structural control using tuned liquid column dampers

Bauhaus Summer School in Forecast Engineering: From Past Design to Future Decisions

5 – 16 August 2019, Weimar, Germany

Structural control using tuned liquid column dampers: An experimental study

RIMAL, Prashant, ZAFAR, Usama, AZAM, Sakia, REFAIE, Abdelrahman, IBANEZ, Stalin, MIRBOLAND, Mahsa

Faculty of Civil Engineering, Bauhaus University Weimar, Germany

STARC, Jure

Faculty of Civil Engineering, University in Ljubljana, Slovenia

Abstract

This paper summarizes the results of a student project conducted within the scope of the “Bauhaus Summer School 2019” at Weimar, Germany. Climate change and manmade disasters increasingly cause adverse variations in loading civil infrastructures have not been designed for. Control systems mounted on civil infrastructure provide additional capacities that help resist loads by controlling structural responses. Passive control systems, the most basic type, are add ons integrated into civil infrastructure providing counter actions against dynamic loads. The design of passive control systems is easily done and external power sources are not needed. However, one disadvantage of passive control systems is the inability to work under unknown load conditions, producing negative effects on structures. To overcome the disadvantages of passive control systems, semi-active control systems, such as semi-active tuned liquid column dampers (STLCD), have been proposed. STLCD may be distinguished according to the valve used for controlling the liquid flow, e.g. vertical valves or rotational valves, where, in the case of rotational valves, further studies are needed to investigate the effects of the opening angle to the behavior of STLCDs. In this paper, an experimental study is conducted for evaluating the optimal valve opening of a STLCD mounted on a shear-frame structure and exposed to different excitations. Specifically, a shear-frame structure, instrumented with a tuned liquid column damper system and a rotational valve, is subject to different valve openings, and the structural response is compared in time-domain and frequency-domain for the different use cases. The results of this study may serve as a basis for mathematically describing relations between the opening valve angle and the structural control performance of STLCD systems.

1 Introduction

Civil structures are designed for resisting different loading scenarios. When excited by dynamic loads, e.g. wind and earthquakes, structures may experience resonance events, which occur when the excitation frequency matches one natural frequency of the structure. Resonance may lead to severe damage in structures, thus, it should be carefully considered in structural response studies. To avoid resonance, structural control (SC) systems are key elements for minimizing structural vibrations and for mitigating damage risks.

Structural control systems aim to dissipate energy and to reduce structural vibrations using control devices, which can alter dynamic properties of structures by adding control forces. Various control device types exist, some of which require external power sources for generating control forces. SC systems are categorized into passive, semi-active, active, and hybrid systems, as elucidated in the follow paragraphs.

Passive SC systems, comprising base isolations, vibration absorbers, and fluid or solid dampers, and do not require an external power source nor a control algorithm. The control device in a passive system is tuned to a specific natural frequency of the structure and generates a constant static control

RIMAL, Prashant, et al. / FE 2019

force. Active SC systems use control algorithms to induce varying control forces in accordance with excitation scenarios. Therefore, in active systems control devices equipped with power units and sensor networks can alter the performance of the structure. Control algorithms may only depend on structural responses (feedback or response-based), use loading scenarios and intensities (feedforward or excitation-based), or joint both procedures (feedback-feedforward) for finding optimal performance-related dynamic parameters of SC systems. Active brace and mass systems, as well as pulse generation systems must function continuously and therefore, require a fail-safe design and large power sources, hence resulting in expensive systems. To overcome deployment challenges of active systems and limited capacity of passive systems, semi-active SC systems are developed by combining passive and active systems. In semi-active systems, small power sources are required for actuators, which alter the passive device performance and provide active-alike behavior, thus, in case of power loss, semi-active systems continue to function as sole passive systems. Last but not least, hybrid SC systems are the combination of a passive and an active system. The fundamental mode shape and higher mode shapes are controlled through high capacity passive and small active systems, respectively, making hybrid systems more cost effective than sole active systems.

