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.

Three-Element Vibration Absorber–Inerter for Passive Control of Single-Degree-of-Freedom Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Abdollah Javidialesaadi ◽  
Nicholas E. Wierschem
Keyword(s):  
Passive Control ◽  
Translational Motion ◽  
Tuned Mass Damper ◽  
Degree Of Freedom ◽  
Superior Performance ◽  
Underlying Structure ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Mass Damper

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

A New Design Methodology for Planar Vibration Absorbers

1999 ◽  
Author(s):  
Pat Blanchet ◽  
Harvey Lipkin
Keyword(s):  
Design Methodology ◽  
Exciting Force ◽  
Degree Of Freedom ◽  
Vibration Absorbers ◽  
Specific Design ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Single Degree ◽  
Planar Vibration ◽  
Design Freedom

Abstract A new methodology is presented for the design of planar vibration absorbers. For the most part, previous methods have dealt with systems constrained to a single degree-of-freedom and require the absorber to be along the line of the exciting force. The presented methodology is more versatile and allows the placement of the absorber as a design freedom. Three specific design techniques for force and couple excitations are detailed along with numerical examples illustrating the results.

New Control Algorithms for Semi-Active Dynamic Vibration Absorbers

1995 ◽  
Author(s):  
M. Abé ◽  
T. Igusa
Keyword(s):  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Dynamic Vibration ◽  
Passive Devices ◽  
Active Vibration ◽  
Zero Values ◽  
Dynamic Vibration Absorbers ◽  
Insight Into

Abstract A semi-active dynamic vibration absorber is proposed for controlling the free-vibration impulse response of structures. It is assumed that (i) the initial displacement for the absorber spring can be set to non-zero values and (ii) the viscous damping coefficient for the absorber damping can be adjusted. The theory is first developed for a single-degree-of-freedom structure, and is then generalized to continuous structures. The extensive use of closed-form analytical results provides useful insight into the complex interaction between the structure and absorber. This makes it possible to solve the design problem without recourse to numerical optimization. The semi-active vibration absorber is found to be far more effective than conventional passive devices.

Single-Degree-of-Freedom Dynamic Vibration Absorber for Unknown System

2018 ◽  
Author(s):  
Zhang Pandeng ◽  
Liu Zhao ◽  
Zhang Tianfei ◽  
Zhu Yutian ◽  
Zheng Changlong ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Vibration Absorber ◽  
Evaluation Function ◽  
Vibration System ◽  
Dynamic Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Technology Application ◽  
Single Degree ◽  
Dynamic Vibration ◽  
Unknown System

Vibration causes problems, and the technology of dynamic vibration absorber is always used to control it. So far, the technology is mature, but based on the known of modes, mass, stiffness, damping and other parameters of the vibration system. For an unknown system or complicated system, how to use this technology is what the paper mainly discusses. The dynamic vibration absorber of this paper is a single-degree-of-freedom, and only one direction is to be controlled. The evaluation function is the ratio between the system vibration response after adding dynamic vibration absorber and the original exciting force, which can reflect the effect of dynamic vibration absorber. After separating the unknown system and the dynamic vibration absorber, based on force analysis, we analyze them separately and deduce the calculating formula of the evaluation function. The order of parameters to be determined is mass, stiffness, and damping. Flow chart is presented on how to use the method. The method is validated by a known system of two degree-of-freedom vibration system. The main innovation of this paper is to propose a method of predicting the effect of adding a single-degree-of-freedom dynamic vibration absorber to an unknown system to control a certain direction. This method doesn’t need to consider the system damping factor. This paper extends the scope of technology application of dynamic vibration absorber.

scholarly journals Study on the Vibration Suppression Method of Urban Railway Vehicles Based on a Composite Dynamic Vibration Absorber

2019 ◽  
Vol 296 ◽  
pp. 01010
Author(s):  
Qian Sun ◽  
Yongpeng Wen ◽  
Yu Zou
Keyword(s):  
Vibration Suppression ◽  
Vibration Reduction ◽  
Low Frequency ◽  
Peak Frequency ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dynamic Vibration

To reduce the bounce and the pitch vibration of carbody, a vertical dynamic model for urban rail vehicles is established to analyze the vibration response of the carbody in the low frequency range. In this paper, different methods of single-degree-of-freedom dynamic vibration absorber to suppress the vibration for carbody are investigated. The limits of single-degree-of-freedom dynamic vibration absorber to the vibration reduction effect of carbody are pointed out. After that, the design of a composite dynamic vibration absorber including a double oscillator structure is introduced. A vibration discreteness index is used to evaluate dynamic vibration absorbers with various designs for the vibration damping performance. Finally, the vibration reduction performance of the composite dynamic vibration absorber is verified by Sperling’s riding index. The results demonstrate that the performance of the single degree of freedom dynamic vibration absorber attached to a carbody may increase the vibration within a partial scope, when the peak frequency of vibration is far away from the design frequency. The installation of the composite dynamic vibration absorber vibration provides gentler running experience for passengers.

scholarly journals A novel design of the dynamic vibration absorbers for damped main systems under torsional excitation using least squares estimation of the equivalent linearization method

2018 ◽  
Vol 233 (1) ◽  
pp. 60-70
Author(s):  
Vu Duc Phuc ◽  
Van-The Tran ◽  
Nguyen Van Quyen
Keyword(s):  
Torsional Vibration ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Main System ◽  
Dynamic Vibration Absorbers ◽  
Torsional Excitation

Torsional vibration usually occurs in the working process of machines and equipment such as in transmission drive and working shaft of machine tool. To reduce this vibration, the dynamic balancing method and dual mass flywheel systems are applied. There are fewer researches that used the dynamic vibration absorber for reducing the torsional vibration. However, an analytical solution for designing the optimal parameters of dynamic vibration absorbers attached to the damped main system is found to be difficult and complicated. This paper proposes a novel idea to approximately replace an original damped main system by an equivalent undamped system using the least squares estimation of equivalent linearization method. An explicit closed-form expression of the optimal damping ratio and tuning parameters of dynamic vibration absorber are determined for the undamped main system under torsional excitation. The expressions are quite simple and have effective practical applications. Numerical results for time and frequency responses of the system are presented to reveal stronger effect and accuracy of the proposed solution on the damped main system. It is observed that the torsional vibration of the damped main system has been reduced significantly also in the resonant region. The proposed expressions of the optimal parameters are powerful tools for design dynamic vibration absorber to reduce the torsional vibration of rotary system such as the transmission and working shafts, etc.

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