Liquid dampers such as tuned liquid column dampers and tuned liquid dampers have been adopted to ensure serviceability of a vibratory building subjected to wind. In order to maximize efficiency of the vibration suppression, tuning frequency of the liquid dampers is supposed to be set to the first natural frequency of the building. Therefore, experimental evaluation of the natural frequency of liquid dampers is a primal factory task prior to their installation at the building. In this study, a novel liquid height measurement system based on variable resistance in an electric field is developed for observation of vertical motion of the liquid dampers. The proposed system can simultaneously measure the liquid height of multipoint locations in the electric field. In the experimental phase, natural frequency of the liquid dampers is experimentally evaluated utilizing the developed system. The performance of the proposed system is verified by comparison with the capacitive type wavemeter.
Vibration mitigation of buildings has been emphasized to meet serviceability requirements for residents at high-rise buildings sensitive to wind and earthquakes loads [
The design task of the U-shaped TLCD is to identify its natural frequency and then to tune it to the fundamental natural frequency of a building structure. The natural frequency of the TLCD depends on liquid portion in horizontal column which participates in the tuned reciprocating motion [
To date, capacitive wavemeters have been dominantly used for liquid height measurements. However, a number of intrinsic disadvantages have been constantly addressed: laborious installation, a loss of accuracy due to interference from the liquid medium, for example, parasitic capacitance, and difficulty of measurements at closely adjacent points. While great advances have been made in numerical and analytical studies of dynamic behaviors of the TLCD [
In this study, a novel, high precision, and cost-effective variable voltage sensing system is developed for dynamic wave height measurement of the liquid dampers of both the TLD and TLCD to identify natural frequencies and corresponding modes. The variable voltage sensing principle is introduced with basic electric circuit theory. A practical methodology of experimental estimation of dynamic characteristics is presented based on both dynamic equations of natural frequency derived and experimental data measured. Finally, a series of experimental investigations are conducted for the verification of the variable voltage sensing system and for showcasing the methodology of natural frequency of the TLD and TLCD.
A simplified model of the TLCD built on a primary structure is shown in Figure
Modeling of a SDOF structure with a TLCD.
Three assumptions are made to derive the equation of motion: (i) the sloshing behavior on the liquid surface is negligible; (ii) the flow is incompressible; (iii) the dimension of the column cross section is much smaller than the horizontal length of a TLCD. The dynamic equation of the oscillating liquid in the TLCD subjected to lateral excitation of the primary structure is [
A rigid rectangular TLD shown in Figure
Modeling of a SDOF structure with a TLD.
According to the shallow water wave theory [
Sloshing modes of the TLD: (a) the first mode; (b) the second mode.
Properties of the bulk material used for fabrication of transistors and other semiconductor devices can be estimated by measurement of resistance [
Two-point measurement system: (a) two-probe meter; (b) corresponding circuit diagram.
Using Ohm’s law, the total resistance is determined as
Due to the limitations of the two-point method, the four-point measurement system is used for the low resistance measurements in order to reduce the effect of parasitic resistances [
Four-point measurement system: (a) four-probe meter; (b) corresponding circuit diagram.
Based on the results of resistivity measurement, that is, (
Two-point wave height measurement of a TLCD: (a) elements and dimensions; (b) current flow in liquid column.
The resistance is proportional to the conductor length,
Multipoint wave height measurement of a TLD using electric field: (a) voltage sensing by various wave heights; (b) various voltage drops.
A laboratory-scaled prototype of the TLCD was fabricated with 1 cm thick acrylic plates (Figure
Experiment equipment of the proposed sensing of electric field.
Water column in the TLCD was utilized as conductive media to measure the resistance. In order to increase the conductivity of water, electrically ionized water was prepared by dissolving small amount of electrolytes into tap water. Since the specific resistance of the water was adjusted by ranging at least 100 Ω, the resistance value was accurately determined by the two-point method. Two copper tapes were attached on the corners of a vertical liquid column of the TLCD and connected to a DC power supplier (TDP-303A, TOYOTECH) which controlled a constant current of 0.1 mA. A voltmeter shares the line to measure voltage drop between the electrodes. To measure and record the voltage, a DAQ system from National Instrument was interfaced with the ends of lead wires. Mapping of the measured voltage to the wave height needs determination of beta in (
The accuracy of voltage measurements within an electric field based wave height measurement system was cross-checked with that of a conventional wave height meter, that is, capacitive type wave height sensor (CH-601, KENEK). The wave height meter is a contact sensor; the wave probe was immersed in the liquid column of the TLCD and the sensor body was clamped on top of the TLCD as seen in Figure
Dynamic characteristics of the TLCD: (a) measured heights; (b) corresponding Fourier spectra of the heights.
The transfer functions of the liquid height over input displacement of the shake table are estimated and then given in Figure
Transfer function of the TLCD: (a) magnitude; (b) phase.
The 4-point measurement system was deployed to identify the natural frequency and monitor sloshing in the TLD (Figure
Experiment equipment of the proposed method of RTLD.
Dynamic tests of the TLD with various frequencies of the harmonic excitation of the shake table were undertaken to verify advantages of the proposed sensing system. A total of 23 harmonic excitation tests were undertaken changing the frequencies. Since the first and second sloshing modes are estimated as 0.9 and 2.4 Hz, respectively, from (
Transfer function of the TLD.
Sloshing motions are confirmed through investigating spatially sensed data at each natural frequency. The measured time histories of liquid motion at 0.9 Hz excitation are plotted in Figure
The first sloshing mode at 0.9 Hz; (a) measured wave height; (b) wave motion.
The second sloshing mode at 2.4 Hz; (a) measured wave height; (b) wave motion.
The liquid dampers, such as TLCD and TLD, are passive energy-absorbing devices designed to attenuate vibration of a primary structure through liquid oscillation. The liquid dampers achieve their best control performance when targeted at the harmonic motion of a primary structure. In this study, a novel wave measurement system is proposed for measurement of liquid motion in the liquid dampers. The fundamental principle of the system is based on variable voltage measurement in a constant electric field. Depending on the number of the probes submerged in the liquid, two- and four-point measurement systems are investigated: two-point measurement system is developed utilizing its simplicity. On the other hand, four-point measurement system is developed for the low resistance measurements where the two-point method yields nontrivial errors. Furthermore, the proposed systems can simultaneously measure the liquid height of multipoint locations in the electric field.
As for their applications to the liquid dampers, two-point wave height measurement is deployed for dynamic characterization of the TLCD and multipoint measurement is developed for the TLD. In laboratory tests with a prototype of the TLCD, accuracy of the proposed system is confirmed through comparison with a conventional wavemeter and natural frequency is successfully evaluated. In addition, multipoint wave height measurement is performed with laboratory tests with a prototype of the TLD and various sloshing modes of the TLD are observed. As a result, cost-effectiveness and multipoints are demonstrated.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the Basic Research Programs (NRF-2015R1C1A1A01054155, NRF-2015R1D1A1A01060643) of the National Research Foundation (NRF) of Korea funded by Ministry of Education, Science and Technology (MEST).