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Dynamics Of Structures Clough Penzien
Dynamics Of Structures Clough Penzien
Experimental Study on the Effects of Tuned Mass Damper
Experimental Study On The Effects OF TMD
On Structure Vibration Reduction
M H Pashaei(1), H Sheydaie (2) I Khatami (3) M jazayeri (4)
School of Engineering, University of Mazandaran, P O Box: 484, Babol, Iran
Email: (1) , (2) mn_khatami@yahoo.com >(3)
, mitrajazayeri62@yahoo.com >(4)
___________________________________________________________________________Abstract
Damping is a phenomenon which exists in every system. Some systems have little and some have more. it is related to what elements and how they are assembled with each other in system .such phenomena dissipate energy and reduce the vibrating caused by external applied forces to system like earth quick, wind ,sea wave and thunder .Different types of dampers have been known regarding to their function: passive, active and semi-active. In the field of passive dampers we have many types: tuned mass damper TMD, tuned liquid damper TLD, friction dampers FD and viscose dampers VD.
The present research experimentally studies damping ratio of a three-storey building using TMD and without TMD damper to see how damper increase the damping ratio . To carry out this study A structure and the necessary equipment including a loading system and a data acquisition system are used.. Structure examined under the free vibration in this way: A small displacement implemented to the structure as a free vibrations. And by carrying out more than 150 tests, the damping ratios of the structure using TMD and without TMD in different loading conditions are obtained. The results show that the Tuned mass damper has a major effect on the damping characteristics of the structure The results also show that the increasing the loading applied to structure doesn’t change the damping ratio which is analyses an Ansys software .
Key Word: damping ,tuned mass damper ,damping ratio
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1 Introduction
1.1 Damping concept
Damping is a phenomenon where the amplitude of vibration in a mechanical system steadily diminishes. The effect of damping is to remove energy from the system. Energy in a vibrating system can be dissipated, being converted into heat [1,2,3].
Damping is present in all vibrating systems. Every system which possesses mass and elasticity is capable of vibration. Dampers are kind of device in order to dissipate vibration forces… Different types of dampers have been known .in general they are divided in three categories: passive, active and semi-active.[4,5,6,7].Tuned liquid dampers[8] and Tuned mass dampers[9] are very usual one which are using nowadays in many structural system and the second one is our research topic.
2 Examined model
In present research A structure is being designed and built as a model of a real structure in Fig.1
Fig 1: drawing and picture of model
the weight of the structure is 200 kg and the stiffness of that is k=6.666 N/mm and the natural frequency is w=0.056 Hz which was analyses in a finite element software Ansys
Fig 2: analysed model in software
3 TMD design [11~25]
in order to design the TMD with study of many books and article and the real TMD used in some real structures in the world like Citicope tower in New York [10] we came to this result : the mass of TMD can consider 2 percent of structure’s mass or less, but it should be design in a optimum way . Natural frequency of TMD Should be as the natural frequency of real structure. When the real structure approach to its natural frequency caused by external applied forces, TMD must approach to its natural frequency too. The vibration of TMD at natural frequency causes turbulence in general movement. In this way the frequency of structure go further from its natural frequency.
As a result, the stiffness of TMD also should consider 2 percent of structure’s stiffness to . be as the same.
The Mass Of TMD: (1)
The Stiffness Of TMD: (2)
After determination of mass and stiffness’ amount of TMD, a block and spring design and then manufactured at Fig 4 and 5.
Fig 4: mass dimension Fig 5: spring dimension
After manufacturing the block as a mass and spring as a stiffness element, they attached to each other Fig 6 and assembled on a bearing Fig.7 in order to have soft movement .
Fig 6. Mass and spring attached Fig 7. Mass assembled on bearing
And finally whole commission on our modeled structure to examine how it effect the damping ratio of structure Fig.8.
Fig 8
4. Method of loading and equipment
To apply load to structure we use a method showed in Fig 9. a block will hang using a rope to structure and suddenly the rope will cut then dropping the block cause a loading which apply to structure .this procedure carry both condition the structure using TMD and without TMD .in this way we have the free vibration condition .
Fig.9
The equipment Fig .10 to record the data is:
a) A sensor which is called transducer
b) A hardware which is called Data Logger which transfer the sensor output to computer
c) A computer and the software of Pulse which show the output in Graph as a graph of time-displacement.
Fig 10
4. Methodology of experiment
in order to have free vibration we should apply the initial speed or initial displacement to the structure. Our method is initial displacement .for this purpose the structure will be loaded bye some block and by make them free from the structure the initial displacement will apply to structure .the loading carried out using steel block and different size fro 15 kg until 75 kg with the step of 10 kg. The test carried out nearly 150 times to get to a correct conclusion.
5. Getting Data [26]
Using experiment equipment we come to a time-displacement graph which is being showed in Fig 11 , 12 .the first graph shows the displacement of structure under the free vibration using TMD and the second one not using TMD.
Fig 11.Time –Displacement Graph for system without TMD
Fig 12. Time _Displacement Graph for system with TMD
It is clear if we confess on both graphs it shows the Maximum Displacement reduce from 1.3 mm to 1.1 mm.
For all the graph we use the ‘logarithmic decrement’ method to calculate damping ratio . Fig 13 shows a graphical representation of a damped free vibration. The motion shown in Fig 13 may be represented by the equation:
(3)
Where
Is the natural frequency, is the damping ratio of the system and X and are arbitrary constants determined from initial conditions.
The natural logarithm of the ratio of any two successive amplitudes, for example and in Fig 1, can be written as:
(4)
Where and can be obtained from Eqn 3 at t=t1 and t=t2=t1+τ, respectively. Inserting these values of and in Eqn 4 will result in the following equation:
(5)
For every step of loading we get the result showed in table1.
Table 1
6. Results
- Damping ratios change with applying different loads for the system not using TMD instead it will not change for system using TMD .thus it can be show that using Tmd increase the damping ratio but if the amplitude of system increase cause by Appling more forces, it will not change. . A Tuned Mass Damper has constant behavior.
- For optimize performance of TMD it is better to design optimum range of 0 to 2% of mass and stiffness of real structure
. If we suppose the structure like a cantilever beam, the edge of the beam has more displacement during vibration, so it is rational to locate damper where there is more displacement.
Reference
1- Jeary, A. P., and Ellis, B. R., ‘Vibration Tests on Structures at Varied Amplitudes’ proc. ASCE/EMD Specially conference on Dynamic Response of Structures, ASCE, Atlanta, GA, 1981
2- Barkanov, E., ‘Transient response analysis of structures made from viscoelastic materials’ International J. for numerical methods in engineering, vol. 44, 1999
3- Allen, D. ‘The Mero Space Frame System’ Proceeding of Australian Conference on Space Structures, Melbourne, Australia, 1982.
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6- Kareem A. Mitigation of wind induced motion of tall buildings.J Wind Engng and Industr Aerodyn 1983;11:273–84
7- Structural control by induced stress based stiffness modification by By Katie Patricia Whipp ,Augest 2005 nashaville Tennessee .
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About the Author
hadi sheydaie master of science mechanical engineer mazandaran university iran
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