Tune liquid column dampers (TLCD) are basic but efficient passive systems, which comprise various columns of viscous liquid. Openings (orifice) in the horizontal sections, between columns, let the viscous liquid flow freely, thus through head loss and splashing, the liquid absorbs energy and the damping effect is produced. There are various orifice valve alternatives that can be designed for controlling the liquid flow, i.e. for controlling the contribution of TLCD system in the damping process. TLCD systems can be configured for acting passively, semi–actively, and actively. Passive systems comprise pre-define orifice sizes corresponding to the tuning frequencies and excitations applied to the structure. The semi active system is an upgrade to passive systems, allowing dynamic control over the liquid flow using actuators.

In recent decades, the optimal TLCD performance have been studied by several authors. Yalla and Kareem (1995) have shown the relationship between frequency response functions extracted from time-history records and damping ratios in TLCDs with different opening valve angles and excitation scenarios. The authors have also noted the optimal damping ratio of 9% for the opening valve angle of 40 degrees. Karimi et al. (2018) have tested passive TLCD systems for finding the optimal column angle and have reported best damping performance with 90 degree columns using a fully opened valve. However, the authors have also mentioned that test findings may not apply for different excitation scenarios and more tests are to be conducted for recognizing optimal angles.

In this student project, a set of laboratory tests are conducted on a semi-active TLCD system to find the optimal opening valve angles for different excitation scenarios and to study the effect of different opening valve angles on the damping of a test structure. Acceleration sensors are applied to a 4-story laboratory frame structure and a set of experiments have been conducted to comparatively study the behavior of the semi-active TLCD system. The goal is to extract optimal opening valve angles for different excitation scenarios, exciting higher natural frequencies. In the following, theoretical background information on TLCD systems is provided, followed by descriptions of the experimental setup and the test procedure. Then, the results are compared and discussed. The paper concludes with a summary and conclusion on experimental observations.

2 Theoretical background

2.1 TLCD systems

TLCD systems comprise a U-shaped tank filled with a viscous liquid, which can dissipate energy via hydrodynamic head losses (Linsheng et al. 2013). According to the nonlinear Bernoulli equation (Altay et al. 2014), the dynamic properties of viscous liquid in TLCD systems are described as follows:

| | . (1)


Where is the liquid stream in TLCD columns, is the absolute acceleration of the structure under both dynamic forces and base excitation, and denotes pressure loss as a result of turbulence and friction effects. Finally, is a geometric factor determined by the geometry of the damper that scales the interaction force between the damper and the structure. The equation of motion of a single-degree-of-freedom (SDOF) structure equipped with a TLCD system can be described as:

(2)

Where is the damping force created by the motion of the viscous liquid. Parameters and are the total damping ratio (inherent to the structure plus the added damping from the

damper) and the fundamental angular frequency of the structure, respectively. is the mass ratio of the viscous liquid mass over the modal mass of the structure at the fundamental mode shape, is the ground acceleration, is the excitation force, and is the second geometric factor of TLCD.

The mathematical description of coupled TLCD and structure system is given by:

ẌẌ

+ 0

0 ẊẊ

+ 0

0

=

0

(3)

2.2 Embedded computing

The embedded algorithm used in this study extracts frequency spectrums from acceleration time-history data, which is collected using wireless sensor nodes. For extracting frequency spectrums and amplitudes of mode shapes, fast Fourier transformation (FFT) and peak picking (PP) algorithms are used. Detailed mathematical background regarding FFT and PP algorithms can be found in Dragos et al. Furthermore, the interested reader is referred to the publications listed in the reference section.

2.2.1 Fast Fourier transformation

The discrete Fourier transformation (DFT) is used to analyze time domain signals and extract dynamic properties of mode shapes corresponding to frequency domain, schematized in Figure 1. The expression in Equation 4 represents the DFT with Fk being the complex k-th point of the DFT of an N-point time series f at frequency ω. Time series f represents the acceleration response discretized at time step N.

∙ ∈ 0, ; ∈ ; (4)

2.2.2 Peak picking

Peaks in the frequency spectrum correspond to natural frequencies of the structure. Peak picking algorithm assists in finding and highlighting the value of peak frequencies in frequency spectrum.

