Dynamic analysis for a New Liquid Damper
Yu Guang-zhong Huang Dong-yang
Zhuzhou Times New Material Technology Guangzhou Municipal Construction
Co., Ltd., Zhuzhou 412007, China Co., Ltd., Guangzhou 510115, China
Abstract
A new type of liquid damper device – tuned liquid damper embedded a transverse cylinder (TLDETC) is developed and its dynamic characteristics is discussed in this paper. The dynamic characteristics of a TLDETC are formulated by using the fluid mechanics principle and energy method, then the dynamic characteristics of the optimal designed damper is simulated to compared with the ordinary tune liquid damper (TLD). Results show that the sloshing mass is effectively increased for TLDETC, and the dynamic performance of a TLDETC outperforms an ordinary TLD.
Keywords: tuned liquid damper; tuned liquid damper embedded a transverse cylinder; dynamic characteristics; simulation
1. Introduction
Tuned liquid damper (TLD) has been widely used as a structural vibration control device since the method was proposed by Bauer[1] to suppress structural response using two rectangular containers filled with unsolvable liquids. The sloshing force of liquid dominated by the sloshing mass which can be calculated by using the lumped-mass model[2] plays an important role in the vibration control effectiveness of a TLD. Thus, increasing the sloshing mass is a key task in TLD research in the world. Warnitchai and Pinkaew[3] used energy method to study the dynamic characteristics of TLD with various vertical damping devices and obtained the formulation for additional sloshing mass of TLD when the liquid flowed through these damping devices. In view of this, a new liquid damper – TLD embedded a transverse cylinder (TLDETC) is developed in this paper. A transverse cylinder is embedded in a certain location of the rectangular container, the purpose of which is to obtain additional sloshing mass of liquid using fluid mechanics principle and energy method while the liquid is flowing around the cylinder and therefore achieve better dynamic performance of liquid in this type of TLD.
2. TLDETC model
The cylinder is embedded in a certain location in the middle (half of the container length) of the container, and the surface of the cylinder is assumed to be smooth. Fig. 1 shows the schematic of an ordinary TLD model and a TLDETC model with the same container dimension and liquid mass.
Figure 1 Schematic of damper models:
(a) TLD; (b) TLDETC
As shown in Figure 1, M is the total liquid mass and A is the container length. H is the liquid height of TLD. For TLDETC, H' is the liquid height, R is the radius of the cylinder, while h is the vertical distance from the center of the cylinder to the free surface of liquid. Moreover, the container width is presented as B and the liquid filled in the container is the fire control water with the density ρ=1000kg/m3. It can be observed from Fig. 1 that the liquid height in a container is increased from H to H' due to the embedded cylinder.
3. Equations of TLDETC
According to the assumptions of hydrodynamics theory used in TLD calculation[4, 5] and Fig. 1, the basic parameters (sloshing mass and frequency) of TLD are given as follows
(1)
(2)
where B is the width of the container. The first sloshing mode of liquid sloshing is the most effective in TLD research. Hence, only the first sloshing mode is considered when the dynamic characteristics of TLD (or TLDETC) is discussed in this paper.
When the liquid flows around the cylinder, the flow-induced force on the cylinder along liquid flowing direction can be obtained by Morison’s equation. Then the additional sloshing mass can be obtained by the Warnitchai and Pinkaew’s method[3]
(3)
Hence, the total sloshing mass of liquid in TLDETC is obtained
(4)
Then the total sloshing force of TLDETC can be obtained by base excitation
The sloshing frequency of TLDETC can be obtained by fluid mechanics principle
(6)
4. Optimal sloshing mass of TLDETC
In order to determine the optimal sloshing mass of TLDETC with definite container dimension and liquid mass, h and R are differentiated in Eq. (5).
Hence, the relationships between h and R can be obtained by solving Eq. (7).
(8a)
(8b)
Eq. (8a) and Eq. (8b) present the relationships between h and R for the optimal sloshing mass of TLDETC corresponding to the cases of H' unknown and known, respectively. When the definite h and R meet Eq. (8), the optimal sloshing mass can be obtained in theory; however, both h and R can not be designed too great to disturb the stability of the liquid flowing around the cylinder. Thus, in this paper, the ranges of h and R are set to be H/3≤h≤2H/3, 0≤R≤H/10 (H' unknown) or H'/3≤h≤2 H'/3, 0≤R≤H'/10 (H' known).
