Chaos of Nonlinear Vibratory System With Single Well Potential

1995 ◽  
Author(s):  
Wei Zhang
Keyword(s):  
Nonlinear System ◽  
Torsional Vibration ◽  
Chaotic Motion ◽  
Chaotic Dynamics ◽  
Combustion Engine ◽  
Dynamical Behavior ◽  
Vibration Absorber ◽  
Vibratory System ◽  
Centrifugal Pendulum Vibration Absorber ◽  
Single Well

Abstract In this paper we study chaotic dynamics of nonlinear vibratory system under combined parametric and forcing excitations with single well potential. Especially we focus on chaos of a centrifugal pendulum vibration absorber. The centrifugal pendulum vibration absorber is an efficient device that is used to reduce torsional vibration in crank shaft of internal combustion engine. Because reduced dynamical model of the centrifugal pendulum vibration absorber is a nonlinear system, there is very rich dynamical behavior in this system. We use Meknikov’s method and numerical method to study chaotic dynamics of the centrifugal pendulum vibration absorber and discuss the route from bifurcations of T2 torus to chaotic motion.

Torsional Vibration Suppression by the Roller Type Centrifugal Vibration Absorbers

2007 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue ◽  
Tomohiko Fukami ◽  
Motohiko Ueda
Keyword(s):  
Torsional Vibration ◽  
Vibration Suppression ◽  
Vibration Absorber ◽  
Torsional Vibrations ◽  
Vibration Absorbers ◽  
Dynamical Characteristics ◽  
Centrifugal Pendulum Vibration Absorber ◽  
Automobile Engines ◽  
Long Time ◽  
The Difference

The centrifugal pendulum vibration absorber (CPVA) has been used for a long time as a method to suppress torsional vibrations. Recently, the roller type CPVA, that has a similar characteristic but simpler structure, has been investigated and started to be used in some automobile engines. However, the dynamical characteristics of the roller type CPVA are not known well. In this study, the nonlinear equations motion of the roller type CPVA are derived and their characterictics are investigated theoretically and experimentally. Especially, the difference between pendulum type CPVA and roller type CPVA is discussed from the viewpoint of the effect of a vibration suppression.

Hybrid Torsional Vibration Damper Incorporating Conventional Centrifugal Pendulum Vibration Absorber and Magnetorheological Damper

2014 ◽  
Author(s):  
Ehab Abouobaia ◽  
Rama Bhat ◽  
Ramin Sedaghati
Keyword(s):  
Torsional Vibration ◽  
Mr Damper ◽  
Analytical Investigation ◽  
Rotor System ◽  
Magnetorheological Damper ◽  
Vibration Absorber ◽  
Vibration Damper ◽  
Power Requirement ◽  
Rotor Systems ◽  
Centrifugal Pendulum Vibration Absorber

A hybrid torsional vibration damper is proposed in this study incorporating a conventional Centrifugal Pendulum Vibration Absorber (CPVA) and a Magnetorheological (MR) damper. While CPVAs are simple and reliable passive torsional vibration absorbers, their performance is limited to the designed tune conditions. MR dampers have recently received considerable attention due to their inherent fail-safe feature, low power requirement and capability to attenuate vibration under unpredictable environmental conditions. The present research aims at developing a novel hybrid torsional vibration damper combining conventional CPVA with the MR damper capable of suppressing torsional vibration at varying excitation frequencies. This research presents results from analytical investigation of rotor systems integrated with the proposed hybrid torsional vibration damper. The system under investigation consists of a rotor with attached hybrid torsional MR damper subjected to an external harmonic torque. The CPVA has been connected to the cylindrical housing of the MR damper. Different cases have been investigated including: 1- Rotor system without any damper, 2- Rotor system with only CPVA, 3- Rotor system with only torsional MR damper and 4- Rotor system with the hybrid torsional damper. Results for each case have been illustrated and compared against one another.

Chaotic Motions of a Torsional Vibration Absorber

1988 ◽  
Vol 55 (4) ◽  
pp. 952-958 ◽  
Author(s):  
S. W. Shaw ◽  
S. Wiggins
Keyword(s):  
Torsional Vibration ◽  
Large Amplitude ◽  
Chaotic Dynamics ◽  
Rotating Machinery ◽  
Vibration Absorber ◽  
Chaotic Motions ◽  
Torsional Oscillations ◽  
Large Amplitude Motions ◽  
Parameter Values ◽  
Two Degree Of Freedom

We consider large amplitude motions of a pendulum-type centrifugal vibration absorber which is used for the reduction of torsional oscillations in rotating machinery. The basic two degree-of-freedom model is shown to possess chaotic dynamics for certain ranges of parameter values. The method used is a variation of Melnikov’s method (cf., Guckenheimer and Holmes, (1983), Chapter 4) developed for slowly varying oscillators (Wiggins and Holmes (1987), Wiggins and Shaw (1988)).

Suppressing Chaos in a Nonideal Double-Well Oscillator Using an Based Electromechanical Damped Device

2014 ◽  
Vol 706 ◽  
pp. 25-34 ◽  
Author(s):  
G. Füsun Alişverişçi ◽  
Hüseyin Bayiroğlu ◽  
José Manoel Balthazar ◽  
Jorge Luiz Palacios Felix
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Duffing Oscillator ◽  
Vibration Energy ◽  
Vibration Absorber ◽  
Electrical System ◽  
Chaotic Vibration ◽  
System A ◽  
Ideal System ◽  
Double Well Potential

In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

Multi-Pulse Chaotic Dynamics of Four-Dimensional Non-Autonomous Nonlinear System for a Truss Core Sandwich Plate

2014 ◽  
Author(s):  
Wei Zhang ◽  
Qi-liang Wu
Keyword(s):  
Nonlinear System ◽  
Chaotic Dynamics ◽  
Sandwich Plate ◽  
Melnikov Method ◽  
Order Mode ◽  
Simply Supported ◽  
Truss Core ◽  
Extended Melnikov Method ◽  
Kagome Truss ◽  
Truss Core Sandwich Plate

In this paper, an extended high-dimensional Melnikov method is used to investigate global and chaotic dynamics of a simply supported 3D-kagome truss core sandwich plate subjected to the transverse and the in-plane excitations. Based on the motion equation derived by Zhang and the method of multiple scales, the averaged equation is obtained for the case of principal parametric resonance and 1:2 sub-harmonic resonance for the first-order mode and primary resonance for the second-order mode. From the averaged equation obtained, the system is simplified to a three order standard form with a double zero and a pair of pure imaginary eigenvalues by using the theory of normal form. Then, the extended Melnikov method is utilized to investigate the Shilnikov-type multi-pulse heteroclinic bifurcations and existence of chaos. The analysis of the extended Melnikov method demonstrates that there exist the Shilnikov-type multi-pulse heteroclinic bifurcations and chaos in the four-dimensional non-autonomous nonlinear system. Finally, the results of numerical simulations also show that for the nonlinear system of simply supported 3D-kagome truss core sandwich plate with the transverse and the in-plane excitations, the Shilnikov-type multi-pulse motion of chaos can happen and further verify the result of theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document