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Optimal Seismic Response Control of Adjacent Buildings Coupled with a Double Mass Tuned Damper Inerter

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Optimization of Tuned Mass Dampers

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 432))

Abstract

Adjacent buildings are exposed to a high risk of pounding against each other during seismic events. In recent strong earthquakes events, the separation gap has been found to be insufficient to prevent structural damage related to pounding phenomena. The inerter-based tuned mass damper has been validated as an effective, lightweight passive control device by incorporating the inerter into a conventional tuned mass damper (TMD). The proposed system's optimal design is achieved using a constrained optimization problem based on the Grey Wolf Optimizer (GWO) algorithm. This numerical study investigates the capability of reducing the pounding risk of inertially connected tuned mass dampers (TMDs). The presented system connects two high-rise adjacent buildings as a novel seismic protection system. The optimal design of the proposed system is conducted through a constrained optimization problem via a Grey Wolf Optimizer (GWO) algorithm, wherein the pounding gap distance of the two high-rise adjacent buildings is selected as performance index. Optimal results obtained are critically analyzed and compared. For comparison purposes, two separate TMDs are mounted on the rooftop of each of the adjacent buildings, and the two systems are optimized independently under the constraint of the same total mass. Performance of these independent TMDs is evaluated to compared to that of inertially connected ones using a large number of ground motions selected from a set of 462 ground motion records. The main response parameters of interest are the minimum seismic gap for pounding mitigation, along with inter-storey drift. When the two buildings have different natural frequencies, the results reveal that the suggested new device outperforms the non-connected TMDs system.

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Author information

Authors and Affiliations

  1. LARGHYDE Laboratory, Department of Civil Engineering and Hydraulics, Faculty of Sciences and Technology, Mohamed Khider University, BP 145 RP, 07000, Biskra, Algeria

    Salah Djerouni & Mahdi Abdeddaim

  2. Earthquake Engineering Research Centre, Faculty of Civil and Environmental Engineering, School of Engineering and Natural Sciences, University of Iceland, Austurvegur 2a, 800, Selfoss, Iceland

    Salah Djerouni, Said Elias & Rajesh Rupakhety

  3. Department of Construction Management and Engineering (CME), Faculty of Engineering Technology (ET), University of Twente (UTWENTE), Enschede, Netherlands

    Said Elias

  4. Department of Engineering, University of Messina, Messina, Italy

    Dario De Domenico

Authors
  1. Salah Djerouni
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  2. Mahdi Abdeddaim
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  3. Said Elias
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  4. Dario De Domenico
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  5. Rajesh Rupakhety
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Corresponding author

Correspondence to Said Elias .

Editor information

Editors and Affiliations

  1. Department of Civil Engineering, Istanbul University-Cerrahpaşa, Avcılar, Istanbul, Turkey

    Gebrail Bekdaş

  2. Department of Civil Engineering, Istanbul University-Cerrahpaşa, Avcılar, Istanbul, Turkey

    Sinan Melih Nigdeli

Appendix

Appendix

The mass matrix, stiffness and damping matrices for the two buildings (Fig. 9)

