Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Vibration Absorber

1999 ◽  
Vol 121 (3) ◽  
pp. 309-315 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Yasuhiro Endo ◽  
Nobuharu Aoshima
Keyword(s):  
Magnetic Force ◽  
Frequency Component ◽  
Harmonic Excitation ◽  
Subharmonic Resonance ◽  
Vibration Absorber ◽  
Spring Stiffness ◽  
Stabilization Method ◽  
Pendulum System ◽  
Main System ◽  
Subharmonic Frequency

The paper proposes a stabilization method for 1/3-Order subharmonic resonance with an autoparametric vibration absorber. A main system with nonlinear spring stiffness and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces 1/3-Order subharmonic resonance. A damped pendulum system, whose natural frequency is in the neighborhood of one-half of the main system, is attached to the main system as an absorber, in order to induce 1:2 internal resonance. The 1/3-Order subharmonic resonance which occurs in the case of locked pendulum is avoided due to energy transfer between the main system and the absorber, and due to energy dissipation by the absorber. It is also theoretically shown that a stable nontrivial steady state with respect to the 1/3-Order subharmonic frequency component is changed into an unstable one due to the absorber. Experimental results show the validity of the autoparametric vibration absorber for the 1/3-Order subharmonic resonance.

Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Absorber

1997 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Yasuhiro Endo ◽  
Nobuharu Aoshima
Keyword(s):  
Magnetic Force ◽  
Frequency Component ◽  
Harmonic Excitation ◽  
Subharmonic Resonance ◽  
Vibration Absorber ◽  
Spring Stiffness ◽  
Stabilization Method ◽  
Pendulum System ◽  
Main System ◽  
Subharmonic Frequency

Abstract The paper proposes a stabilization method for 1/3-order subharmonic resonance with an autoparametric vibration absorber. A main system with nonlinear spring stiffness and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces 1/3-order subharmonic resonance. A damped pendulum system, whose natural frequency is in the neighborhood of one-half of the main system, is attached to the main system as an absorber, in order to induce 1:2 internal resonance. The 1/3-order subharmonic resonance which occurs in the case of locked pendulum is avoided due to energy transfer between the main system and the absorber, and due to energy dissipation by the absorber. It is also theoretically shown that a stable nontrivial steady state with respect to the 1/3-order subharmonic frequency component is changed into an unstable one due to the absorber. Experimental results show the validity of the autoparametric vibration absorber for the 1/3-order subharmonic resonance.

Reduction of Primary Resonance Amplitude of Nonlinear Oscillator by a New Type of Nonlinear Dynamic Vibration Absorber

2007 ◽  
Author(s):  
Hoonhee Jo ◽  
Hiroshi Yabuno
Keyword(s):  
Frequency Response ◽  
Nonlinear Dynamic ◽  
Primary Resonance ◽  
Vibration Absorber ◽  
Spring Stiffness ◽  
Dynamic Vibration Absorber ◽  
Resonance Amplitude ◽  
Nonlinear Spring ◽  
Dynamic Vibration ◽  
Main System

The paper proposes a nonlinear dynamic vibration absorber for primary external resonance of system having cubic nonlinearity. A main system with nonlinear spring stiffness and subjected to harmonic excitation is considered. We calculate nonlinear spring stiffness produced by repulsive force of permanent magnets using Coulomb’s law. A damped pendulum system, whose natural frequency is in the neighborhood of twice that of the main system, is nonlinear coupled to the main system by link as a dynamic vibration absorber. This nonlinear dynamic vibration bsorber does not utilize linear coupling to the main system but utilizes nonlinear coupling. Therefore, the attachment of the nonlinear dynamic vibration absorber does not increase the number of degrees of freedom of the main system. Primary resonance amplitude is decreased in the case when pendulum is unlocked and hysteresis of the frequency response curve is disappeared. This means that attachment of dynamic vibration absorber has the same effect that increases directly the damping coefficent of the main system. Experimental results for this type of device are compared with a numerical results obtained from Runge-Kutta method. Comparison of the frequency response curves with and without nonlinear dynamic vibration absorber show validity of the proposed absorber.

scholarly journals Chaos control in a special pendulum system for ultra-subharmonic resonance

