Numerical Tuning of Nonlinear Energy Sinks in Shear Buildings

Eliot Motato1, Fabio G. Guerrero2
1R.B. Annis School of Engineering, University of Indianapolis, Indianapolis, USA
2Electrical and Electronics Engineering School, Universidad del Valle, Cali, Colombia

Tóm tắt

A nonlinear energy sink (NES) is an energy-dependent absorber that has gained popularity as it can resonate with any mode of the primary structure. An NES mitigates the primary structure’s vibrations in two different forms. In the first form, a one-directional energy flow is generated from the structure to the NES where the vibrating energy is consumed by the absorber damping. In the second form, the NES induces an irreversible energy flow from the structure’s low-damped, low-frequency modes to the high-damped, high-frequency ones where the vibrating energy is more easily dissipated by the damping of the structure. These two NES mechanisms, however, are very sensitive to energy variations and is common that the performance of previously tuned NES can be dramatically reduced even by small variations in the primary system energy. In this work, we present a numerical method to tune arrays of NES connected to shear building structures subject to random vibrations. The methodology guarantees that each NES in the array is tuned at a different energy level, providing robust vibration attenuation against random excitations in a broader range of input energies intensities. To introduce the proposed method, the dynamic model of a shear building is used. This structure is numerically excited using a seismic accelerogram scaled to obtain different energy intensities.

