Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Lei Zuo
Keyword(s):  
Total Mass ◽  
Primary System ◽  
Vibration Absorbers ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
In Series ◽  
New Type ◽  
Parameter Variance ◽  
Stiffness And Damping ◽  
Optimal Series

Various types of tuned-mass dampers (TMDs), or dynamic vibration absorbers, have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multidegree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Decentralized H2 and H∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio of 5% can appear to have 31–66% more mass than the classical TMD, and it can perform better than the optimal parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter variance of the primary system than other TMD(s). Unlike in the parallel multiple TMDs where at the optimum the absorber mass is almost equally distributed, in the optimal series TMDs the mass of the first absorber is generally much larger than the second one. Similar to the 2DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections, and further increased effectiveness can be obtained if a negative dashpot is allowed. The optimal performance and parameters of series two TMDs are obtained and presented in a form of ready-to-use design charts.

Characteristics and Optimization of Series Multiple Tuned-Mass Dampers

2007 ◽  
Author(s):  
Lei Zuo
Keyword(s):  
Total Mass ◽  
Vibration Suppression ◽  
Primary System ◽  
Mass Ratio ◽  
Dynamic Vibration Absorber ◽  
Tuned Mass Dampers ◽  
In Series ◽  
New Type ◽  
Stiffness And Damping ◽  
Better Than

Tuned-mass damper (TMD), or dynamic vibration absorber (DVA), is a very practical and effective device for vibration suppression. Various types of tuned-mass dampers have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multi-degree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Structured H2 and H∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio 5% can appear to have 31%–66% more mass than the classical TMD, and it can perform better than parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter changes of the primary system than other TMD(s). Unlike the parallel multiple TMDs, the optimal mass distribution among absorbers in series TMDs is far from the case of equal masses, but instead the first absorber mass is much larger than the second one. Similar to the two-DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections and further increased effectiveness can be obtained if negative dashpot is allowed.

scholarly journals A methodology for identifying optimum vibration absorbers with a reaction mass

2019 ◽  
Vol 475 (2228) ◽  
pp. 20190232 ◽  
Author(s):  
Sara Ying Zhang ◽  
Yi-Yuan Li ◽  
Jason Zheng Jiang ◽  
Simon A. Neild ◽  
John H. G. Macdonald
Keyword(s):  
Vibration Suppression ◽  
Dynamic Properties ◽  
Reaction Mass ◽  
Vibration Absorbers ◽  
Tuned Mass Dampers ◽  
Wide Range ◽  
Mass Damper ◽  
In Series ◽  
Significant Performance ◽  
Full Class

Tuned mass dampers (TMDs), in which a reaction mass is attached to a structural system via a spring–parallel–damper connection, are commonly used in a wide range of applications to suppress deleterious vibrations. Recently, a mass-included absorber layout with an inerter element, termed the tuned mass damper inerter (TMDI), was introduced, showing significant performance benefits on vibration suppression. However, there are countless mass-included absorber layouts with springs, dampers and inerters, which could potentially provide more preferred dynamic properties. Currently, because there is no systematic methodology for accessing them, only an extremely limited number of mass-included absorber layouts have been investigated. This paper proposes an approach to identify optimum vibration absorbers with a reaction mass. Using this approach, a full class of absorber layouts with a reaction mass and a pre-determined number of inerters, dampers and springs connected in series and parallel, can be systematically investigated using generic Immittance-Function-Networks. The advan- tages of the proposed approach are demonstrated via a 3 d.f. structure example.

Design and Optimization of Multiple Single-DOF Tuned Mass Dampers Based on Flexure Design Theory

2018 ◽  
Author(s):  
Wenshuo Ma ◽  
Yiqing Yang ◽  
Jingjun Yu
Keyword(s):  
Design Theory ◽  
Dynamic Performance ◽  
Maximum Amplitude ◽  
Single Mode ◽  
Primary System ◽  
Tuned Mass Dampers ◽  
Precision Engineering ◽  
Element Analysis ◽  
Design And Optimization ◽  
Stiffness And Damping

