Skip to main content
SpringerLink
Log in

Optimal Design of Tuned Mass and Negative Stiffness Amplifier Dampers with Inerter by H2 Optimal Control Under Bidirectional Seismic Load

  • Research Article-Civil Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The combination of a negative stiffness damper and an inerter is a novel system that acts as an energy dissipation device for the structures under seismic loading. In the present study, a damped system with a single degree of freedom (SDOF) and supplementary dampers, including negative stiffness and inerter-based damper, was considered to control the response based on H2 optimum control strategies. Five different configurations were investigated as supplementary dampers that included a tuned mass damper inerter (TMDI), clutching inerter damper (CID), and three configurations of negative stiffness amplifier damper inerter (NSADI). Structural responses under stochastic or random excitations were controlled by using the H2 optimal control strategy based on minimizing the root mean square. The random white noise process was modeled as ground acceleration excitations. Optimum parameters were obtained from closed-form of expressions, and the corresponding equations of motion of the SDOF system with supplementary dampers were expressed in a state space form. Closed-forms of expressions were obtained for TMDI, NSADI, and CID from two-stage processes that consisted of firstly using techniques to search for the minimum of the H2 form and secondly using a numerical search technique of curve fitting at a sequence scheme for arriving at the closed-form of expressions. Two different ground motions (horizontal and vertical ground motion excitations) and two sets of ground motions (near-fault and far-field) for input excitations for base-isolated structures were considered. A parametric study was carried out to optimize TMDI, CID and NSADI parameters, including mass ratio, negative stiffness ratio, positive stiffness ratio, natural frequency and damping ratio, according to the maximum reduction of the response maxima. The H2 optimum technique plays a vital role in the response mitigation of base isolated structures under real seismic excitations. In addition, the base-isolated structure with NSADI and CID performs better compared to other supplementary dampers, considering the response reduction. Consequently, the response of both the negative stiffness damper and the tuned mass damper is boosted by adding an inerter mechanism for controlling the response of structures under seismic load.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data availability

The data for producing the presented results will be made available by request.

Abbreviations

SDOF:

Single degree of freedom

TMDI:

Tuned mass damper inerter

CID:

Clutching inerter damper

NSADI:

Negative stiffness amplifier damper inerter

NSD:

Negative stiffness damper

TMD:

Tuned mass damper

NF:

Near-fault

FF:

Far-field

TLCD:

Tuned liquid column dampers

TLSD:

Tuned liquid sloshing dampers

MDOF:

Multiple degree of freedom

RMS:

Root mean square

PSDF:

Power spectral density function

DOF:

Degree of freedom

BITMDI:

Base isolation with TMDI

BINSADI-1:

Base isolation with NSADI-1

BINSADI-2:

Base isolation with NSADI-2

BINSADI-3:

Base isolation with NSADI-3

BICID:

Base isolation with CID

PGA:

Peak ground acceleration

FFT:

Fast Fourier transform

BIS:

Base isolation system without control device

\(\alpha\) :

Negative stiffness ratio

\(\mu^{opt}\) :

Optimum inertance to mass ratio

\(T_{b}\) :

Base period of isolation

\(\alpha_{opt}\) :

Optimum negative stiffness ratio

\(\beta\) :

Positive stiffness ratio

\(\beta_{opt}\) :

Optimum positive stiffness ratio

\(\lambda\) :

Damper position vector

\(\mu\) :

Inertance to mass ratio

\(\mu_{opt}\) :

Optimum inertance to mass ratio

\(\xi\) :

Inherent damping ratio

\(\xi_{d}\) :

Damper damping ratio

\(\xi_{d,opt}\) :

Optimum damper damping ratio

\(\gamma\) :

Damper damping to inherent damping ratio

\(\omega\) :

Forcing natural frequency

\(\omega_{n}\) :

Natural frequency

\(\sigma_{x}^{2}\) :

Controlled mean square response for displacement

\(\sigma_{x,0}^{2} {\text{t}}\) :

Uncontrolled mean square response for displacement

\(\tilde{\sigma }_{x}^{2}\) :

Normalized mean square response for displacement

A :

State matrix

B :

Input excitation vector

B i :

Ith element of vector B

b :

Inertance

c :