. Figure 1: Frequency spectrum calculation using Fourier transform


3 Experimental analysis

3.1 Experimental setup

For conducting the experiments, a laboratory frame structure is utilized. The laboratory frame is composed of 4 stories of 200 mm × 300 mm × 15 mm (width × length × thickness) steel plates, connected to four aluminum columns with a cross section of 20 mm × 2 mm (width × thickness) with a total height of 1200 mm (300 mm per floor). The structure is mounted on a wooden block and fixed with a steel plate at the bottom.

Two systems are installed for measuring and modifying the dynamic properties of the laboratory frame. The first is the structural health monitoring (SHM) system, composed of two sensor nodes and two accelerometers each sensor node. The sensor node is built with Raspberry Pi board (Figure 2, left), in which a button, two 3.5 mm jack inputs, and a led has been integrated, as shown in Figure 2 (right). The accelerometers are connected to the sensor nodes using the 3.5 mm jack inputs. In addition, the sensor nodes are connected to power banks for allowing decentralized processing.

Figure 2: Raspberry Pi board (left) and sensor node (right)

The second system, a tuned liquid column damper (TLCD), is the control system. The TLCD is provided with a valve for controlling the liquid flow, and the valve opening is controlled by a stepper motor (Figure 3). The opening angle of the valve is defined in a Raspberry P connected to the stepper motor.

Figure 3: Structural control system

Accelerometers are placed at each floor for measuring acceleration data in one direction. The sensor nodes are wirelessly connected with the server for transferring data. The sensor nodes performs embedded processing before sending the acceleration data to the server. The embedded processing consist in a baseline correction of the data and a frequency analysis of the data, for obtaining the natural frequencies of the structure. The test setup, including the laboratory frame, the SHM system, and the control system is presented in Figure 4.


Figure 4: Test setup

3.2 Test procedure

The main objective of the work is to find experimentally the best opening angle of the valve under various excitation scenarios. Therefore, three set of experiments are developed based on the excitation floor as described in Table XX, e.g. the first set of experiments consist is applying a displacement of 4 cm to the top floor and then measuring the structural response using various opening valve angles, from 0 (fully-opened) to 90°(fully-closed). The experimental procedure is as follows:

- First, initial input parameters are defined in the server, which in this case is the laptop used for the experiments. The input parameters defined are the sampling frequency, the number of nodes to be used, and the direction of measurements

- After defining the parameters, the software in the server is run simultaneously with the software in the nodes

- Next, the nodes start recording data, and then, an initial displacement is applied to the structure in the defined floor depending on the experimental set

- Finally, data is collected and sent it back to the server for further processing

The further processing consists in comparing the response of the structure under different opening angles by looking into the time history. Moreover, the data is also evaluated in the frequency-domain for assessing the modal contribution of the responses.

Table 1: Experimental catalogue

Set of experiments Excitation scenario Valve opening angle

T1 4th Floor

0°, 18°, 36°, 45°, 54°, 90° T2 3rd Floor

T3 1st Floor


4 Results and discussion

4.1 Experimental results

The results from the experiments are summarized in Figure 5, 6, and 7 showing the time-history and the frequency domain results. For conciseness matters, the results show a summary of the experiments, focusing on the extreme cases of fully opened, fully closed, and the optimal angle for the set of experiment.

In the set of experiments 1, in which the top floor has been excited, the time-history results are shown in Figure 5 (top). From the time-history of T1, it is noticeable that the fully opened case (0°) is not showing the best damping, being outdone by the 18° opening and 45° opening. Nevertheless, the fully-opened case is better than the fully closed case, as expected. When looking into the frequency responses in Figure 5 (bottom), the fully-closed case shows that the first frequency has been mainly excited, but also a considerable contribution of the second and the third frequency is obtained. In the case of the fully-opened valve, the third frequency is amplified, while with the 18° opening the third frequency contribution is reduced. As a summary, in the first set of experiments the optimal angle in 18°.