Vibration is an undesirable phenomenon in engineering, and its avoidance has received considerable attention, especially for the cases of precision engineering. Since the dynamic performance of precision mechanisms are most likely to be restricted by their 1st modes, multiple single degree of freedom (SDOF) tuned mass dampers (TMDs) are designed to suppress a translational moving platform with single mode. The TMDs are designed with optimal stiffness and damping ratios, which are acquired by numerical optimization using minimax algorithm. Each SDOF TMD is implemented via the graphical approach and modeled by substructure dynamic modeling techniques. Results of finite element analysis (FEA) show that the maximum amplitude of frequency response function (FRF) of the primary system can be damped to 89.14% when N is 3, which validates the vibration mitigation by employing the designed TMDs. Furthermore, the proposed design routine provides a guidance for implementation of multiple SDOF TMDs.

Application of Tuned Mass Dampers and Lever Type Vibration Isolator to the Quarter-Car Model in Order to Increase Ride Comfort

2010 ◽  
Author(s):  
Go¨ksu Aydan ◽  
Ender Cig˘erog˘lu ◽  
S. C¸ag˘lar Bas¸lamıs¸lı
Keyword(s):  
Ride Comfort ◽  
Small Mass ◽  
Vibration Isolator ◽  
Tuned Mass Dampers ◽  
Suspension Spring ◽  
Vibration Isolators ◽  
Quarter Car Model ◽  
Suspension Systems ◽  
In Series ◽  
Stiffness And Damping

In this paper, performance of passive vibration isolators, namely rotational / linear tuned mass dampers (TMD) and lever type vibration isolators (LVI), are investigated under different configurations for optimal ride comfort. TMDs reduce vibration levels by absorbing the energy of the system, especially around natural frequencies with the help of viscous dampers. Two types of TMDs, rotational and linear, are investigated in this study. Although linear TMDs can be more easily implemented on suspension systems, rotational TMDs show better performance in reducing vibration levels. The reason is that, the inertia effect of rotational TMDs is higher than linear TMDs. In order to obtain better results with TMDs, a study on different possible configurations is conducted. A plate, with very small mass, is added between sprung and unsprung masses without changing the original suspension spring stiffness and damping coefficients and acts as a support for in-series TMD applications. Finally, LVIs are implemented to reduce sprung mass acceleration and more satisfactory results are obtained especially around body bounce frequency.

Comparing the Performance of Optimally Tuned Dynamic Vibration Absorbers With Very Large or Very Small Moment of Inertia

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
S.-J. Jang ◽  
M. J. Brennan ◽  
E. Rustighi
Keyword(s):  
Moment Of Inertia ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
In Series ◽  
Dynamic Vibration Absorbers ◽  
Stiffness And Damping ◽  
Physical Reasons ◽  
Two Degree Of Freedom ◽  
Large Moment

In this article, the performance of a two degree-of-freedom dynamic vibration absorber (DVA) with very large or very small moment of inertia is studied. Although it has been shown previously that an optimally tuned DVA with a negligibly small moment of inertia marginally outperforms the optimally tuned DVA with a very large moment of inertia, the physical reasons for this have not been made clear. Using a simplified model of the stiffness elements of the DVA, it is shown that the two sets of parallel combinations of stiffness and damping elements of the DVA with negligibly small moments of inertia effectively act in series, rather than in parallel as in the other case. Furthermore, it is shown that the stiffness and damping elements can be represented as a single stiffness and a single damping element whose properties are frequency dependent. This frequency dependency means that there is additional freedom in choosing the optimum stiffness and damping of the DVA, which results in better performance.

Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems

2005 ◽  
Vol 127 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Parameter Optimization ◽  
Substantial Improvement ◽  
Design Parameters ◽  
Feedback Gain ◽  
Primary System ◽  
Tuned Mass Dampers ◽  
H2 Control ◽  
Damping Coefficients ◽  
The Individual ◽  
Stiffness And Damping

The characteristics of multiple tuned-mass-dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers. Several papers have included some parameter optimization, all based on restrictive assumptions. In this paper, we propose an efficient numerical algorithm to directly optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system. We formulate the parameter optimization as a decentralized H2 control problem where the block-diagonal feedback gain matrix is composed of the stiffness and damping coefficients of the TMDs. The gradient of the root-mean-square response with respect to the design parameters is evaluated explicitly, and the optimization can be carried out efficiently. The effects of the mass distribution, number of dampers, total mass ratio, and uncertainties in system parameters are studied. Numerical results indicate that the optimal designs have neither uniformly spaced tuning frequencies nor identical damping coefficients, and that optimization of the individual parameters in the MTMD system yields a substantial improvement in performance. We also find that the distribution of mass among the TMDs has little impact on the performance of the system provided that the stiffness and damping can be individually optimized.