Inherent damping of SDOF system

c d :

Damper damping

[c]:

Damping matrix of fixed base structure

f d :

Damper force

\(H\left( \omega \right)\) :

Displacement transfer function

H 2 :

RMS of impulse response of SDFO system

H ∞ :

Maximum frequency domain response

k :

Inherent stiffness of SDOF system

k p :

Positive stiffness of SDOF system

k ns :

Negative stiffness of damper

[k]:

Stiffness matrix of fixed base structure

M :

Primary mass of SDOF system

m t :

Total mass of all floors including base slab

[m]:

Mass matrix of fixed base structure

P :

Matrix containing element < Bi Bj >

q :

Displacement between terminals 4 and 2 of NSADI-3

r :

Influence coefficient vector

R 2 :

Coefficient of determination

S o :

Constant power spectral density

x :

Displacement of SDOF system

\(x\) :

Relative displacement vector for MDOF system

\(x_{b}\) :

Base displacement

\(\ddot{x}_{g}\) :

Ground acceleration

\(V\) :

Covariance matrix

\(Y\) :

Displacement between terminals 2 and 3 of dampers

\(z\) :

State variable vector

\(z_{i}\) :

Ith element of vector z

\(\left\langle \cdot \right\rangle\) :

Expectation operator

References

  1. Lingxin, Z.; Mingyuan, Z.; Yongsheng, C.: Preliminary study on performance-based seismic design of nonstructural components. World Earthq. Eng. 32, 293–302 (2016)

    Google Scholar 

  2. Jangid, R.S.: Performance and optimal design of base-isolated structures with clutching inerter damper. Struct. Control Heal. Monit. (2022). https://doi.org/10.1002/stc.3000

    Article  Google Scholar 

  3. Naeim, F.; Kelly, J.M.: Design of Seismic Isolated Structures, p. 10.1002/9780470172742. Wiley, Hoboken (1999)

    Book  Google Scholar 

  4. Jangid, R.S.: Computational numerical models for seismic response of structures isolated by sliding systems. Struct. Control Heal. Monit. 12, 117–137 (2005). https://doi.org/10.1002/stc.59

    Article  Google Scholar 

  5. Matsagar, V.A.; Jangid, R.S.: Base isolation for seismic retrofitting of structures. Pract. Period. Struct. Des. Constr. 13, 175–185 (2008). https://doi.org/10.1061/(asce)1084-0680(2008)13:4(175)

    Article  Google Scholar 

  6. Makris, N.: Seismic isolation: early history. Earthq. Eng. Struct. Dyn. 48, 269–283 (2019). https://doi.org/10.1002/eqe.3124

    Article  Google Scholar 

  7. Jangid, R.S.; Kelly, J.M.: Base isolation for near-fault motions. Earthq. Eng. Struct. Dyn. 30, 691–707 (2001). https://doi.org/10.1002/eqe.31

    Article  Google Scholar 

  8. Rao, P.B.; Jangid, R.S.: Performance of sliding systems under near-fault motions. Nucl. Eng. Des. 203, 259–272 (2001). https://doi.org/10.1016/s0029-5493(00)00344-7

    Article  Google Scholar 

  9. Jadhav, M.B.; Jangid, R.S.: Response of base-isolated liquid storage tanks to near-fault motions. Struct. Eng. Mech. 23, 615–634 (2006). https://doi.org/10.12989/sem.2006.23.6.615

    Article  Google Scholar 

  10. Providakis, C.P.: Effect of LRB isolators and supplemental viscous dampers on seismic isolated buildings under near-fault excitations. Eng. Struct. 30, 1187–1198 (2008). https://doi.org/10.1016/j.engstruct.2007.07.020

    Article  Google Scholar 

  11. Rong, Q.: Optimum parameters of a five-story building supported by lead-rubber bearings under near-fault ground motions. J. Low Freq. Noise Vib. Act. Control 39, 98–113 (2019). https://doi.org/10.1177/1461348419845829

    Article  Google Scholar 

  12. Lee, J.J.; Kelly, J.M.: The effect of damping in isolation system on the performance of base-isolated system. J. Rubber Res. 22, 77–89 (2019). https://doi.org/10.1007/s42464-019-00012-z

