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A state-of-the-art review on negative stiffness mechanism for safer structures in seismic areas

  • Civil Engineering and Sustainable Infrastructures
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Abstract

In recent years, the concept of negative stiffness mechanism (NSM) has become a prominent research area and cherished a noteworthy amount of observations in the design of dampers for effective seismic protection of structures, and the NSM can be developed by employing negative stiffness device (NSD) which has a stored pre-compressive force and it simulates structural system weakening without inelastic excursions or irreversible deformations. Large base deformation is a fundamental restriction in base-isolated structural systems, but this can be solved with NSD in which the isolation of the structure is achieved throughout the building, not specifically at the base. According to simulations, placing NSDs on the lower levels can significantly reduce the acceleration of the superstructure and base shear without influencing the drifts. This article provides a thorough overview of contemporary research and advancements in the domain of negative stiffness vibration isolation, which initiates with an introduction on the concept of base isolation, negative stiffness device, its origin, working principle, and besides the employment of the negative stiffness concept in various fields for vibration isolation with solid conclusions.

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References

  • Abe M (1996) Semi-active tuned mass dampers for seismic protection of civil structures. Earthquake Eng Struct Dynam 25(7):743–749

    Google Scholar 

  • Abé M (1996) Rule-based control algorithm for active tuned mass dampers. J Eng Mech 122(8):705–713

    Google Scholar 

  • Ahn HJ (2008) Performance limit of a passive vertical isolator using a negative stiffness mechanism. J Mech Sci Technol 22(12):2357–2364

    Google Scholar 

  • Attary N, Symans M, Nagarajaiah S (2017) Development of a rotation-based negative stiffness device for seismic protection of structures. J Vib Control 23(5):853–867

    Google Scholar 

  • Attary N, Symans MD, Nagarajaiah S, Reinhorn AM, Constantinou MC, Sarlis AA, ..., Taylor DP (2014) Shake table testing of a highway bridge structure with passive negative stiffness devices for seismic response control

  • Attary N, Symans M, Nagarajaiah S, Reinhorn AM, Constantinou MC, Sarlis AA, ..., Taylor D (2015) Performance evaluation of negative stiffness devices for seismic response control of bridge structures via experimental shake table tests. J Earthquake Eng19(2):249-276

  • Azizi S, Karami K, Nagarajaiah S (2021) Developing a semi-active adjustable stiffness device using integrated damage tracking and adaptive stiffness mechanism. Eng Struct 238:112036

    Google Scholar 

  • Chang JC, Soong TT (1980) Structural control using active tuned mass dampers. J Eng Mech Div 106(6):1091–1098

    Google Scholar 

  • Chen Q, Wang Y, Zhao Z (2020) A novel negative stiffness amplification system based isolation method for the vibration control of underground structures. Appl Sci 10(16):5421

    CAS  Google Scholar 

  • Cimellaro GP, Domaneschi M, Warn G (2020) Three-dimensional base isolation using vertical negative stiffness devices. J Earthquake Eng 24(12):2004–2032

    Google Scholar 

  • Constantinou MC, Symans MD, Tsopelas P, Taylor DP (1993) Fluid viscous dampers in applications of seismic energy dissipation and seismic isolation. Proceedings ATC 17(1):581–592

    Google Scholar 

  • Dijkstra, K., Videc, B. P., & Huizinga, J. (1988). Mechanical spring having negative spring stiffness useful in an electroacoustic transducer. The Journal of the Acoustical Society of America, 84(2), 804-805.

