Experimental Investigation of Nonlinear Vibration Absorbers

1999 ◽  
Author(s):  
Gregory S. Agnes
Keyword(s):  
Experimental Investigation ◽  
Nonlinear Systems ◽  
Nonlinear Vibration ◽  
Chaotic Behavior ◽  
System Response ◽  
Hopf Bifurcations ◽  
Vibration Absorbers ◽  
Nonlinear Case ◽  
Nonlinear Absorber ◽  
Poor Absorption

Abstract An experimental investigation of the performance of nonlinear vibration absorbers on nonlinear systems was performed. The results verify the previous analytical findings of the authors. Initially, for low excitation, the nonlinear absorber gives better results than the nonlinear case. However as the forcing level is increased, the system response undergoes a series of Hopf bifurcations leading to chaotic behavior and poor absorption of the vibrations.

A New Cluster-Based Harmonic Balance Aided Optimization Procedure With Application to Nonlinear Vibration Absorbers

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
V. P. Premchand ◽  
M. D. Narayanan ◽  
A. S. Sajith
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Vibration ◽  
Periodic Solutions ◽  
Parameter Space ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Optimization Technique ◽  
Force Balance ◽  
Design Parameters ◽  
Vibration Absorbers

This work presents a new strategy in design optimization of nonlinear vibration absorbers with continuous and discontinuous motions. A cluster-based harmonic balance aided optimization technique using force balance or energy balance as the basis is generalized and adapted for nonlinear systems. It is found that optimal design parameters form a cluster in the parameter space and points from the parameter space inside the cluster satisfies design considerations. One of the main disadvantages of using existing optimization methods in nonlinear systems is that the parameter regimes, which provide periodic solutions, are not known beforehand, so one has to first do bifurcation studies to arrive at periodic regimes and optimization has to be conducted in the range. Proposed method combines these two steps as it converges to periodic clusters alone. Since the method admits only periodic solutions, occurrence of conditions such as chaos and quasi periodicity can be eliminated from the dynamics of the system. The proposed method can also be used to find the optimal parameters of both linear and nonlinear dynamical systems.

ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

2014 ◽  
Vol 06 (05) ◽  
pp. 1450053 ◽  
Author(s):  
FATHI DJEMAL ◽  
FAKHER CHAARI ◽  
JEAN LUC DION ◽  
FRANCK RENAUD ◽  
IMAD TAWFIQ ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Vibration Control ◽  
Numerical Method ◽  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Equation Of Motion ◽  
Vibration Absorbers ◽  
Asymptotic Numerical Method ◽  
Dynamic Absorber ◽  
Newton Raphson

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

CHAOTIC BEHAVIOR OF INTERVAL MAPS AND TOTAL VARIATIONS OF ITERATES

2004 ◽  
Vol 14 (07) ◽  
pp. 2161-2186 ◽  
Author(s):  
GOONG CHEN ◽  
TINGWEN HUANG ◽  
YU HUANG
Keyword(s):  
Nonlinear Systems ◽  
Initial Data ◽  
Topological Entropy ◽  
Chaotic Behavior ◽  
Homoclinic Orbits ◽  
Oscillatory Behavior ◽  
Exponential Rate ◽  
Interval Maps ◽  
Interval Map ◽  
Sensitive Dependence

Interval maps reveal precious information about the chaotic behavior of general nonlinear systems. If an interval map f:I→I is chaotic, then its iterates fnwill display heightened oscillatory behavior or profiles as n→∞. This manifestation is quite intuitive and is, here in this paper, studied analytically in terms of the total variations of fnon subintervals. There are four distinctive cases of the growth of total variations of fnas n→∞:(i) the total variations of fnon I remain bounded;(ii) they grow unbounded, but not exponentially with respect to n;(iii) they grow with an exponential rate with respect to n;(iv) they grow unbounded on every subinterval of I.We study in detail these four cases in relations to the well-known notions such as sensitive dependence on initial data, topological entropy, homoclinic orbits, nonwandering sets, etc. This paper is divided into three parts. There are eight main theorems, which show that when the oscillatory profiles of the graphs of fnare more extreme, the more complex is the behavior of the system.

NONLINEAR VIBRATION ANALYSIS FOR AN AIRFLOW-EXCITED TRANSLATING STRING

2012 ◽  
Vol 09 (04) ◽  
pp. 1250051 ◽  
Author(s):  
YUEFANG WANG ◽  
LEFENG LÜ ◽  
LIHUA HUANG
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Equilibrium Configuration ◽  
Excitation Frequency ◽  
Transverse Motion ◽  
Hopf Bifurcations ◽  
Flip Bifurcation ◽  
Wind Force ◽  
Incremental Harmonic Balance ◽  
The Stability

The nonlinear vibration of transverse motion of a translating string excited by steady wind force is investigated in this paper. The stability of the equilibrium configuration is analyzed and the generation of limit cycles via multiple Hopf bifurcations is presented. Single-, double-, and quadruple-Hopf bifurcations are determined in the parametric space. The limit-cycle response is solved through the method of Incremental Harmonic Balance, with its stability determined by Floquet multipliers. For the forced vibration, the coexistence of periodic and quasiperiodic motions is found with varying excitation frequency and amplitude. The Neimark–Sacker (NS) bifurcation and the flip bifurcation are demonstrated in an example. The continuation software MATCONT is adopted to identify the fold and NS bifurcations of periodic motions, as well as other codim-2 bifurcations of NS–NS, the Chenciner and the 1:1, 1:3, and 1:4 resonances. These bifurcations present the complexity of the string dynamics induced by steady wind excitations.

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