Study on Tuningcharacteristics of THMD

Study on TuningCharacteristics of THMD

Yu Guang-zhong

Zhuzhou Times New Material Technology Co., Ltd., Zhuzhou 412007, China

Abstract

The tuning characteristics of THMD (tuned hybrid-tank/mass damper) under different sloshing effects of liquid and perturbation coefficients of structural frequency are studied by using the phasic difference method in this paper. The control equation of THMD is formulated and numerical simulation is also carried out by MATLAB. Results show that the sloshing effect of liquid adversely affects the tuning characteristics of THMD. However, when the structural frequency perturbs, THMD can reach a better performance level compared with an ordinary TMD. Then the optimized designintervals are obtained to make suggestions in practical engineering design.

Keywords: tuned hybrid-tank/mass damper; tuning characteristics; optimized designintervals; simulation

1. Introduction

Tuned hybrid-tank/mass damper (THMD) is a new kind of tunning damper in engineering field[1]. THMD can be taken place of tuned mass damper (TMD) using in vibration control due to its economical and practical properties similar to the tuned liquid column/mass damper[2, 3]. However, both excess liquid sloshing effect and the perturbation of structural frequency may reduce the tuning effectiveness of THMD. In view of that, the phasic difference method is used to analyze the tuning characteristics of THMD under different sloshing effects of liquid and different perturbation coefficients of structural frequency, the optimized designintervals obtained are expected to make suggestions in practical engineering design.

2. Dynamical system

A THMD system is composed of damping, stiffness, solid mass and liquid mass in a d hybrid-tank comprising a tuned liquid column damper (TLCD) and a tuned liquid damper (TLD). The model of a THMD is shown in Figure 1.

Figure 1 Model of a THMD

As shown in Figure 1,mS, cS and kSare the mass, damping and stiffness of a structure, respectively. M1 is the container mass while m2 and m3 are liquid mass in TLCD and TLD, respectively. cTHMD and kTHMD are the damping and stiffness of the THMD system, respectively. Moreover, the density of liquid filled in the system is ρ=1000kg/m3.

The dynamic equation of the THMD system in the matrix form is given by Literature [1]

(1)

In Eq. (1),,and are the horizontal acceleration vector, velocity vector and displacement vector of structure-THMD system. {F(t)}THMD is the externalexcitation vector. The mass matrix [M]THMD, the damping matrix [C]THMDand the stiffness matrix [K]THMD of the structure-THMD systemcan be expressed as follows:

(2)

(3)

(4)

In Eqs. (2)~(4), A, B are the cross-sectional area and horizontal length of the TLCD, respectively.mh, cTLD and kTLD are the mass, damper and stiffness of TLD obtained by lumped mass method[4].ceq is the equivalent linear damping factors of TLCD which can be obtained by Xu’s method[5]. Numerical simulation uses the model of state equations which can be operated by state equations tool box of MATLAB.

3. Simulation for tuning characteristics of THMD

A series of structural parameters are given as follows: mS=1.500×106kg, kS=9.375×106 N/m (ω0=2.500 rad/s), cS=1.50×105N·s/m. Simulation of external force is f(t)= 5×105·e-jωt N, while the perturbation coefficients of structural frequency are Rω=[0.90, 1.00, 1.10]. The ratio of THMD mass to structure mass is assumed to be μ= 0.02, then the total mass of the THMD is m1+m2+m3=30000 kg, in which the solidmass is m1=10000 kg yields the liquid mass mL=20000 kg. In addition, water mass in the TLD is assumed to be 1/4 of that in the TLCD by considering the practicable usage. Thus, in this example, we havem2=16000 kg and m3=4000 kg. Tabs. 1~3 show the tuning performances of THMD with different container design (L, a, h, where a and h are the length and water height in TLD, respectively).

Table 1 Tuning characteristics of THMD (1)