For the second set of experiments, the frequency domain results for the fully-closed valve show that the frequency most excited is the third one (Figure 6 bottom). The major contribution of the third frequency shows that the structure is mainly excited in the third mode due to the excitation on the 3rd floor. The time-domain results, shown in Figure 6 (top), demonstrate that the optimal opening is 36°, damping the movement faster than the fully-opened case. In terms of frequency response, the 36° opening damped all the frequencies while the fully opened case damped only the first frequency.

In the last set of experiments, in which the 1st floor has been excited, the frequency domain result of the fully-closed case (Figure 7 bottom) show that the frequency most excited is the third one. The 45° opening shows the best damping of the structure, reducing all the frequency contribution, while the fully-opened case amplifies considerably the third frequency. The results in time-domain in Figure 7 (top) agree with the frequency domain, showing faster damping of the structure using an opening angle of 45° while the fully-opened case amplifies the acceleration of the structure.

Figure 5 Time history (top) and frequency response (bottom) experiment set T1

-0,5

-0,3

-0,1

0,1

0,3

6 7 8 9 10 11 12 13 14 15

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)

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0

5

10

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0 1 2 3 4 5 6 7 8 9

Am

plitu

de

Frequency (Hz)

90°45°18°0°


Figure 6: Time history (top) and frequency response (bottom) experiment set T2

Figure 7: Time history (top) and frequency response (bottom) experiment set T3

-0,5

-0,3

-0,1

0,1

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0,5 2,5 4,5 6,5 8,5 10,5 12,5 14,5

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0 1 2 3 4 5 6 7 8 9 10

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4.2 Numerical analysis

In addition to the laboratory tests, the shear-frame structure is modeled using a finite element software for extracting the frequencies. The numerical model includes an additional mass for representing the TLCD using a closed valve, i.e. not adding additional damping to the structure.

Figure 8: Numerical model of the test structure with the corresponding 1st, 2nd, and 3rd mode shapes

The numerical modeling assumptions include full-fixed column-to-plate joints and rigid behavior of plates. In addition, the connections at the base level of the columns are considered clamped. The modulus of elasticity of aluminum is assumed equal to 69 GPa and the mass density is equal to 2.66 t/m3. For implementing the mass of the TLCD, a point mass is added to the top floor with a corresponding eccentricity.

As a result, the modal analysis yields the eigenfrequencies and mode shapes shown in Figure 8. The results of the eigenfrequencies obtained numerically are 1.16 Hz, 3.48 Hz, 5.74 Hz, while experimentally, for the experimental set 1 and fully closed valve, are 1.12 Hz, 3.61 Hz, 5.91 Hz. The results of the model and the experiments show good correlation.

5 Summary and conclusions

In this student project, a structural health monitoring system has been developed for evaluating the structural response under various valve openings of a tuned liquid column damper mounted on the roof of a shear-frame structure. Several tests have been conducted, measuring time and frequency responses of the structure, for determining the optimal valve opening under different excitation scenarios. Moreover, a numerical model of the structure considering the TLCD has been developed for comparing frequency results.

The results of the numerical model show good agreement with the experimental frequencies extracted from the data, i.e. the numerical model is represents the structure with the TLCD on its roof, however limited to the fully-closed valve. From the results of the frequency response, it can be seen that, depending on the excitation applied to the structure, different frequencies are excited. Moreover, due to the different excitation frequencies, the valve performs poorly under different excitations that do not match the natural frequency of the structure. From the experiments, it is noticeable that when the first floor of the structure is excited, an opening of 45° would be the best option, if the third floor is excited, an opening of 36° performs better, and if the top floor is excited, an opining of 18° provides the best results, i.e. the optimum opening valve angle depends on the excitation applied to the structure.


The performance of the TLCD may be enhanced by developing a control algorithm to automatically (i.e., in real time) adjust the valve opening between 15° to 50°, according the structural response. Future research may as well focus on various viscous liquids for experimentally testing the damping effects.

Acknowledgements

The authors wish to acknowledge the organizers and instructors Bauhaus Summer School, 2019 (“Forecast Engineering – from past designs to future decisions”) for organizing the course. The authors would like to express their gratitude for the continuous support and invaluable feedback offered by Professor Smarsly, Ms. Mirboland, and Mr. Ibáñez.

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structural control using tuned liquid column dampers

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