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)).

Multi-Pulse Chaotic Motion for a Non-Autonomous Buckled Plate by Using the Extended Melnikov Method

2007 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Two Degree Of Freedom

The multi-pulse Shilnikov orbits and chaotic dynamics for a parametrically excited, simply supported rectangular buckled thin plate are studied by using the extended Melnikov method. Based on von Karman type equation and the Galerkin’s approach, two-degree-of-freedom nonlinear system is obtained for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of the thin plate. The results obtained here show that the multipulse chaotic motions can occur in the thin plate.

Vibration Suppression of Rotating Machinery Utilizing Discontinuous Spring Characteristics

2005 ◽  
Author(s):  
Yukio Ishida ◽  
Jun Liu
Keyword(s):  
Periodic Motion ◽  
Large Amplitude ◽  
Critical Speed ◽  
Vibration Suppression ◽  
Rotating Machinery ◽  
Almost Periodic ◽  
Suppression Method ◽  
Rotor Stiffness ◽  
Parameter Values ◽  
Almost Periodic Motion

In rotating machinery, resonance phenomena occur with large amplitude in the vicinities of the major critical speeds. In this paper, a new vibration suppression method utilizing a discontinuous spring characteristic is proposed. This spring characteristic is made by additional springs with preload. This method has the following advantages: In designing these additional springs, we need not adjust their parameter values to the rotor stiffness and the system damping. The amplitude of vibration can be suppressed to any desired level. Although this method has a disadvantage that an almost periodic motion occurs above the major critical speed, two countermeasures are proposed to diminish it. We clarified these phenomena theoretically and experimentally.

Non-Linear Torsional Vibration of a Two-Degree-of-Freedom System Having Variable Inertia

1965 ◽  
Vol 7 (1) ◽  
pp. 101-113 ◽  
Author(s):  
B. Porter
Keyword(s):  
Normal Mode ◽  
Torsional Vibration ◽  
Large Amplitude ◽  
Critical Speed ◽  
Degree Of Freedom ◽  
Reciprocating Engine ◽  
Non Linear ◽  
Two Degree Of Freedom

A variant of Kryloff and Bogoliuboff's method is used to analyse the periodic vibrations of a non-linear two-degree-of-freedom system which is an idealization of the crankshaft of a two-cylinder in-line reciprocating engine. It is shown that there are two critical speed ranges associated with each normal mode of the system within which periodic harmonic or subharmonic vibrations of large amplitude can occur as a result of variable-inertia excitation. Extensions of the results to homogeneous in-line engines having any number of cylinders are indicated.

scholarly journals Flutter Control of a Two-Degrees-of-Freedom Airfoil Using a Nonlinear Tuned Vibration Absorber

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Arnaud Malher ◽  
Cyril Touzé ◽  
Olivier Doaré ◽  
Giuseppe Habib ◽  
Gaëtan Kerschen
Keyword(s):  
Limit Cycle ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Vibration Absorber ◽  
Aerodynamic Loads ◽  
Linear Approach ◽  
Aeroelastic Model ◽  
Large Amplitude Motions ◽  
Restoring Forces ◽  
Tuned Vibration Absorber

The influence of a nonlinear tuned vibration absorber (NLTVA) on the airfoil flutter is investigated. In particular, its effect on the instability threshold and the potential subcriticality of the bifurcation is analyzed. For that purpose, the airfoil is modeled using the classical pitch and plunge aeroelastic model together with a linear approach for the aerodynamic loads. Large amplitude motions of the airfoil are taken into account with nonlinear restoring forces for the pitch and plunge degrees-of-freedom. The two cases of a hardening and a softening spring behavior are investigated. The influence of each NLTVA parameter is studied, and an optimum tuning of these parameters is found. The study reveals the ability of the NLTVA to shift the instability, avoid its possible subcriticality, and reduce the limit cycle oscillations (LCOs) amplitude.

Coupling Effects on Torsional Vibration with Clearance of a Two-Degree-of-Freedom System

2011 ◽  
Vol 199-200 ◽  
pp. 824-830
Author(s):  
Md. Hossain Zahid ◽  
Enaiyat Ghani Ovy
Keyword(s):  
Torsional Vibration ◽  
Degree Of Freedom ◽  
Impact Model ◽  
Vibration Characteristic ◽  
Bifurcation Diagrams ◽  
Coupling Effects ◽  
Chaotic Motions ◽  
Low Stiffness ◽  
Clearance Nonlinearity ◽  
Two Degree Of Freedom

Two-degree-of-freedom vibro-impact model with clearance nonlinearity of torsional vibration is presented in this paper. Clearance in coupling in any rotating machinery can exhibit chaotic and multiple periodic phenomena. Coupling inertia also contributes to change the vibration characteristic significantly. In this paper, coupling effects, from a small inertia to large inertia compare to rotor, have been investigated for a wide frequency zone by simulation and some experiments focusing on resonance and bifurcation diagrams. As the spring in the clearance usually possesses quite low stiffness compared to shaft stiffness, symmetric and asymmetric characteristics can be exhibited. The results found are noticeably different from each other for the symmetric and asymmetric conditions. The presence of vibro-impact due to clearance can cause periodic, multiple periodic and chaotic motions.