5. Numerical simulation
The simulation is conducted to compare the dynamic characteristics of TLDETC and TLD. External excitation is assumed to be and the liquid masses of TLDETC and TLD are the same in the scheme: The container dimensions of TLDETC and TLD are the same while the liquid depths in TLDETC and TLD are different: ATLD=ATLDETC=5 m, BTLD=BTLDETC=5 m, while HTLD=4 m. The curve diagram for the relationship between R and h can be obtained from Eq. (8)
h (m) /R (m)
Figure 2 Relationship between R and h
As shown in Figure 2, R is not in the range of 0≤R≤0.4 m when h is in the range of 1.333≤h≤2.666 m for the optimal sloshing mass, but it can be observed that the curve goes closer to R’s value range as h goes lower. Hence, h can be ascertained as h=1.333 m, then R can be ascertained as R=0.4 m to obtained the optimal sloshing mass. Meanwhile, HTLDETC=4.100 m can be obtained. Then the increasing amplitude of sloshing force between TLDETC and TLD under different excitation frequency in this scheme is presented in Figure 3. While the sloshing force curves of TLDETC and TLD are shown in Figure 4.
ΔF (100%) /ω0 (rad/s)
Figure 3 Increasing amplitude of sloshing force between TLDETC and TLD
F (N) /
ω0 (rad/s)
Figure 4 Sloshing forces of TLDETC and TLD
As shown in Figure 3, when the dimensions of TLDETC and TLD are the same, the sloshing force produced by TLDETC is greater than that produced by TLD over most of the excitation frequency range, the maximal increasing amplitude reaches up to about 9%. On the other hand, decreasing amplitude only happens in a short frequency segment and the maximal decreasing amplitude is about 5%.
As shown in Figure 4, the peak sloshing force of TLDETC appears in advance of that of TLD in this scheme, and the reason is that the sloshing frequency of TLDETC (ωTLDETC=2.446 rad/s) is a bit lower than that of TLD (ωTLD=2.466 rad/s). Hence, the sloshing force of TLDETC will be lower than that of TLD in a certain frequency segment after the peak value due to the advancing of TLDETC as compared with TLD. However, this frequency segment is very short (2.450≤ω0≤2.776 rad/s). Meanwhile, it can be observed from the tendencies of the two sloshing force curves that the sloshing force of TLDETC shows stronger ‘robustness’ than TLD.
6. Conclusion
This paper presents a new type of TLD device –TLDETC, and the optimal dynamic design of this liquid damper is discussed. The comparison analysis of dynamic characteristics between TLDETC and ordinary TLD are made through the simulation. Analysis results indicate that the sloshing force produced by TLDETC is greater than that produced by TLD in most cases, the decreasing amplitude of sloshing force appears only in a short frequency segment where TLDETC and TLD behave with different sloshing frequencies; moreover, the sloshing force of TLDETC shows stronger ‘robustness’ than TLD. Hence, the dynamic performance of TLDETC outperforms that of ordinary TLD.
Because of the outstanding dynamic performance of TLDETC, the vibration control performance of TLDETC should be further studied for the practical engineering design in the near future.
References
[1] H. F. Bauer, “Oscillations of Immiscible Liquids in a Rectangular Container: a New Damper for Excited Structures”, Journal of Sound and Vibration, 1984(1), pp. 117-133.
[2] G. W. Housner, “Dynamic Pressure on Accelerated Fluid Containers”, Bulletin of the Seismological Of America, 1957(1), pp. 15-35.
[3] P. Warnitchai, T. Pinkaew, “Modelling of Liquid Sloshing in Rectangular Tanks with Flow-Dampening Devices”, Engineering Structures, 2008(7), pp. 593-600.
[4] J. R. Qian, P. Warnitchai, X. Ding, “Modelling of Liquid Sloshing in the Annular Region for Damper Application”, Engineering Mechanics, 1995(4), pp. 36-46.
[5] Q. Z. Liang, J. M. Xiong, “An Analysis of Oscillation Characteristics of Two-Layer Fluids TLD Using Circular Cylinder Container”, Engineering Mechanics, 2001(1), pp. 7-13.