissipative LM shows that a further extension of NFL, which may appear throughout the spatial mode-mode interactions rooted in the nonlinear temperature advection, is capable of producing one more incommensurate frequency.

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 A Symplectic Mapping Model as a Tool to Understand The Dynamics of 2/1 Resonant Asteroid Motion

1999 ◽  
Vol 172 ◽  
pp. 65-76
Author(s):  
John D. Hadjidemetriou
Keyword(s):  
Chaotic Motion ◽  
The Sun ◽  
Symplectic Mapping ◽  
Mapping Model ◽  
The Third ◽  
Secondary Resonances ◽  
Mean Motion ◽  
Slow Diffusion ◽  
Third Dimension ◽  
Asteroid Orbit

AbstractWe present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear. The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.

scholarly journals On the Role of Chaos and Instability in the Evolution of Nonlinear Nonstationary Stellar Systems

1993 ◽  
Vol 132 ◽  
pp. 39-44
Author(s):  
S.N. Nuritdinov
Keyword(s):  
Stationary State ◽  
Chaotic Motion ◽  
Stellar System ◽  
Stellar Systems

AbstractThe role of chaos and instability in evolution of nonlinear, non-stationary stellar system have been discussed. It is possible to distinguish between the only two different cases (i) strongly non-stationary stage when we have the violent relaxation accompanied by the compulsive mixing (ii) weakly non-stationary state or quasilinear case, when the quasidiffusion mixing takes place. In case (i), the chaos and chaotic motion g stars play very important role and in case (ii) the role of any type of instability is important.

An Advanced Test Method to Determine Viscous Damping of Floating Structures

2010 ◽  
Author(s):  
Z. J. Huang ◽  
B. J. O’Donnell ◽  
T. W. Yung ◽  
S. T. Slocum
Keyword(s):  
Low Frequency ◽  
Test Method ◽  
Total Force ◽  
Viscous Damping ◽  
Damping Force ◽  
Restoring Force ◽  
Viscous Forces ◽  
Motion Time ◽  
Research Company ◽  
Time Histories

ExxonMobil Upstream Research Company developed an advanced model test method to determine reliable damping values for predicting low frequency motions of an FLNG barge and an LNG carrier. Since viscous damping forces are a very small portion of the total force on the model, how to separate the viscous forces from the total forces is the key technical challenge. To better isolate viscous damping forces, an inertial compensation system consisting of springs was employed in the test. The spring stiffness was designed such that the restoring force cancelled the large inertial loads at the oscillation frequency. Furthermore, double-body models were built and were deeply submerged to minimize surface wave damping. With such an experimental setup, the total force measured was mainly the viscous damping force. Viscous damping was derived from the measured force and motion time histories.

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