On the Dynamics of Vibration Absorbers With Motion-Limiting Stops

1998 ◽  
Vol 65 (1) ◽  
pp. 223-233 ◽  
Author(s):  
H. Luo ◽  
S. Hanagud
Keyword(s):  
Steady State ◽  
Mechanical Model ◽  
Piecewise Linear ◽  
Nonlinear Effects ◽  
Vibration Absorbers ◽  
Chaotic Vibrations ◽  
Piecewise Linear System ◽  
Period 2 ◽  
Steady State Solutions ◽  
Theoretical Results

The dynamics of a class of vibration absorbers with elastic stops is discussed in this paper. The mechanical model proposed in previously published papers are modified to explain certain nonlinear effects, chaotic vibrations, and lower damping observed in our studies. Refined contact-noncontact criteria are presented. Exact steady-state solutions are obtained for a piecewise linear system by using the proposed contact-noncontact criteria. Numerical simulations are presented and compared with the results of the previous work. Significant differences that have been found include some chaotic responses of the system. Experiments are conducted to validate the theoretical results. Chaotic and period-2 responses are also detected experimentally.

Bifurcation Phenomena Caused by Multiple Nonlinear Vibration Absorbers

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Steady State ◽  
Nonlinear Vibration ◽  
Excitation Frequency ◽  
Pitchfork Bifurcation ◽  
Harmonic Excitation ◽  
Vibration Absorbers ◽  
Response Curves ◽  
System Parameters ◽  
Chaotic Vibrations ◽  
Steady State Solutions

The characteristics of two, three, and four nonlinear vibration absorbers or nonlinear tuned mass dampers (NTMDs) attached to a structure under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. When the parameters of the absorbers are equal, it is found from the theoretical analysis that pitchfork bifurcations may occur on the part of the response curves, which are unstable in the multi-absorber systems, but are stable in a system with one NTMD. Multivalued steady-state solutions, such as three steady-state solutions for a dual-absorber system with different amplitudes, five steady-state solutions for a triple-absorber system, and seven steady-state solutions for a quadruple-absorber system, appear near bifurcation points. The NTMDs behave in that one of them vibrates at high amplitudes while the others vibrate at low amplitudes, even if the dimensions of the NTMDs are identical. Namely, “localization phenomenon” or “mode localization” occurs. After the pitchfork bifurcation, Hopf bifurcations may occur depending on the values of the system parameters, and amplitude- and phase-modulated motions, including chaotic vibrations, appear after the Hopf bifurcation when the excitation frequency decreases. Lyapunov exponents are numerically calculated to prove the occurrence of chaotic vibrations. Bifurcation sets are also calculated to investigate the influence of the system parameters on the response of the systems.

Identification of Vibration of Cooler Tubes With Tube-to-Baffle Impacts

1998 ◽  
Vol 120 (2) ◽  
pp. 419-425 ◽  
Author(s):  
S. C. N. Wong ◽  
J. K. T. Chan
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Effects ◽  
Site Investigation ◽  
Power Station ◽  
Piecewise Linear System ◽  
System Method ◽  
Spring Type ◽  
Theoretical Results ◽  
Tube Structure ◽  
Good Agreement

A random series of impacts method was introduced for vibration test on tube bundles of coolers. A non-normal Poisson process was employed to establish a model for the method. Experimental analysis of the forcing functions showed good agreement with the model. The method was found to be appropriate for extracting modal parameters of such tube structure. Site investigation on power station coolers proved this method to be convenient and reliable. Tube-to-baffle impactions created nonlinear effects which were shown to be of hard-spring type. A piecewise linear system method was used to handle such situation. The theoretical results were closely correlated with the experimental results.

Dynamic Analysis of the Optical Disk Drive System Equipped With an Automatic Ball Balancer With Consideration of Torsional Motion

2003 ◽  
Author(s):  
Chun-Chieh Wang ◽  
Cheng-Kuo Sung ◽  
Paul C. P. Chao
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Substantial Reduction ◽  
Disk Drive ◽  
Optical Disk ◽  
Balance System ◽  
Optical Disk Drive ◽  
The Stability ◽  
Steady State Solutions ◽  
Theoretical Results

This study is dedicated to evaluate the stability of an automatic ball-type balance system (ABS) installed in Optical Disk Drives (ODD). There have been researchers devoted to study the performance of ABS by investigating the dynamics of the system, but few consider the motions in torsional direction of ODD foundation. To solve this problem, a mathematical model including the foundation is established. The method of multiple scales is then utilized to find all possible steady-state solutions and perform related stability analysis. The obtained results are used to predict the level of residual vibrations and then the performance of the ABS can be evaluated. Numerical simulations are conducted to verify the theoretical results. It is obtained from both analytical and numerical results that the spindle speed of the motor ought to be operated above primary translational and secondary torsional resonances to stabilize the desired steady-state solutions for a substantial reduction in radial vibration.

STABILITY OF SPATIALLY PERIODIC SOLUTIONS IN COUPLED MAP LATTICES

2003 ◽  
Vol 13 (02) ◽  
pp. 343-356 ◽  
Author(s):  
M. DUBCOVÁ ◽  
A. KLÍČ ◽  
P. POKORNÝ ◽  
D. TURZÍK
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Evolution Operators ◽  
Spatially Periodic ◽  
The Stability ◽  
Steady State Solutions ◽  
Theoretical Results

Stability of steady-state solutions of 1-dim coupled map lattices is studied. The stability is determined by the spectrum of linear operators on two-sided sequences of vectors in [Formula: see text] arising as a linearization of the corresponding nonlinear evolution operators. Theoretical results are applied to several examples.

scholarly journals Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 190
Author(s):  
Riadh Chteoui ◽  
Abdulrahman F. Aljohani ◽  
Anouar Ben Mabrouk
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Nehari Manifold ◽  
Nonlinear Pdes ◽  
Nonlinear Part ◽  
Numerical Investigations ◽  
Physical Phenomena ◽  
Steady State Solutions ◽  
Schrödinger System ◽  
Theoretical Results

Systems of coupled nonlinear PDEs are applied in many fields as suitable models for many natural and physical phenomena. This makes them active and attractive subjects for both theoretical and numerical investigations. In the present paper, a symmetric nonlinear Schrödinger (NLS) system is considered for the existence of the steady state solutions by applying a minimizing problem on some modified Nehari manifold. The nonlinear part is a mixture of cubic and superlinear nonlinearities and cubic correlations. Some numerical simulations are also illustrated graphically to confirm the theoretical results.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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