    Article  Google Scholar 

  13. Zelleke, D.H.; Elias, S.; Matsagar, V.A.; Jain, A.K.: Supplemental dampers in base-isolated buildings to mitigate large isolator displacement under earthquake excitations. Bull. N. Z. Soc. Earthq. Eng. 48, 100–117 (2015). https://doi.org/10.5459/bnzsee.48.2.100-117

    Article  Google Scholar 

  14. Hao, H.; Bi, K.; Chen, W.; Pham, T.M.; Li, J.: Towards next generation design of sustainable, durable, multi-hazard resistant, resilient, and smart civil engineering structures. Eng. Struct. 277, 115477 (2023). https://doi.org/10.1016/j.engstruct.2022.115477

    Article  Google Scholar 

  15. Shen, W.; Niyitangamahoro, A.; Feng, Z.; Zhu, H.: Tuned inerter dampers for civil structures subjected to earthquake ground motions: optimum design and seismic performance. Eng. Struct. 198, 109470 (2019). https://doi.org/10.1016/j.engstruct.2019.109470

    Article  Google Scholar 

  16. Yu, C.; Fu, Q.; Zhang, J.; Zhang, N.: The vibration isolation characteristics of torsion bar spring with negative stiffness structure. Mech. Syst. Signal Process. 180, 109378 (2022). https://doi.org/10.1016/j.ymssp.2022.109378

    Article  Google Scholar 

  17. Carrella, A.; Brennan, M.J.; Kovacic, I.; Waters, T.P.: On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vib. 322, 707–717 (2009). https://doi.org/10.1016/j.jsv.2008.11.034

    Article  Google Scholar 

  18. Rivin, E.I.: Passive vibration isolation. Appl. Mech. Rev. 57, B31–B32 (2004). https://doi.org/10.1115/1.1849173

    Article  Google Scholar 

  19. Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314, 371–452 (2008). https://doi.org/10.1016/j.jsv.2008.01.014

    Article  Google Scholar 

  20. Saaed, T.E.; Nikolakopoulos, G.; Jonasson, J.-E.; Hedlund, H.: A state-of-the-art review of structural control systems. J. Vib. Control 21, 919–937 (2013). https://doi.org/10.1177/1077546313478294

    Article  Google Scholar 

  21. Buckle, I.G.; Mayes, R.L.: Seismic isolation: history, application, and performance—a world view. Earthq. Spectra 6, 161–201 (1990). https://doi.org/10.1193/1.1585564

    Article  Google Scholar 

  22. Jangid, R.S.; Datta, T.K.: Seismic behaviour of base-isolated buildings: a State-of-the art review. Proc. Inst. Civ. Eng. Struct. Build. 110, 186–203 (1995). https://doi.org/10.1680/istbu.1995.27599

    Article  Google Scholar 

  23. Connor, J.; Laflamme, S.: Structural Motion Engineering. Springer, London (2014) https://doi.org/10.1007/978-3-319-06281-5

    Book  Google Scholar 

  24. Buckle, I.G.: Passive control of structures for seismic loads. Bull. N. Z. Soc. Earthq. Eng. 33, 209–221 (2000). https://doi.org/10.5459/bnzsee.33.3.209-221

    Article  Google Scholar 

  25. Balaji, P.S.; Karthik SelvaKumar, K.: Applications of nonlinearity in passive vibration control: a review. J. Vib. Eng. Technol. 9, 183–213 (2021). https://doi.org/10.1007/s42417-020-00216-3

    Article  Google Scholar 

  26. Sheikh, H.; Van Engelen, N.C.; Ruparathna, R.: A review of base isolation systems with adaptive characteristics. Structures 38, 1542–1555 (2022). https://doi.org/10.1016/j.istruc.2022.02.067

    Article  Google Scholar 

  27. Housner, G.W.; Bergman, L.A.; Caughey, T.K.; Chassiakos, A.G.; Claus, R.O.; Masri, S.F.; Skelton, R.E.; Soong, T.T.; Spencer, B.F.; Yao, J.T.P.: Structural control: past, present, and future. J. Eng. Mech. 123, 897–971 (1997). https://doi.org/10.1061/(asce)0733-9399(1997)123:9(897)