$$\left[{M}_{L}\right]=\left[{M}_{R}\right]=\left[\begin{array}{ccccccccc}90.718& & & & & & & & \\ & 90.718& & & & & & & \\ & & 90.718& & & & & & \\ & & & 90.718& & & & & \\ & & & & 90.718& & & & \\ & & & & & 90.718& & & \\ & & & & & & 90.718& & \\ & & & & & & & 90.718& \\ & & & & & & & & 90.718\end{array}\right]tons$$
(A.1)
$$\left[{K}_{L}\right]=\left[\begin{array}{ccccccccc}6714.53& -4753.16& 1194.81& -235.21& 39.01& -6.64& 1.02& -0.14& 0.01\\ -4753.16& 7156.12& -4666.16& 1349.70& -223.85& 38.10& -5.87& 0.78& -0.07\\ 1194.81& -4666.16& 7139.68& -4523.12& 1176.88& -200.34& 30.84& -4.12& 0.36\\ -235.21& 1349.70& -4523.12& 6480.87& -3998.04& 1036.57& -159.55& 21.32& -1.84\\ 39.01& -223.85& 1176.88& -3998.04& 5702.41& -3402.84& 810.21& -108.26& 9.35\\ -6.64& 38.10& -200.34& 1036.57& -3402.84& 4640.55& -2598.39& 538.66& -46.50\\ 1.02& -5.87& 30.84& -159.55& 810.21& -2598.39& 3322.87& -1624.16& 223.16\\ -0.14& 0.78& -4.12& 21.32& -108.26& 538.66& -1624.16& 1764.20& -588.30\\ 0.01& -0.07& 0.36& -1.84& 9.35& -46.50& 223.16& -588.30& 403.84\end{array}\right]\times {10}^{2}KN/m$$
(A.2)
$$\left[{K}_{R}\right]=\left[\begin{array}{ccccccccc}2522.11& -1793.13& 455.38& -90.54& 15.19& -2.62& 0.41& -0.06& 0.00\\ -1793.13& 2716.65& -1785.22& 521.17& -87.45& 15.07& -2.35& 0.32& -0.03\\ 455.38& -1785.22& 2747.85& -1754.81& 462.03& -79.63& 12.41& -1.68& 0.15\\ -90.54& 521.17& -1754.81& 2533.61& -1578.28& 414.21& -64.57& 8.74& -0.76\\ 15.19& -87.45& 462.03& -1578.28& 2268.72& -1367.35& 329.75& -44.61& 3.89\\ -2.62& 15.07& -79.63& 414.21& -1367.35& 1879.57& -1063.32& 223.22& -19.48\\ 0.41& -2.35& 12.41& -64.57& 329.75& -1063.32& 1369.88& -676.12& 93.97\\ -0.06& 0.32& -1.68& 8.74& -44.61& 223.22& -676.12& 738.54& -248.35\\ 0.00& -0.03& 0.15& -0.76& 3.89& -19.48& 93.97& -248.35& 170.61\end{array}\right]\times {10}^{2}KN/m$$
(A.3)
$$\left[{C}_{R}\right]=\left[\begin{array}{ccccccccc}168.82& -116.55& 29.30& -5.77& 0.96& -0.16& 0.03& 0.00& 0.00\\ -116.55& 179.65& -114.41& 33.09& -5.49& 0.93& -0.14& 0.02& 0.00\\ 29.30& -114.41& 179.25& -110.91& 28.86& -4.91& 0.76& -0.10& 0.01\\ -5.77& 33.09& -110.91& 163.09& -98.03& 25.42& -3.91& 0.52& -0.05\\ 0.96& -5.49& 28.86& -98.03& 144.01& -83.44& 19.87& -2.65& 0.23\\ -0.16& 0.93& -4.91& 25.42& -83.44& 117.97& -63.71& 13.21& -1.14\\ 0.03& -0.14& 0.76& -3.91& 19.87& -63.71& 85.66& -39.82& 5.47\\ 0.00& 0.02& -0.10& 0.52& -2.65& 13.21& -39.82& 47.44& -14.43\\ 0.00& 0.00& 0.01& -0.05& 0.23& -1.14& 5.47& -14.43& 14.09\end{array}\right]\times {10}^{1}KN.s/m$$
(A.4)
$$\left[{C}_{L}\right]=\left[\begin{array}{ccccccccc}66.03& -43.97& 11.17& -2.22& 0.37& -0.06& 0.01& 0.00& 0.00\\ -43.97& 70.80& -43.77& 12.78& -2.14& 0.37& -0.06& 0.01& 0.00\\ 11.17& -43.77& 71.56& -43.03& 11.33& -1.95& 0.30& -0.04& 0.00\\ -2.22& 12.78& -43.03& 66.31& -38.70& 10.16& -1.58& 0.21& -0.02\\ 0.37& -2.14& 11.33& -38.70& 59.81& -33.53& 8.09& -1.09& 0.10\\ -0.06& 0.37& -1.95& 10.16& -33.53& 50.27& -26.07& 5.47& -0.48\\ 0.01& -0.06& 0.30& -1.58& 8.09& -26.07& 37.77& -16.58& 2.30\\ 0.00& 0.01& -0.04& 0.21& -1.09& 5.47& -16.58& 22.29& -6.09\\ 0.00& 0.00& 0.00& -0.02& 0.10& -0.48& 2.30& -6.09& 8.37\end{array}\right]\times {10}^{1}KN.s/m$$
(A.5)
Fig. 9
figure 9

The complete flowchart of the grey wolf optimizer (GWO) algorithm

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Djerouni, S., Abdeddaim, M., Elias, S., De Domenico, D., Rupakhety, R. (2022). Optimal Seismic Response Control of Adjacent Buildings Coupled with a Double Mass Tuned Damper Inerter. In: Bekdaş, G., Nigdeli, S.M. (eds) Optimization of Tuned Mass Dampers. Studies in Systems, Decision and Control, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-030-98343-7_6

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