A method for vibration absorber tuning based on baseline frequency response functions

2007 ◽  
Vol 221 (9) ◽  
pp. 1071-1078 ◽  
Author(s):  
C Q Liu ◽  
C C Chang
Keyword(s):  
Frequency Response ◽  
Experimental Methods ◽  
Vibration Absorber ◽  
Physical Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Baseline Frequency ◽  
Stiffness And Damping

This paper presents explicit expressions for new frequency response functions (FRFs) of a primary system when a vibration absorber is attached to it. The new FRF is expressed in terms of the baseline (‘old’) FRFs of the primary system and the physical parameters (the mass, stiffness, and damping) of the vibration absorber. The baseline FRF of the primary system can be obtained by either analytical or experimental methods. This approach allows engineers and designers to evaluate a number of alternative vibration absorbers before these absorbers are physically implemented on the structure. Therefore a considerable amount of time and effort for engineers and designers can be saved. Several examples are provided to illustrate the use of the method.

Effectiveness of Location and Number of Multiple Tuned Mass Damper for Seismic Structures

2020 ◽  
Vol 9 (6) ◽  
pp. 780-783
Keyword(s):  
Seismic Response ◽  
Software Tool ◽  
Tuned Mass Damper ◽  
Structure Study ◽  
Structural Performance ◽  
Mass Ratio ◽  
Tuned Mass Dampers ◽  
Maximum Reduction ◽  
Mass Damper ◽  
Earthquake Data

Tuned mass dampers (TMD) are one of the most reliable devices to control the vibration of the structure. The optimum mass ratio required for a single tuned mass damper (STMD) is evaluated corresponding to the fundamental natural frequency of the structure. The effect of STMD and Multiple tuned mass dampers (MTMD) on a G+20 storey structure are studied to demonstrate the damper’s effectiveness in seismic application. The location and number of tuned mass dampers are studied to give best structural performance in maximum reduction of seismic response for El Centro earthquake data. The analysis results from SAP 2000 software tool shows damper weighing 2.5% of the total weight of the structure effectively reduce the response of the structure. Study shows that introduction of 4-MTMD at top storey can effectively reduce the response by 10% more in comparison to single tuned mass damper. The use of MTMD of same mass ratio that of STMD is more effective in seismic response.

scholarly journals Galaxy Formation: Some Comparisons between Theory and Observation

1983 ◽  
Vol 100 ◽  
pp. 391-399 ◽  
Author(s):  
S. Michael Fall
Keyword(s):  
Galaxy Formation ◽  
Total Mass ◽  
Virial Theorem ◽  
Velocity Dispersion ◽  
Rotation Velocity ◽  
Morphological Type ◽  
Fundamental Parameter ◽  
Mass Ratio ◽  
First Approximation ◽  
Type Form

Before theoretical ideas in this subject can be compared with observational data, it is necessary to consider the properties of galaxies that are likely to be relics of their formation. Most astronomers would agree that the list of important parameters should be headed by the total mass M, energy E and angular momentum J. Next on the list should probably be the relative contributions to these quantities from the disc and bulge components of galaxies and denoted D/B for the mass ratio. They can be estimated from the median (i.e. half-mass) radius R, velocity dispersion σ and rotation velocity v of each component, either through the virial theorem or through the luminosity L and an assumed value of M/L. As a first approximation, it is reasonable to suppose that galaxies of a given disc-to-bulge ratio or morphological type form a sequence with mass as the fundamental parameter. The comparison of theory with data is further simplified by considering the extreme cases of ellipticals, with D/B << 1, and late-type spirals, with D/B >> 1. The approach outlined below is to explore the consequences of relaxing in succession the constraints that E, J and M be conserved during the collapse of proto-galaxies. In this article I concentrate on theories that are based on some form of hierarchical clustering because the pancake and related theories are not yet refined enough for a detailed confrontation with observations.

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