  • Erazo K, Nagarajaiah S (2018) Bayesian structural identification of a hysteretic negative stiffness earthquake protection system using unscented Kalman filtering. Struct Control Health Monit 25(9):e2203

    Google Scholar 

  • Gao H, Wang H, Li J, Mao J, Wang Z (2022) Dynamic behavior and damping enhancement of cable with negative stiffness inerter damper. Int J Mech Sci 235:107664

    Google Scholar 

  • Gong W, Xiong S (2016) Probabilistic seismic risk assessment of modified pseudo-negative stiffness control of a base-isolated building. Struct Infrastruct Eng 12(10):1295–1309

    Google Scholar 

  • Gong W, Xiong S (2017) A new filter-based pseudo-negative-stiffness control for base-isolated buildings. Struct Control Health Monit 24(5):e1912

    Google Scholar 

  • Gong W, Xiong S, Tan P (2019) Experimental and numerical studies on pseudo-negative-stiffness control of a base isolated building using magneto-rheological dampers. Smart Mater Struct 28(10):105020

    CAS  Google Scholar 

  • Høgsberg J (2011) The role of negative stiffness in semi-active control of magneto-rheological dampers. Struct Control Health Monit 18(3):289–304

    Google Scholar 

  • Hua Y, Zhu S, Shi X (2022) High-performance semiactive secondary suspension of high-speed trains using negative stiffness and magnetorheological dampers. Veh Syst Dyn 60(7):2290–2311

    Google Scholar 

  • Iemura H, Pradono MH (2009) Advances in the development of pseudo‐negative‐stiffness dampers for seismic response control. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures 16(7‐8):784-799

  • Iemura H, Igarashi A, Pradono MH, Kalantari A (2006) Negative stiffness friction damping for seismically isolated structures. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures 13(2‐3):775-791

  • Iemura H, Pradono MH (2002) Passive and semi-active seismic response control of a cable-stayed bridge. J Struct Control 9(3):189–204

    Google Scholar 

  • Iemura H, Pradono MH (2003a) Application of pseudo-negative stiffness control to the benchmark cable-stayed bridge. J Struct Control 10(3–4):187–203

    Google Scholar 

  • Iemura H, Pradono MH (2003b) Pseudo negative stiffness dampers for seismic response control of cable-stayed bridges. J Earthquake Eng 27:46–46

    Google Scholar 

  • Iemura H, Pradono MH (2005) Simple algorithm for semi-active seismic response control of cable-stayed bridges. Earthquake Eng Struct Dynam 34(4–5):409–423

    Google Scholar 

  • Islam NU, Jangid RS, (2021) Seismic performance of inerter and negative stiffness-based dampers for vibration control of structures. Front Built Environ 174

  • Islam NU, Jangid RS (2022) Optimum parameters and performance of negative stiffness and inerter based dampers for base-isolated structures. Bull Earthquake Eng 1–28

  • Jadhav PA, Shaikh SA (2019) Optimization of seismic response of steel structure using negative stiffness damper. Int J Adv Struct Eng 11(3):351–360

    CAS  Google Scholar 

  • Jangid RS, Datta TK (1995) Performance of base isolation systems for asymmetric building subject to random excitation. Eng Struct 17(6):443–454

    Google Scholar 

  • Javanbakht M, Cheng S, Ghrib F (2020) Multimode vibration control of stay cables using optimized negative stiffness damper. Struct Control Health Monit 27(4):e2503

    Google Scholar 

  • Junshu H, Lingshuai M, Jinggong S (2018) Design and characteristics analysis of a nonlinear isolator using a curved-mount-spring-roller mechanism as negative stiffness element. Math Problems Eng 2018

  • Kapasakalis KA, Antoniadis IA, Sapountzakis EJ (2021a) A soil-dependent approach for the design of novel negative stiffness seismic protection devices. Appl Sci 11(14):6295

    CAS  Google Scholar 

  • Kapasakalis KA, Florakis GI, Antoniadis IA, Sapountzakis EJ (2021b) Seismic protection of multi-story structures with novel vibration absorption devices combining negative stiffness and inerter

  • Kaynia AM, Veneziano D, Biggs JM (1981) Seismic effectiveness of tuned mass dampers. J Struct Div 107(8):1465–1484

    Google Scholar 

  • Kelly JM (1986) Aseismic base isolation: review and bibliography. Soil Dyn Earthq Eng 5(4):202–216

    Google Scholar 

  • Kiran KK, Noroozinejad Farsangi E, Gharehbaghi V (2022) An innovative negative stiffness-inerter hybrid control device toward seismic-resilient structures. Innov Infrastruct Solut 7(5):1–20