    Article  Google Scholar 

  28. Huang, X.; Bae, J.: Evaluation of genetic algorithms for optimizing the height-wise viscous damper distribution in regular and irregular buildings. Arab. J. Sci. Eng. 47, 12945–12962 (2022). https://doi.org/10.1007/s13369-022-06646-3

    Article  Google Scholar 

  29. Spencer, B.F.; Nagarajaiah, S.: State of the art of structural control. J. Struct. Eng. 129, 845–856 (2003). https://doi.org/10.1061/(asce)0733-9445(2003)129:7(845)

    Article  Google Scholar 

  30. Cheng, F.Y.; Jiang, H.; Lou, K.: Smart Structures: Innovative Systems for Seismic Response Control. CRC Press (2008). https://doi.org/10.1201/9781420008173

    Book  Google Scholar 

  31. Symans, M.D.; Charney, F.A.; Whittaker, A.S.; Constantinou, M.C.; Kircher, C.A.; Johnson, M.W.; McNamara, R.J.: Energy dissipation systems for seismic applications: current practice and recent developments. J. Struct. Eng. 134, 3–21 (2008). https://doi.org/10.1061/(asce)0733-9445(2008)134:1(3)

    Article  Google Scholar 

  32. Kela, L.; Vähäoja, P.: Recent studies of adaptive tuned vibration absorbers/neutralizers. Appl. Mech. Rev. (2009). https://doi.org/10.1115/1.3183639

    Article  Google Scholar 

  33. Konar, T.; Ghosh, A.D.: Flow damping devices in tuned liquid damper for structural vibration control: a review. Arch. Comput. Methods Eng. 28, 2195–2207 (2020). https://doi.org/10.1007/s11831-020-09450-0

    Article  MathSciNet  Google Scholar 

  34. Konar, T.; Ghosh, A.: A review on various configurations of the passive tuned liquid damper. J. Vib. Control 29, 1945–1980 (2022). https://doi.org/10.1177/10775463221074077

    Article  MathSciNet  Google Scholar 

  35. Yalla, S.K.; Kareem, A.: Optimum absorber parameters for tuned liquid column dampers. J. Struct. Eng. 126, 906–915 (2000). https://doi.org/10.1061/(asce)0733-9445(2000)126:8(906)

    Article  Google Scholar 

  36. Elias, S.; Matsagar, V.: Research developments in vibration control of structures using passive tuned mass dampers. Annu. Rev. Control. 44, 129–156 (2017). https://doi.org/10.1016/j.arcontrol.2017.09.015

    Article  Google Scholar 

  37. Yang, F.; Sedaghati, R.; Esmailzadeh, E.: Vibration suppression of structures using tuned mass damper technology: a state-of-the-art review. J. Vib. Control 28, 812–836 (2021). https://doi.org/10.1177/1077546320984305

    Article  MathSciNet  Google Scholar 

  38. Suthar, S.J.; Jangid, R.S.: Design of tuned liquid sloshing dampers using nonlinear constraint optimization for across-wind response control of benchmark tall building. Structures 33, 2675–2688 (2021). https://doi.org/10.1016/j.istruc.2021.05.059

    Article  Google Scholar 

  39. Ding, H.; Wang, J.T.; Wang, J.W.; Jia, R.F.: Optimized parameters of toroidal tuned liquid column dampers for multidirectional pitching vibration mitigation of structures. Struct Multidisc Optim. 64, 3401–3421 (2021). https://doi.org/10.1007/s00158-021-03015-w

    Article  MathSciNet  Google Scholar 

  40. Basu, B.; Bursi, O.S.; Casciati, F.; Casciati, S.; Del Grosso, A.E.; Domaneschi, M.; Faravelli, L.; Holnicki-Szulc, J.; Irschik, H.; Krommer, M.; Lepidi, M.; Martelli, A.; Ozturk, B.; Pozo, F.; Pujol, G.; Rakicevic, Z.; Rodellar, J.: A European association for the control of structures joint perspective recent studies in civil structural control across Europe. Struct. Control Heal. Monit. 21, 1414–1436 (2014). https://doi.org/10.1002/stc.1652