Perturbation coefficient of structural frequency:
Rω=1.00 (no perturbation)
L
/m / a
/m / h
/m / Sloshing
phasic
difference
Ф / Peak
responses
D
/cm / A
/m·s-2
THMD
controls / 2 / 1 / 0.80 / 171º / 4.64 / 0.30
1.2 / 0.67 / 171º / 4.59 / 0.29
3 / 1.5 / 0.53 / 152º / 6.35 / 0.47
2 / 0.4 / 151.7º / 6.33 / 0.46
3.83 / 1.5 / 0.53 / 90º / 12.04 / 0.79
2 / 0.40 / 89.5º / 11.99 / 0.78
4 / 1.5 / 0.53 / 24º / 11.74 / 0.70
2 / 0.40 / 23.8º / 11.69 / 0.68
6 / 3 / 0.27 / 9º / 10.10 / 0.58
4 / 0.20 / 9º / 9.99 / 0.57
8 / 4 / 0.20 / 8º / 9.19 / 0.53
5 / 0.16 / 7.9º / 8.99 / 0.49
10 / 4 / 0.20 / 7º / 7.94 / 0.47
5 / 0.16 / 6.8º / 7.81 / 0.46
12 / 4 / 0.20 / 6º / 6.81 / 0.43
5 / 0.16 / 5.9º / 6.76 / 0.40
14 / 4 / 0.20 / 5º / 6.39 / 0.36
5 / 0.16 / 5º / 6.37 / 0.34
16 / 4 / 0.20 / 4º / 5.88 / 0.33
5 / 0.16 / 4º / 5.86 / 0.32
18 / 4 / 0.20 / 3º / 5.84 / 0.32
5 / 0.16 / 3º / 5.84 / 0.31
TMD
controls / 4.39 / 0.26
non
control / 13.34 / 0.83

Table2Tuning characteristics of THMD (2)

Perturbation coefficient of structural frequency:
Rω=0.90
L
/m / a
/m / h
/m / Sloshing
phasic
difference
Ф / Peak
responses
D
/cm / A
/m·s-2
THMD
controls / 2 / 1 / 0.80 / 171º / 8.76 / 0.39
1.2 / 0.67 / 171º / 8.74 / 0.39
3 / 1.5 / 0.53 / 152º / 7.39 / 0.36
2 / 0.4 / 151.7º / 7.39 / 0.36
3.83 / 1.5 / 0.53 / 90º / 10.48 / 0.53
2 / 0.40 / 89.5º / 10.46 / 0.52
4 / 1.5 / 0.53 / 24º / 11.69 / 0.57
2 / 0.40 / 23.8º / 11.68 / 0.56
6 / 3 / 0.27 / 9º / 12.86 / 0.63
4 / 0.20 / 9º / 12.85 / 0.62
8 / 4 / 0.20 / 8º / 12.48 / 0.62
5 / 0.16 / 7.9º / 12.45 / 0.61
10 / 4 / 0.20 / 7º / 11.74 / 0.59
5 / 0.16 / 6.8º / 11.73 / 0.58
12 / 4 / 0.20 / 6º / 11.38 / 0.56
5 / 0.16 / 5.9º / 11.37 / 0.55
14 / 4 / 0.20 / 5º / 10.99 / 0.55
5 / 0.16 / 5º / 10.98 / 0.54
16 / 4 / 0.20 / 4º / 10.60 / 0.53
5 / 0.16 / 4º / 10.59 / 0.52
18 / 4 / 0.20 / 3º / 10.38 / 0.51
5 / 0.16 / 3º / 10.38 / 0.50
TMD
controls / 8.98 / 0.42
non
control / 14.82 / 0.75

Table3 Tuning characteristics of THMD (3)

Perturbation coefficient of structural frequency:
Rω=1.10
L
/m / a
/m / h
/m / Sloshing
phasic
difference
Ф / Peak
responses
D
/cm / A
/m·s-2
THMD
controls / 2 / 1 / 0.80 / 171º / 6.31 / 0.50
1.2 / 0.67 / 171º / 6.29 / 0.49
3 / 1.5 / 0.53 / 152º / 8.28 / 0.66
2 / 0.4 / 151.7º / 8.27 / 0.65
3.83 / 1.5 / 0.53 / 90º / 10.82 / 0.83
2 / 0.40 / 89.5º / 10.82 / 0.82
4 / 1.5 / 0.53 / 24º / 8.71 / 0.65
2 / 0.40 / 23.8º / 8.70 / 0.64
6 / 3 / 0.27 / 9º / 6.20 / 0.44
4 / 0.20 / 9º / 6.19 / 0.43
8 / 4 / 0.20 / 8º / 5.18 / 0.37
5 / 0.16 / 7.9º / 5.17 / 0.36
10 / 4 / 0.20 / 7º / 4.96 / 0.36
5 / 0.16 / 6.8º / 4.95 / 0.35
12 / 4 / 0.20 / 6º / 4.69 / 0.34
5 / 0.16 / 5.9º / 4.68 / 0.33
14 / 4 / 0.20 / 5º / 4.95 / 0.36
5 / 0.16 / 5º / 4.94 / 0.35
16 / 4 / 0.20 / 4º / 5.30 / 0.36
5 / 0.16 / 4º / 5.29 / 0.36
18 / 4 / 0.20 / 3º / 5.47 / 0.37
5 / 0.16 / 3º / 5.46 / 0.37
TMD
controls / 5.70 / 0.46
non
control / 12.12 / 0.92