Multi-Pulse Chaotic Dynamics of a Composite Laminated Plate with Strong Coupling

2014 ◽  
Vol 548-549 ◽  
pp. 431-437
Author(s):  
Y. Zhao ◽  
W. Xu ◽  
J.H. Zhang
Keyword(s):  
Strong Coupling ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Laminated Plate ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Two Degree Of Freedom

In this paper, the multi-pulse chaotic dynamics of a simply-supported symmetric cross-ply composite laminated rectangular plate with the parametric and forcing excitations is investigated by using the extended Melnikov method. The two-degree-of-freedom non-autonomous nonlinear dynamical system of the plate with strong coupling is considered. The results obtained here indicate that multi-pulse chaotic motions can occur in the plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the plate based on the theoretical analysis.

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.

Resonant Chaotic Dynamics of a Symmetric Cross-Ply Composite Laminated Plate Under Transverse and In-Plane Excitations

2020 ◽  
Vol 30 (07) ◽  
pp. 2050106
Author(s):  
W. S. Ma ◽  
W. Zhang
Keyword(s):  
Nonlinear System ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Laminated Plate ◽  
Governing Equations ◽  
Partial Differential ◽  
Chaotic Motions ◽  
Composite Laminated Plate ◽  
Two Degree Of Freedom

The resonant chaotic dynamics of a symmetric cross-ply composite laminated plate are studied using the exponential dichotomies and an averaging procedure for the first time. The partial differential governing equations of motion for the symmetric cross-ply composite laminated plate are derived by using Reddy’s third-order shear deformation plate theory and von Karman type equation. The partial differential governing equations of motion are discretized into two-degree-of-freedom nonlinear systems including the quadratic and cubic nonlinear terms by using Galerkin method. There exists a fixed point of saddle-focus in the linear part for two-degree-of-freedom nonlinear system. The Melnikov method containing the terms of the nonhyperbolic mode is developed to investigate the resonant chaotic motions of the symmetric cross-ply composite laminated plate. The obtained results indicate that the nonhyperbolic mode of the symmetric cross-ply composite laminated plate does not affect the critical conditions in the occurrence of chaotic motions in the resonant case. When the resonant chaotic motion occurs, we can draw a conclusion that the resonant chaotic motions of the hyperbolic subsystem are shadowed for the full nonlinear system of the symmetric cross-ply composite laminated plate.

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.

scholarly journals Understanding (coupled) large amplitude motions: the interplay of microwave spectroscopy, spectral modeling, and quantum chemistry

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ha Vinh Lam Nguyen ◽  
Isabelle Kleiner
Keyword(s):  
Fourier Transform ◽  
Quantum Chemistry ◽  
Large Amplitude ◽  
Environmental Chemistry ◽  
Broad Band ◽  
Microwave Spectroscopy ◽  
Rotational Spectrum ◽  
Spectral Modeling ◽  
Rotational Spectra ◽  
Large Amplitude Motions

AbstractA large variety of molecules contain large amplitude motions (LAMs), inter alia internal rotation and inversion tunneling, resulting in tunneling splittings in their rotational spectrum. We will present the modern strategy to study LAMs using a combination of molecular jet Fourier transform microwave spectroscopy, spectral modeling, and quantum chemical calculations to characterize such systems by the analysis of their rotational spectra. This interplay is particularly successful in decoding complex spectra revealing LAMs and providing reference data for fundamental physics, astrochemistry, atmospheric/environmental chemistry and analytics, or fundamental researches in physical chemistry. Addressing experimental key aspects, a brief presentation on the two most popular types of state-of-the-art Fourier transform microwave spectrometer technology, i.e., pulsed supersonic jet expansion–based spectrometers employing narrow-band pulse or broad-band chirp excitation, will be given first. Secondly, the use of quantum chemistry as a supporting tool for rotational spectroscopy will be discussed with emphasis on conformational analysis. Several computer codes for fitting rotational spectra exhibiting fine structure arising from LAMs are discussed with their advantages and drawbacks. Furthermore, a number of examples will provide an overview on the wealth of information that can be drawn from the rotational spectra, leading to new insights into the molecular structure and dynamics. The focus will be on the interpretation of potential barriers and how LAMs can act as sensors within molecules to help us understand the molecular behavior in the laboratory and nature.

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