    Article  Google Scholar 

  41. Hu, R.; Hu, S.; Yang, M.; Zhang, Y.: Metallic yielding dampers and fluid viscous dampers for vibration control in civil engineering: a review. Int. J. Struct. Stab. Dyn. (2022). https://doi.org/10.1142/s0219455422300063

    Article  MathSciNet  Google Scholar 

  42. Bedon, C.; Amadio, C.: Numerical assessment of vibration control systems for multi-hazard design and mitigation of glass curtain walls. J. Build. Eng. 15, 1–13 (2018). https://doi.org/10.1016/j.jobe.2017.11.004

    Article  Google Scholar 

  43. Ocak, A.; Bekdaş, G.; Nigdeli, S.M.: A metaheuristic-based optimum tuning approach for tuned liquid dampers for structures. Struct. Des. Tall Spec. Build. (2022). https://doi.org/10.1002/tal.1907

    Article  Google Scholar 

  44. Pandey, D.K.; Sharma, M.K.; Mishra, S.K.: A compliant tuned liquid damper for controlling seismic vibration of short period structures. Mech. Syst. Signal Process. 132, 405–428 (2019). https://doi.org/10.1016/j.ymssp.2019.07.002

    Article  Google Scholar 

  45. Amadio, C.; Bedon, C.: Viscoelastic spider connectors for the mitigation of cable-supported façades subjected to air blast loading. Eng. Struct. 42, 190–200 (2012). https://doi.org/10.1016/j.engstruct.2012.04.023

    Article  Google Scholar 

  46. McNamara, R.J.: Tuned mass dampers for buildings. J. Struct. Div. 103, 1785–1798 (1977). https://doi.org/10.1061/jsdeag.0004721

    Article  Google Scholar 

  47. Ghorbanzadeh, M.; Sensoy, S.; Uygar, E.: Seismic performance assessment of semi active tuned mass damper in an MRF steel building including nonlinear soil–pile–structure interaction. Arab. J. Sci. Eng. 48, 4675–4693 (2023). https://doi.org/10.1007/s13369-022-07138-0

    Article  Google Scholar 

  48. Kaynia, A.M.; Veneziano, D.; Biggs, J.M.: Seismic effectiveness of tuned mass dampers. J. Struct. Div. 107, 1465–1484 (1981). https://doi.org/10.1061/jsdeag.0005760

    Article  Google Scholar 

  49. Warburton, G.B.: Optimum absorber parameters for various combinations of response and excitation parameters. Earthq. Eng. Struct. Dyn. 10, 381–401 (1982). https://doi.org/10.1002/eqe.4290100304

    Article  Google Scholar 

  50. Tigli, O.F.: Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads. J. Sound Vib. 331, 3035–3049 (2012). https://doi.org/10.1016/j.jsv.2012.02.017

    Article  Google Scholar 

  51. Sun, H.; Luo, Y.; Wang, X.; Zuo, L.: Seismic control of a SDOF structure through electromagnetic resonant shunt tuned mass-damper-inerter and the exact H2 optimal solutions. J. Vibroeng. 19, 2063–2079 (2017). https://doi.org/10.21595/jve.2017.18256

    Article  Google Scholar 

  52. Sun, H.; Zuo, L.; Wang, X.; Peng, J.; Wang, W.: Exact H 2 optimal solutions to inerter-based isolation systems for building structures. Struct. Control Heal. Monit. 26, e2357 (2019). https://doi.org/10.1002/stc.2357

    Article  Google Scholar 

  53. Kaveh, A.; Farzam, M.F.; Maroofiazar, R.: Comparing H2 and H∞ algorithms for optimum design of tuned mass dampers under near-fault and far-fault earthquake motions. Period. Polytech Civ. Eng. 64, 828–844 (2020). https://doi.org/10.3311/PPci.16389

    Google Scholar 

  54. Marian, L.; Giaralis, A.: Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems. Probab. Eng. Mech. 38, 156–164 (2014). https://doi.org/10.1016/j.probengmech.2014.03.007

    Article  Google Scholar 

  55. Javidialesaadi, A.; Wierschem, N.E.: Optimal design of rotational inertial double tuned mass dampers under random excitation. Eng. Struct. 165, 412–421 (2018). https://doi.org/10.1016/j.engstruct.2018.03.033