    Google Scholar 

  • Lakes RS (2001) Extreme damping in composite materials with a negative stiffness phase. Phys Rev Lett 86(13):2897

    CAS  Google Scholar 

  • Le TD, Ahn KK (2011) A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. J Sound Vib 330(26):6311–6335

    Google Scholar 

  • Lee CM, Goverdovskiy VN, Temnikov AI (2007) Design of springs with “negative” stiffness to improve vehicle driver vibration isolation. J Sound Vib 302(4–5):865–874

    Google Scholar 

  • Li H, Liu J, Ou J (2011) Seismic response control of a cable-stayed bridge using negative stiffness dampers. Struct Control Health Monit 18(3):265–288

    Google Scholar 

  • Li J, Fu K, Gu Y, Zhao Z (2019) Torsional negative stiffness mechanism by thin strips. Theor Appl Mech Lett 9(3):206–211

    CAS  Google Scholar 

  • Li H, Li Y, Li J (2020) Negative stiffness devices for vibration isolation applications: a review. Adv Struct Eng 23(8):1739–1755

    Google Scholar 

  • Li H, Yu Y, Li J, Li Y, Askari M (2021) Multi-objective optimisation for improving the seismic protection performance of a multi-storey adaptive negative stiffness system based on modified NSGA-II with DCD. J Build Eng 43:103145

    Google Scholar 

  • Li H, Li J, Bi K (2022a) A quasi-active negative stiffness damper for structural vibration control under earthquakes. Mech Syst Signal Process 173:109071

    Google Scholar 

  • Li H, Liu M, Ou J (2008) Negative stiffness characteristics of active and semi‐active control systems for stay cables. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures 15(2):120-142

  • Li J, Gu X, Zhu S, Yu C, Yang X (2022b) Parameter optimization for a novel inerter-based dynamic vibration absorber with negative stiffness. J Nonlinear Math Phys 1–16

  • Madhekar SN, Jangid RS (2012) Use of pseudo-negative stiffness dampers for reducing the seismic response of bridges: a benchmark study. Bull Earthq Eng 10(5):1561–1583

    Google Scholar 

  • Mathew GM, Qureshi A, Jangid RS (2015) Optimal placement of negative stiffness damping system. In Smart Materials, Adaptive Structures and Intelligent Systems (Vol. 57298, p. V001T03A018). Am Soc Mech Eng

  • Mathew GM, Jangid RS (2018) Seismic response control of a building by negative stiffness devices. Asian J Civ Eng 19(7):849–866

    Google Scholar 

  • Mirza MB, Chakrabarti MA (2017) Optimal use of negative stiffness damper for seismic resistant frames. IOSR J Mech Civ Eng 14(6):23–31

    Google Scholar 

  • Mizuno T, Toumiya T, Takasaki M (2003) Vibration isolation system using negative stiffness. JSME Int j, Ser C 46(3):807–812

    Google Scholar 

  • Molyneux WG (1957) “Supports for vibration isolation”, ARC/CP-322, Aeronautical Research Council, Great Britain

  • Nagarajaiah S, Varadarajan N (2005) Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD. Eng Struct 27(3):431–441

    Google Scholar 

  • Nagarajaiah S, Sonmez E (2007) Structures with semiactive variable stiffness single/multiple tuned mass dampers. J Struct Eng 133(1):67–77

    Google Scholar 

  • Nagarajaiah S, Reinhorn AM, Constantinou MC, Taylor D, Pasala DTR, Sarlis AA (2010) “True adaptive negative stiffness: A new structural modification approach for seismic protection.” 5th World Conf. on Structural Control and Monitoring, Tokyo

  • Nagarajaiah S, Pasala DT, Reinhorn A, Constantinou M, Sirilis AA, Taylor D (2013) Adaptive negative stiffness: a new structural modification approach for seismic protection. In Advanced Materials Research (Vol. 639, pp. 54–66). Trans Tech Publications Ltd