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Xianwei Chen ◽  
◽  
Xiangling Fu ◽  
Zhujun Jing ◽  
Keyword(s):  
Chaos Control ◽  
Subharmonic Resonance ◽  
Pendulum System

scholarly journals A New Design of Vibration Absorber for Periodic Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Kao-An Lin
Keyword(s):  
Mechanical Systems ◽  
Harmonic Excitation ◽  
Design Parameters ◽  
Vibration Absorber ◽  
Periodic Excitation ◽  
Dynamic Vibration Absorber ◽  
Dual Beam ◽  
Design Variables ◽  
Resonance Frequencies ◽  
Engineering Significance

The authors designed a novel type of dynamic vibration absorber, called periodic vibration absorber (PVA), for mechanical systems subjected to periodic excitation. Since the periodic rather than single harmonic excitation is themost occurring case in mechanical systems, the design of PVA is hence of engineering significance. The PVA designed in this paper is composed of a dual-beam interconnected with a discrete spring in between. By appropriately choosing the design parameters, the PVA can be of resonance frequencies in integer multiples of the base frequency such that the PVA can absorb significant amount of higher harmonics in addition to the base harmonic. The designed PVA was first experimentally verified for its resonance frequencies. The PVA implemented onto a mechanical system was then tested for its absorption ability. From both tests, satisfying agreement between experiments and numerical calculations has been obtained. The sensitivities of the design variables, such as the discrete spring’s stiffness and location, were discussed as well. The parameters’ sensitivities provided us with the PVA’s adjustable room for excitation frequency’s mismatch. Numerical results showed that within 3% of frequency mismatch, the PVA still performed better than a single DVA via adjusting the spring’s constant and location. All the results proved that the novel type of PVA could be a very effective device for vibration reduction of mechanical systems subjected to periodic excitation.

Extending Den Hartog’s Vibration Absorber Technique to Multi-Degree-of-Freedom Systems

2004 ◽  
Vol 127 (4) ◽  
pp. 341-350 ◽  
Author(s):  
Mehmet Bulent Ozer ◽  
Thomas J. Royston
Keyword(s):  
Matrix Inversion ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Single Degree Of Freedom ◽  
Inversion Theorem ◽  
Single Degree ◽  
Main System ◽  
Dynamic Vibration Absorbers ◽  
Invariant Points

The most common method to design tuned dynamic vibration absorbers is still that of Den Hartog, based on the principle of invariant points. However, this method is optimal only when attaching the absorber to a single-degree-of-freedom undamped main system. In the present paper, an extension of the classical Den Hartog approach to a multi-degree-of-freedom undamped main system is presented. The Sherman-Morrison matrix inversion theorem is used to obtain an expression that leads to invariant points for a multi-degree-of-freedom undamped main system. Using this expression, an analytical solution for the optimal damper value of the absorber is derived. Also, the effect of location of the absorber in the multi-degree-of-freedom system and the effect of the absorber on neighboring modes are discussed.

Pendulum as Vibration Absorber for Flexible Structures: Experiments and Theory

1996 ◽  
Vol 118 (4) ◽  
pp. 558-566 ◽  
Author(s):  
O. Cuvalci ◽  
A. Ertas
Keyword(s):  
Energy Transfer ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Pendulum System ◽  
Nonlinear Equations Of Motion ◽  
Tip Mass ◽  
Sinusoidal Excitation

The dynamic response of a beam-tip mass-pendulum system subjected to a sinusoidal excitation is investigated. A simple pendulum mounted to a tip mass of a beam is used as a vibration absorber. The nonlinear equations of motion are developed to investigate the autoparametric interaction between the first two modes of the system. The nonlinear terms appear due to the curvature of the beam and the coupling effect between the beam and pendulum. Complete energy transfer between modes is shown to occur when the beam frequency is twice the pendulum frequency. Experimental results are compared with a theoretical solution obtained using numerical integration. The experimental results are in qualitative agreement with the theory.

scholarly journals Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation

2020 ◽  
Author(s):  
Vu Duc Phuc ◽  
Tong Van Canh ◽  
Pham Van Lieu
Keyword(s):  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Damping Ratio ◽  
Harmonic Excitation ◽  
Tuning Parameter ◽  
Vibration Absorber ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Practical Applications ◽  
Dynamic Vibration

Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a   method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters are possible to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA.

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