    Article  Google Scholar 

  56. Wen, Y.; Chen, Z.; Hua, X.: Design and evaluation of tuned inerter-based dampers for the seismic control of MDOF structures. J. Struct. Eng. (2017). https://doi.org/10.1061/(asce)st.1943-541x.0001680

    Article  Google Scholar 

  57. Zhao, Z.; Chen, Q.; Zhang, R.; Pan, C.; Jiang, Y.: Optimal design of an inerter isolation system considering the soil condition. Eng. Struct. 196, 109324 (2019). https://doi.org/10.1016/j.engstruct.2019.109324

    Article  Google Scholar 

  58. Zhao, Z.; Zhang, R.; Jiang, Y.; Pan, C.: Seismic response mitigation of structures with a friction pendulum inerter system. Eng. Struct. 193, 110–120 (2019). https://doi.org/10.1016/j.engstruct.2019.05.024

    Article  Google Scholar 

  59. Weiss, M.: Robust and optimal control. Automatica 33, 2095 (1997). https://doi.org/10.1016/s0005-1098(97)00132-5

    Article  Google Scholar 

  60. Talley, P.C.; Sarkar, A.T.; Wierschem, N.E.; Denavit, M.D.: Performance of structures with clutch inerter dampers subjected to seismic excitation. Bull. Earthq. Eng. 21, 1577–1598 (2023). https://doi.org/10.1007/s10518-022-01514-9

    Article  Google Scholar 

  61. Tsourekas, A.; Athanatopoulou, A.; Kostinakis, K.: Maximum mean square response and critical orientation under bi-directional seismic excitation. Eng. Struct. 233, 111881 (2021). https://doi.org/10.1016/j.engstruct.2021.111881

    Article  Google Scholar 

  62. Banerjee, S.; Nayak, S.; Das, S.: Seismic performance enhancement of masonry building models strengthened with the cost-effective materials under bi-directional excitation. Eng. Struct. 242, 112516 (2021). https://doi.org/10.1016/j.engstruct.2021.112516

    Article  Google Scholar 

  63. Vern, S.; Shrimali, M.K.; Bharti, S.D.; Datta, T.K.: Response and damage evaluation of base-isolated concrete liquid storage tank under seismic excitations. Eng. Res. Express. 3, 45002 (2021)

    Article  Google Scholar 

  64. Zeris, C.; Lalas, A.; Spacone, E.: Performance of torsionally eccentric RC wall frame buildings designed to DDBD under bi-directional seismic excitation. Bull. Earthq. Eng. 18, 3137–3165 (2020). https://doi.org/10.1007/s10518-020-00813-3

    Article  Google Scholar 

  65. Liu, Y.; Lin, C.-C.; Parker, J.; Zuo, L.: Exact H2 optimal tuning and experimental verification of energy-harvesting series electromagnetic tuned-mass dampers. J. Vib. Acoust. (2016). https://doi.org/10.1115/1.4034081

    Article  Google Scholar 

  66. Spanos, P.-T.D.: An approach to calculating random vibration integrals. J. Appl. Mech. 54, 409–413 (1987). https://doi.org/10.1115/1.3173028

    Article  MathSciNet  Google Scholar 

  67. Roberts, J.B.; Spanos, P.D.: Random Vibration and Statistical Linearization. Courier Corporation (2003)

    Google Scholar 

  68. Kelly, J.M.: Isolation for earthquake resistance. In: Earthquake-Resistant Des. with Rubber, pp. 1–10. Springer, London (1993).

  69. Kulkarni, J.A.; Jangid, R.S.: Effects of superstructure flexibility on the response of base-isolated structures. Shock. Vib. 10, 1–13 (2003). https://doi.org/10.1155/2003/368693

    Article  Google Scholar 

  70. Islam, N.U.; Jangid, R.S.: Optimum parameters of tuned inerter damper for damped structures. J. Sound Vib. 537, 117218 (2022). https://doi.org/10.1016/j.jsv.2022.117218

    Article  Google Scholar 

  71. Islam, N.U.; Jangid, R.S.: Closed form expressions for H2 optimal control of negative stiffness and inerter-based dampers for damped structures. Structures 50, 791–809 (2023). https://doi.org/10.1016/j.istruc.2023.02.065