  • Nagarajaiah S, Sen D (2020) Apparent-weakening by adaptive passive stiffness shaping along the height of multistory building using negative stiffness devices and dampers for seismic protection. Eng Struct 220:110754

    Google Scholar 

  • Ou J, Li H (2010) Analysis of capability for semi-active or passive damping systems to achieve the performance of active control systems. Struct Control Health Monit 17(7):778–794

    Google Scholar 

  • Pasala DTR, Sarlis AA, Reinhorn AM, Nagarajaiah S, Constantinou MC, Taylor D (2014) Simulated bilinear-elastic behavior in a SDOF elastic structure using negative stiffness device: Experimental and analytical study. J Struct Eng 140(2):04013049

    Google Scholar 

  • Pasala DTR, Sarlis AA, Reinhorn AM, Nagarajaiah S, Constantinou MC, Taylor D (2015) Apparent weakening in SDOF yielding structures using a negative stiffness device: Experimental and analytical study. J Struct Eng 141(4):04014130

    Google Scholar 

  • Pasala DTR, Sarlis AAS, Nagarajaiah S, Reinhorn AM, Constantinou MC, Taylor D (2011) A new structural modification approach for seismic protection based on adaptive negative stiffness device: conceptual analysis. In Structures Congress 2011 (pp. 2892–2904)

  • Pasala DTR, Sarlis AA, Nagarajaiah S, Reinhorn AM, Constantinou MC, Taylor D (2012) Negative stiffness device for seismic response control of multi-story buildings. In 20th Analysis and Computation Specialty Conference (pp. 83–96)

  • Platus DL (1992) Negative-stiffness-mechanism vibration isolation systems. In Vibration control in microelectronics, optics, and metrology (Vol. 1619, pp. 44–54). International Society for Optics and Photonics

  • Pradono MH, Iemura H, Igarashi A, Toyooka A, Kalantari A (2009) Passively controlled MR damper in the benchmark structural control problem for seismically excited highway bridge. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures 16(6):626-638

  • Providakis CP (2008) Effect of LRB isolators and supplemental viscous dampers on seismic isolated buildings under near-fault excitations. Eng Struct 30(5):1187–1198

    Google Scholar 

  • Raheja AH, Waghmare MV, Awari UR (2015) Seismic analysis of high-rise building using negative stiffness device. Int J Adv Foundation Res Sci Eng 1:33–45

    Google Scholar 

  • Rao PB, Jangid RS (2001a) Experimental study of base-isolated structures. ISET J Earthq Technol 38(1):1–15

    Google Scholar 

  • Rao PB, Jangid RS (2001b) Performance of sliding systems under near-fault motions. Nucl Eng Des 203(2–3):259–272

    Google Scholar 

  • Reinhorn AM, Viti S, Cimellaro G (2005) Retrofit of structures: strength reduction with damping enhancement. In Proceedings of the 37th UJNR panel meeting on wind and seismic effects (pp. 16–21)

  • Reinhorn AM, Ray T, Pasala DTR, Sarlis AA, Nagarajaiah S, Constantinou MC (2012) Control of inelastic structures by weakening and damping. In 20th Analysis and Computation Specialty Conference (pp. 37–48)

  • Sarlis AA, Pasala DTR, Constantinou MC, Reinhorn AM, Nagarajaiah S, Taylor DP (2013) Negative stiffness device for seismic protection of structures. J Struct Eng 139(7):1124–1133

    Google Scholar 

  • Sarlis AA, Pasala DTR, Constantinou MC, Reinhorn AM, Nagarajaiah S, Taylor DP (2016) Negative stiffness device for seismic protection of structures: shake table testing of a seismically isolated structure. J Struct Eng 142(5):04016005

    Google Scholar 

  • Sarlis AA, Pasala DTR, Constantinou MC, Reinhorn AM, Nagarajaiah S Taylor D (2011) Negative stiffness device for seismic protection of structures–an analytical and experimental study. In COMPDYN 2011, Proc. of 3rd ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece

