Global Bifurcation of a Tuning Mass Damper with Plastic Impacts

2011 ◽  
Vol 243-249 ◽  
pp. 6225-6229
Author(s):  
An Zhi Yan ◽  
Xiao Hua Li
Keyword(s):  
Excitation Frequency ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Tuned Mass Damper ◽  
Gradual Change ◽  
Periodic Excitation ◽  
Vibratory System ◽  
Mass Damper ◽  
The Relationship ◽  
Two Degree Of Freedom

Many Literatures pay attention to the location and parameter optimization of Tuned Mass Damper (TMD). Yet there are few studies on the case where both the TMD and the main system have plastic impacts under large stroke of TMD fixed in limitation space. A two degree-of-freedom (DOF) vibratory system having symmetrically placed rigid stops and subjected to periodic excitation is considered in this paper. The equations of the vibratory system are constructed, and then for simplification the dimensionless equations are obtained. Poincaré map was used to study the relationship between the motion stability and parameters. Period-doubling bifurcation of motion was found by numerical simulations. With the gradual change in excitation frequency, the routes of quasi-periodic impact motions to chaos are observed from simulation results.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

Analytical Investigation of Vibration Attenuation With a Nonlinear Tuned Mass Damper

2015 ◽  
Author(s):  
Andrew J. Dick ◽  
Aaron Atzil ◽  
Satish Nagarajaiah
Keyword(s):  
Primary Structure ◽  
Multiple Scales ◽  
Tuned Mass Damper ◽  
Analytical Investigation ◽  
Degree Of Freedom ◽  
Approximate Analytical Solutions ◽  
Vibration Attenuation ◽  
Mass Damper ◽  
Two Degree Of Freedom ◽  
Nonlinear Tuned Mass Damper

Vibration attenuation devices are used to reduce the vibrations of various mechanical systems and structures. In this work, an analytical method is proposed to provide the means to investigate the influence of system parameters on the dynamic response of a system. The method of multiple scales is used to calculate an approximate broadband solution for a two degree-of-freedom system consisting of a linear primary structure and a nonlinear tuned mass damper. The model is decoupled, approximate analytical solutions are calculated, and then they are combined to produce the desired frequency-response information. The approach is initially applied to a linear two degree-of-freedom system in order to verify its performance. The approach is then applied to the nonlinear system in order to study how varying the values of parameters associated with the nonlinear absorber affect its ability to attenuate the response of the primary structure.

Design and control performance of a frictional tuned mass damper with bearing–shaft assemblies

2019 ◽  
Vol 25 (12) ◽  
pp. 1812-1822 ◽  
Author(s):  
Jinwei Jiang ◽  
Siu Chun Michael Ho ◽  
Nathanael J Markle ◽  
Ning Wang ◽  
Gangbing Song
Keyword(s):  
Damping Ratio ◽  
Excitation Frequency ◽  
Structural Response ◽  
Tuned Mass Damper ◽  
Resonant Peak ◽  
Equivalent Viscous Damping ◽  
Optimal Damping ◽  
Mass Damper ◽  
And Control ◽  
Equivalent Viscous Damping Ratio

This paper explores the feasibility of leveraging the damping generated by the friction between movable flange-mounted ball bearings and a stationary shaft. This bearing–shaft assembly is integrated with a tuned mass damper to form a frictional tuned mass damper (FTMD). The friction coefficient and the equivalent viscous damping ratio of the proposed FTMD were experimentally obtained based on different cases of glass, steel, and aluminum slide shafts. The proposed FTMD was modeled and simulated numerically to study its ability to suppress vibrations on a single degree of freedom structure. Furthermore, a parallel experimental validation of the FTMD was also executed to verify simulation results. Results from both experiments and simulations demonstrated that the proposed FTMD device was able to significantly improve the damping ratio of the primary structure from 0.35% to 5.326% during free vibration, and also to suppress around 90% of uncontrolled structural response at a tuned frequency. In particular, the frequency responses, among the tested shaft materials, suggested that the selected steel slide shaft practically provided a near-optimal damping coefficient, thus the proposed FTMD was able to considerably reduce structural resonant peak amplitudes over the tested excitation frequency domain.

Tuned mass damper and high static low dynamic stiffness isolator for vibration reduction of beam structure

2019 ◽  
Vol 234 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Meysam Raei ◽  
Morteza Dardel
Keyword(s):  
Natural Frequency ◽  
Dynamic Stiffness ◽  
Excitation Amplitude ◽  
Tuned Mass Damper ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Low Frequencies ◽  
First Case ◽  
Mass Damper ◽  
Two Degree Of Freedom

In this work, the combination effect of tuned mass damper and high static low dynamic stiffness (HSLDS) isolator is investigated in reducing the vibration amplitude of Euler–Bernoulli beam with a nonlinear attachment. The performance of the absorber is studied in two cases; the first case, HSLDS isolator is one degree of freedom and the second case, two degree of freedom isolator is combined of HSLDS isolator and tuned mass damper absorber. By comparing the performance of these two isolators, it is revealed the two degree of freedom isolator has much better performance in direct force excitation and also improves the system performance in the base excitation. This isolator reduces the system amplitude at all frequencies, especially ultra-low frequencies, which is the main advantage to this isolator with respect to other isolators and reduces the natural frequency until the phenomenon of resonance occurs at a lower frequency. Moreover, decreasing the natural frequency increases the damping and in quasi zero stiffness and negative stiffness structure, the system has supercritical damping. This isolator is studied for positive, quasi zero and negative stiffness. The results show that the system with quasi zero stiffness has the best performances. Also, by increasing the excitation amplitude, the isolator loses its effectiveness.