Table1 shows the case of structure being in steady state (Rω=1.00), when the phasic difference between sloshing liquid and the whole damper system Ф=90º, the peak values of responses of the structure are the largest and the values are close to those in uncontrolled case; the impact force of liquid completely restrain the system which yields the poorest performance of the damper system at this moment. As Фdeviates 90º, the responses reduce gradually, especially when Фapproaches 0º, the responses are lowest and it is close to that controlled by TMD; the sloshing force of liquid column affects the system so slightly which yields the best performance of THMD at this moment. On the other hand, as Фapproaches 180º, the total liquid column length will be less then 1 m, which is not reasonable in practical usage, thus this case is not discussed in this paper.

It can be observed from Table 2 that the tuning effectiveness of TMD goes worse when the structural frequency reduces; meanwhile, the poorest performance of THMD happens in the interval of 0ºФ<90º. As Фapproaching 0º, the performance of THMD approaches that of TMD whereas better tuning performances of THMD compared with TMD can be obtained as Фgoing towards 180º. It can also be observed that the settings of THMD with Ф>151º will make the tuning performance of THMD better than that of TMD. Better performances can be obtained in the interval of 90ºФ<180º when the structural frequency reduces, which means that the sloshing effect performs an ‘anti-shock’ function towards the system in this interval. The sloshing effect depress the tuning frequency of THMD and makes it be close to or even equate to the perturbed structural frequency, therefore, the ‘mistuned’ of TMD is made up.

It can be observed from Table 3 that the tuning effectiveness of TMD goes worse when the structural frequency increases similar to the case of the structural frequency reducing, and the poorest performance of THMD happens in the interval of 90ºФ<180º. As Фgoing towards 0º, the performance of THMD approaches that of TMD whereas better performances of THMD compared with TMD can be obtained as Фgoing towards 0º. It can also be observed that the settings of THMD with Ф<8º will make the performance of THMD better than that of TMD. Better tuning performances can be obtained in the interval of 0ºФ<90º when the structural frequency increases, which means that the sloshing effect of liquid column performs an ‘add-shock’ function towards the system in this interval.

In addition, the TLD in the backside space of the TLCD can fine tune the THMD system. When the frequency of TLCD is close to ω0 (lower a and greater h are in this case), THMD shows a worse control performance; oppositely, when The frequency of TLCD is away from ω0 (greater a and lower h are in this case), THMD shows a better control performance. It is believed that as the mass ratio of the TLD rises, the influence of the TLD will be more significant.

4. Conclusion

The tuning characteristics of THMD under different sloshing effect of liquid and perturbation coefficient of structural frequency are studied by the phasic difference method. When the structure is in steady state, the sloshing effect of liquid will make the tuning performance of THMD worse than that of TMD; when the structural frequency perturbs and becomes lower, the performance of THMD can be better than that of TMD with some specific settings in theinterval 90ºФ<180º, and the optimized designintervalФ>151º is obtained in this paper; when the structural frequency becomes larger, the performance of THMD can be better than that of TMD with some specific settings in the interval 0ºФ<90º, and the optimized designintervalФ<8º is also obtained. Moreover, the TLD in the can fine tune the THMD system, but is still restricted by the dimension of the backside space of the U-shaped tank.

References

[1] D. Y. Huang, F. L. Zhou, P. Tan, “Tuned Hybrid-tank/Mass Damper and its Engineering Setting Method”, Journal of PLA Universityof Science and Technology, 2009(2), pp. 187-190.

[2] G. J. Yan, G. P. Yan, Y. X. Hao, “Analytical Methodology and Seismic Application of TLCMD System”, Journal of Northern JiaotongUniversity, 2004(1), pp. 23-27.

[3] D. Y. Huang, P. Tan, N. X. Dai, et al, “Dynamic Analysis on TLCMD”, Science Technology and Engineering, 2008(3), pp. 694-699.

[4] G. W. Housner, “Dynamic Pressure on Accelerated Fluid Containers”, Bulletin of the Seismological Of America, 1957(1), pp. 15-35.

[5] Y. L. Xu, B. Samali, K. C. S. Kwok, “Control of Along-Wind Response of Structure by Mass and Liquid Dampers”, ASCE Journal of Engineering Mechanics, 1992(1), pp. 20-39.