  • Sarlis AA, Constantinou MC, Reinhorn AM, Pasala DTR, Nagarajaiah S, Taylor D (2012) Seismic protection of structures using novel negative stiffness device. In Proceedings 15th World Conference on Earthquake Engineering, September 23–28, 2012, Lisbon Portugal-Paper 5498

  • Scozzese F, Dall’Asta A, Tubaldi E (2019) Seismic risk sensitivity of structures equipped with anti-seismic devices with uncertain properties. Struct Saf 77:30–47

    Google Scholar 

  • Shen Y, Peng H, Li X, Yang S (2017) Analytically optimal parameters of dynamic vibration absorber with negative stiffness. Mech Syst Signal Process 85:193–203

    Google Scholar 

  • Shi X, Zhu S (2015) Magnetic negative stiffness dampers. Smart Mater Struct 24(7):072002

    Google Scholar 

  • Shi X, Zhu S (2017) Simulation and optimization of magnetic negative stiffness dampers. Sens Actuators, A 259:14–33

    CAS  Google Scholar 

  • Shi X, Zhao F, Yan Z, Zhu S, Li JY (2021) High-performance vibration isolation technique using passive negative stiffness and semiactive damping. Computer-Aided Civ Infrastruct Eng 36(8):1034–1055

    Google Scholar 

  • Sladek JR, Klingner RE (1983) Effect of tuned-mass dampers on seismic response. J Struct Eng 109(8):2004–2009

    Google Scholar 

  • Stribersky A, Kienberger A, Wagner G, Müller H (1998) Design and evaluation of a semi-active damping system for rail vehicles. Veh Syst Dyn 29(S1):669–681

    Google Scholar 

  • Sun T, Lai Z, Nagarajaiah S, Li HN (2017) Negative stiffness device for seismic protection of smart base isolated benchmark building. Struct Control Health Monit 24(11):e1968

    Google Scholar 

  • Sun M, Song G, Li Y, Huang Z (2019) Effect of negative stiffness mechanism in a vibration isolator with asymmetric and high-static-low-dynamic stiffness. Mech Syst Signal Process 124:388–407

    Google Scholar 

  • Sun FF, Wang M, Nagarajaiah S (2021) Multi-objective optimal design and seismic performance of negative stiffness damped outrigger structures considering damping cost. Eng Struct 229:111615

    Google Scholar 

  • Tang JS (1996) Passive and semi-active airspring suspensions for rail passenger vehicles—theory and practice. Proc Inst Mech Eng F: J Rail Rapid Transit 210(2):103–117

    Google Scholar 

  • Varadarajan N, Nagarajaiah S (2004) Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/Hilbert transform. J Eng Mech 130(4):451–458

    Google Scholar 

  • Viti S, Cimellaro GP, Reinhorn AM (2006) Retrofit of a hospital through strength reduction and enhanced damping. Smart Struct Syst 2(4):339–355

    Google Scholar 

  • Walsh KK, Boso E, Steinberg EP, Haftman JT, Littell WN (2018) Variable negative stiffness device for seismic protection of building structures through apparent weakening. J Eng Mech 144(9):04018090

    Google Scholar 

  • Wang DH, Liao WH (2009a) Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis. Vehicle Syst Dyn 47(12):1439–1471

    Google Scholar 

  • Wang DH, Liao WH (2009b) Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part I: system integration and modelling. Vehicle Syst Dyn 47(11):1305–1325

    Google Scholar 

  • Wang M, Sun FF, Jin HJ (2018a) Performance evaluation of existing isolated buildings with supplemental passive pseudo-negative stiffness devices. Eng Struct 177:30–46

    Google Scholar 

  • Wang X, Liu X, Shan Y, Shen Y, He T (2018b) Analysis and optimization of the novel inerter-based dynamic vibration absorbers. IEEE Access 6:33169–33182

    Google Scholar 

  • Wang M, Sun FF, Yang JQ, Nagarajaiah S (2019) Seismic protection of SDOF systems with a negative stiffness amplifying damper. Eng Struct 190:128–141

    Google Scholar 

  • Weber F (2013) Dynamic characteristics of controlled MR-STMDs of Wolgograd Bridge. Smart Mater Struct 22(9):095008