Subharmonic solution of a vibration system with two mass elastic connecting rods

2019 ◽  
Vol 50 (5) ◽  
pp. 135-142
Author(s):  
Guo Feng
Keyword(s):  
Periodic Motion ◽  
Excitation Frequency ◽  
Melnikov Method ◽  
Periodic Excitation ◽  
Vibration System ◽  
Subharmonic Solution ◽  
Subharmonic Bifurcation ◽  
Double Mass ◽  
Relationship Of ◽  
The Relationship

In this article, the dynamic characteristic of linkage bobbing machine with balanced double-mass bearing periodic excitation and damping is studied. Subharmonic Melnikov function of the oscillating periodic orbits is computed through Melnikov method. And, the relationship of parameters is given when the subharmonic bifurcation occurs. The periodic motion is simulated. Through analysis, as the excitation frequency varies, the periodic motion undergoes flip bifurcations and subharmonic bifurcation occurs, which finally leads to chaos. In addition, the ultra-subharmonic solution of the system is given.

Study of the Relationship Between Parameters and Effectiveness of Essential Nonlinear Absorber

2009 ◽  
Author(s):  
Tang Simi ◽  
Shijian Zhu ◽  
Jingjun Lou
Keyword(s):  
Harmonic Balance ◽  
Linear Oscillator ◽  
Periodic Excitation ◽  
Parameter Region ◽  
Modulation Equation ◽  
Nonlinear Absorber ◽  
Balance Technique ◽  
The Relationship ◽  
Two Degree Of Freedom ◽  
Harmonic Balance Technique

The two degree-of-freedom (dof) system consisting of a linear oscillator coupled with a essential nonlinear absorber is studied, which is under periodic excitation. Applying harmonic balance technique, we derive a set of modulation equation that is directly amenable to characteristic of amplitude-frequency of the system. Conclusion can be summarized: With some parameters, the absorber performs effectively over a broad range of frequency; but the amplitude of linear oscillator may jump suddenly for the change of parameters. The effectiveness of absorber is also affected by the forcing, that is different from classical absorber. The relationship between parameters and effectiveness of essential nonlinear absorber are determined and the parameter region seems to comply with some rules.

scholarly journals The Stick-Slip Vibration and Bifurcation of a Vibro-Impact System with Dry Friction

2014 ◽  
Vol 8 (1) ◽  
pp. 308-313 ◽  
Author(s):  
Quanfu Gao ◽  
Xingxiao Cao
Keyword(s):  
Periodic Motion ◽  
Dry Friction ◽  
Low Frequency ◽  
Period Doubling ◽  
Periodic Motions ◽  
Vibratory System ◽  
Stick Slip ◽  
The Impact ◽  
Two Degree Of Freedom ◽  
Impact Motion

In this paper, the periodic motion, bifurcation and chatter of two-degree-of-freedom vibratory system with dry friction and clearance were studied. Slip-stick motion and the impact of system motions were analyzed and numerical simulations were also carried out. The results showed that the system possesses rich dynamics characterized by periodic motion, stick-slip-impact motion, quasi-periodic motion and chaotic attractors, and the routs from periodic motions to chaos observed via Hof bifurcation or period-doubling bifurcation. Furthermore, it was found that there exists the chatter phenomena induced by dry friction in low frequency, and the windows of chaotic motion are broadened in the area of higher excitation frequencies as the dry friction increases.

Coupled Tuned Mass Dampers for the Seismic Control of Asymmetric-Plan Buildings

2010 ◽  
Vol 26 (3) ◽  
pp. 749-778 ◽  
Author(s):  
Jui-Liang Lin ◽  
Keh-Chyuan Tsai ◽  
Yi-Jer Yu
Keyword(s):  
Physical Space ◽  
Tuned Mass Damper ◽  
Tuned Mass Dampers ◽  
Seismic Control ◽  
Mass Damper ◽  
Torsionally Stiff ◽  
Torsionally Flexible ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Modal Vibration

An innovative tuned mass damper, referred to as a coupled tuned mass damper (CTMD), is proposed for the control of a coupled vibration mode of one-way asymmetric-plan buildings. The CTMD simultaneously translates and rotates almost resonantly with the vibration of the controlled mode, which actually vibrates in translation, as well as rotation. Thus, the CTMD can be viewed as a direct approach for controlling the modal vibration of asymmetric-plan buildings. First, the CTMD is developed from the two-degree-of-freedom modal system, which has one active and one spurious vibration frequency. It is illustrated that the optimum parameter values of the CTMD can be conveniently determined from those of the corresponding tuned mass damper (TMD). Second, in order to apply the CTMD to a building structure, the properties of the CTMD obtained in the modal space are transformed into the physical space. Finally, the effectiveness of the CTMD in reducing the vibrations of asymmetric-plan structures is verified by investigating the frequency response functions and the response histories of three eight-story asymmetric-plan buildings with and without dampers. These three buildings are respectively torsionally stiff, torsionally similarly stiff, and torsionally flexible. This study confirms that the CTMD is an effective alternative for the seismic control of asymmetric-plan buildings.

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