    Article  Google Scholar 

  72. Matsagar, V.A.; Jangid, R.S.: Impact response of torsionally coupled base-isolated structures. J. Vib. Control 16, 1623–1649 (2010). https://doi.org/10.1177/1077546309103271

    Article  Google Scholar 

  73. Li, L.; Liang, Q.: Seismic assessment and optimal design for structures with clutching inerter dampers. J. Eng. Mech. (2020). https://doi.org/10.1061/(asce)em.1943-7889.0001732

    Article  Google Scholar 

  74. Wang, J.; Zheng, Y.: Experimental validation, analytical investigation, and design method of tuned mass damper-clutching inerter for robust control of structures. Earthq. Eng. Struct. Dyn. 52, 500–523 (2023). https://doi.org/10.1002/eqe.3770

    Article  Google Scholar 

  75. Jangid, R.S.: Optimum parameters and performance of tuned mass damper-inerter for base-isolated structures. Smart Struct. Syst. 29, 549–560 (2022). https://doi.org/10.12989/sss.2022.29.4.549

  76. Kiran, K.K.; Ahmad, S.; Al-Osta, M.A.; Bahraq, A.A.: Enhancing the seismic resilience of structures by using optimum combination of tuned mass damper inerter and negative stiffness damper. Structures 57, 105253 (2023). https://doi.org/10.1016/j.istruc.2023.105253

    Article  Google Scholar 

  77. Yang, J.N.; Agrawal, A.K.; Samali, B.; Wu, J.-C.: Benchmark problem for response control of wind-excited tall buildings. J. Eng. Mech. 130, 437–446 (2004). https://doi.org/10.1061/(ASCE)0733-9399

    Article  Google Scholar 

  78. Cheng, Y.; Ji, X.; Ikago, K.; Luo, H.: Analytical solutions of H 2 control and efficiency-based design of structural systems equipped with a tuned viscous mass damper. Struct. Control Heal. Monit. (2022). https://doi.org/10.1002/stc.2932

    Article  Google Scholar 

  79. Kiran, K.K.; Al-Osta, M.A.; Ahmad, S.: Optimum design and performance of a base-isolated structure with tuned mass negative stiffness inerter damper. Sci. Rep. 13, 4980 (2023). https://doi.org/10.1038/s41598-023-31482-2

    Article  Google Scholar 

Download references

Acknowledgements

K.K. Kiran acknowledges the support provided by the SJB Institute of Technology, Bangalore, Karnataka, India. Mohammed A. Al-Osta, Shamsad Ahmad, and Ashraf A. Bahraq acknowledge the support provided by the King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, S.J.B. Institute of Technology, Bangalore, Karnataka, India

    K. K. Kiran

  2. Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261, Dhahran, Saudi Arabia

    Mohammed A. Al-Osta & Shamsad Ahmad

  3. Interdisciplinary Research Center for Construction and Building Materials, King Fahd University of Petroleum & Minerals, 31261, Dhahran, Saudi Arabia

    Mohammed A. Al-Osta, Shamsad Ahmad & Ashraf A. Bahraq

Authors
  1. K. K. Kiran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed A. Al-Osta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shamsad Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ashraf A. Bahraq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashraf A. Bahraq.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Appendices

Appendix A: Tables

See Table A1, A2, A3, A4 and A5.

Table A1 Numerical search technique used for obtaining optimum TMDI parameters
Full size table
Table A2 Numerical search technique used for obtaining optimum NSADI-1 parameters
Full size table
Table A3 Numerical search technique used for obtaining optimum NSADI-2 parameters
Full size table
Table A4 Numerical search technique used for obtaining optimum NSADI-3 parameters
Full size table
Table A5 Numerical search technique used for obtaining optimum CID parameters
Full size table

Appendix B: Algorithm Representing Dynamic Response of Structural System Under Time Histories Analysis

figure a

Appendix C: Algorithm Representing Supplementary Damper Works for Base Isolated Structure

figure b

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kiran, K.K., Al-Osta, M.A., Ahmad, S. et al. Optimal Design of Tuned Mass and Negative Stiffness Amplifier Dampers with Inerter by H2 Optimal Control Under Bidirectional Seismic Load. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-08960-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13369-024-08960-4

Keywords

Search

Navigation