    Google Scholar 

  • Weber F, Boston C (2010) Energy based optimization of viscous–friction dampers on cables. Smart Mater Struct 19(4):045025

    Google Scholar 

  • Weber F, Boston C (2011) Clipped viscous damping with negative stiffness for semi-active cable damping. Smart Mater Struct 20(4):045007

    Google Scholar 

  • Weber F, Distl H (2015) Semi-active damping with negative stiffness for multi-mode cable vibration mitigation: approximate collocated control solution. Smart Mater Struct 24(11):115015

    Google Scholar 

  • Weber F, Maślanka M (2013) Precise stiffness and damping emulation with MR dampers and its application to semi-active tuned mass dampers of Wolgograd Bridge. Smart Mater Struct 23(1):015019

    Google Scholar 

  • Weber F, Boston C, Maślanka M (2010) An adaptive tuned mass damper based on the emulation of positive and negative stiffness with an MR damper. Smart Mater Struct 20(1):015012

    Google Scholar 

  • Wu B, Shi P, Ou J (2013) Seismic performance of structures incorporating magnetorheological dampers with pseudo-negative stiffness. Struct Control Health Monit 20(3):405–421

    Google Scholar 

  • Xu YW, Xu ZD, Guo YQ, Zhou M, Zhao YL, Yang Y, ..., Chen ZQ (2022) A programmable pseudo negative stiffness control device and its role in stay cable vibration control. Mech Syst Signal Process 173:109054

  • Yang J, Xiong YP, Xing JT (2013) Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism. J Sound Vib 332(1):167–183

    Google Scholar 

  • Yang J, Ning D, Sun SS, Zheng J, Lu H, Nakano M, ..., Li WH (2021) A semi-active suspension using a magnetorheological damper with nonlinear negative-stiffness component. Mech Syst Signal Process 147:107071

  • Ye K, Nyangi P (2020) H∞ optimization of tuned inerter damper with negative stiffness device subjected to support excitation. Shock and Vibration 2020

  • Zelleke DH, Elias S, Matsagar VA, Jain AK (2015) Supplemental dampers in base-isolated buildings to mitigate large isolator displacement under earthquake excitations. Bull N Z Soc Earthq Eng 48(2):100–117

    Google Scholar 

  • Zhang F, Xu M, Shao S, Xie S (2020a) A new high-static-low-dynamic stiffness vibration isolator based on magnetic negative stiffness mechanism employing variable reluctance stress. J Sound Vib 476:115322

    Google Scholar 

  • Zhang Y, Wang S, Fang H, Han H, Xu Y (2020b) Design and simulation of a damper with negative stiffness for vibration mitigation from drilling equipment to a semi-submersible platform. Shock Vib 2020b

  • Zhang Y, Ye K, Nyangi P (2022) Optimum design of a tuned‐mass damper with negative stiffness device subjected to ground excitation. Struct Control Health Monit e3086

  • Zhao Z, Wang Y, Hu X, Weng D (2022) Seismic performance upgrading of containment structures using a negative-stiffness amplification system. Eng Struct 262:114394

    Google Scholar 

  • Zong LH, Gong XL, Xuan SH, Guo CY (2013) Semi-active H∞ control of high-speed railway vehicle suspension with magnetorheological dampers. Veh Syst Dyn 51(5):600–626

    Google Scholar 

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  1. Civil Engineering Department, NIT Raipur, G.E. Road, Raipur, Chhattisgarh, 492010, India

    Satya Eswara SanyasiRao Kolli & Govardhan Bhatt

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Dr. Govardhan Bhatt presented the idea for the article, and Satya Eswara SanyasiRao Kolli did the literature review, concept and data analysis, drafting, and critical revision of the work.

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Kolli, S.E.S., Bhatt, G. A state-of-the-art review on negative stiffness mechanism for safer structures in seismic areas. Environ Sci Pollut Res 30, 99160–99175 (2023). https://doi.org/10.1007/s11356-022-24477-5

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