Tài liệu tham khảo

Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2009) Nonlinear targeted energy transfer in mechanical and structural systems. Springer, Amsterdam. https://doi.org/10.1007/978-1-4020-9130-8 Haris A, Motato E, Mohammadpour M, Theodossiades S, Rahnejat H, O’ Mahony M, Vakakis AF, Bergman LA, McFarland DM, (2017) On the effect of multiple parallel nonlinear absorbers in palliation of torsional response of automotive drivetrain. Int J Non-Linear Mech 96:22–35. https://doi.org/10.1016/j.ijnonlinmec.2017.06.008 Vakakis AF (2001) Inducing passive nonlinear energy sinks in vibrating systems. J Vib Acoust 123(3):324–332. https://doi.org/10.1115/1.1368883 Gendelman OV (2001) Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn 25(1):237–253. https://doi.org/10.1023/A:1012967003477 Saeed AS, Abdul Nasar R, AL-Shudeifat MA (2023) A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types. Nonlinear Dyn 111(x):1–37. https://doi.org/10.1007/s11071-022-08094-y AL-Shudeifat MA, Vakakis AF, Bergman LA, (2015) Shock mitigation by means of low- to high-frequency nonlinear targeted energy transfers in a large-scale structure. J Comput Nonlinear Dyn. https://doi.org/10.1115/1.4030540.021006 Motato E, Haris A, Theodossiades S, Mohammadpour M, Rahnejat H, Kelly P, Vakakis AF, McFarland DM, Bergman LA (2017) Targeted energy transfer and modal energy redistribution in automotive drivetrains. Nonlinear Dyn 87(1):169–190. https://doi.org/10.1007/s11071-016-3034-4 Matta E (2021) Seismic effectiveness and robustness of tuned mass dampers versus nonlinear energy sinks in a lifecycle cost perspective. Bull Earthq Eng 19(1):513–551. https://doi.org/10.1007/s10518-020-00973-2 Wierschem N.E., Spencer B.F Jr, (2011) Numerical study of nonlinear energy sinks for seismic response reduction. In: the 6th international workshop on advanced smart materials and smart structures technology. July 25-26, Dalian, China Shi Y., Li Z., Chang C. (2016) Output-only subspace identification of structural properties and unknown ground excitation for shear-beam buildings. Adv Mech Eng. https://doi.org/10.1177/1687814016679908 Zacchei E., Lyra H.C P. (2022) Recalibration of low seismic excitations in brazil through probabilistic and deterministic analyses: application for shear buildings structures. Struct Concrete 24(1):937–955. https://doi.org/10.1002/suco.202100839 Ganjavi B., Hajirasouliha I., Bolourchi A. (2016) Optimum lateral load distribution for seismic design of nonlinear shear-buildings considering soil-structure interaction. Soil Dyn Earthq Eng 88:356–368. https://doi.org/10.1016/j.soildyn.2016.07.003 García-Illescas M. A., Alvarez-Icaza L. (2016) A matrix projection method for on line stable estimation of 1d and 3d shear building models. Mech Syst Signal Process 81:318–338. https://doi.org/10.1016/j.ymssp.2016.03.019 Gholami N, Garivani S, Askariani SS (2021) State-of-the-art review of energy-based seismic design methods. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-021-09645-z Luo J, Wierschem NE, Hubbard SA, Fahnestock LA, Dane Quinn D, Michael McFarland D, Spencer BF, Vakakis AF, Bergman LA (2014) Large-scale experimental evaluation and numerical simulation of a system of nonlinear energy sinks for seismic mitigation. Eng Struct 77:34–48. https://doi.org/10.1016/j.engstruct.2014.07.020 Ahmadi M, Attari NKA, Shahrouzi M (2015) Structural seismic response mitigation using optimized vibro-impact nonlinear energy sinks. J Earthq Eng 19(2):193–219. https://doi.org/10.1080/13632469.2014.962671 Nucera F, Vakakis AF, McFarland DM, Bergman LA, Kerschen G (2007) Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn 50(3):651–677. https://doi.org/10.1007/s11071-006-9189-7 Wierschem NE, Luo J, AL-Shudeifat M, Hubbard S, Ott R, Fahnestock LA, Quinn DD, McFarland DM, Spencer BF, Vakakis A, Bergman LA, (2014) Experimental testing and numerical simulation of a six-story structure incorporating two-degree-of-freedom nonlinear energy sink. J Struct Eng 140(6):04014027. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000978 Gomez F, Gaston AF, Spencer B (2021) Optimal design of nonlinear energy sinks for mitigation of seismic response on structural systems. Eng Struct. https://doi.org/10.1016/j.engstruct.2020.111756 Motato E (2022) Seismic vibration attenuation in shear buildings using nonlinear energy sink with asymmetric bi-linear element. In: ASME international mechanical engineering congress and exposition, volume 5: dynamics, vibration, and control. https://doi.org/10.1115/IMECE2022-96839.V005T07A057 Hong D, Hill TL, Neild SA (2021) Understanding targeted energy transfer from a symmetry breaking perspective. Proc R Soc A Math Phys Eng Sci. https://doi.org/10.1098/rspa.2021.0045 Habib G, Romeo F (2017) The tuned bistable nonlinear energy sink. Nonlinear Dyn 89(1):179–196. https://doi.org/10.1007/s11071-017-3444-y Dekemele K, Van Torre P, Loccufier M (2019) Performance and tuning of a chaotic bi-stable nes to mitigate transient vibrations. Nonlinear Dyn 98(3):1831–1851. https://doi.org/10.1007/s11071-019-05291-0 Chen Y, Qian Z, Kai Chen PT, Tesfamariam S (2019) Seismic performance of a nonlinear energy sink with negative stiffness and sliding friction. Struct Control Health Monit. https://doi.org/10.1002/stc.2437 Das S, Tesfamariam S, Chen Y, Qian Z, Tan P, Zhou F (2020) Reliability-based optimization of nonlinear energy sink with negative stiffness and sliding friction. J Sound Vib 485:115560. https://doi.org/10.1016/j.jsv.2020.115560 Dang W, Wang Z, Chen L (2022) A high-efficient nonlinear energy sink with a one-way energy converter. Nonlinear Dyn. https://doi.org/10.1007/s11071-022-07575-4 Wang J, C Z, Y Z (2022) An inerter-enhanced asymmetric nonlinear energy sink for response mitigation of structures subject to harmonic and seismic ground excitations. Struct Control Health Monit. https://doi.org/10.1002/stc.3104 Savva K, Haris A, Motato E, Mohammadpour M (2016) Damping effects introduced by a nonlinear vibration absorber in automotive drivelines at idle engine speeds. SAE technical paper, 2016-011765. https://doi.org/10.4271/2016-01-1765. Motato E, Guerrero F (2022) On the effect of nonlinear energy sink damping in seismic vibration attenuation. ASME, Saint Louis, USA. https://doi.org/10.1115/DETC2022-89205 EN1998-1: Eurocode 8: design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. Standard, European Committee for Standardisation, Brussels (2004) Ali M, Gholami F (2016) The influence of seismic intensity parameters on structural damage of rc buildings using principal component analysis. Appl Math Model 40(3):2161–2176. https://doi.org/10.1016/j.apm.2015.09.043 Gourdon E, Alexander NA, Taylor CA, Lamarque CH, Pernot S (2007) Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J Sound Vib 300(3):522–551. https://doi.org/10.1016/j.jsv.2006.06.074 Sun HL, Zhang PQ, Chen HB, Zhang K, Gong XL (2008) Application of dynamic vibration absorbers in structural vibration control under multi-frequency harmonic excitations. Appl Acoust 69(12):1361–1367. https://doi.org/10.1016/j.apacoust.2007.10.004 Nguyen D-C (2019) Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy. Proc Inst Mech Eng Part K J Multi-body Dyn 233(2):327–335. https://doi.org/10.1177/1464419318804064 Zilletti M, Elliott SJ, Rustighi E (2012) Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation. J Sound Vib 331(18):4093–4100. https://doi.org/10.1016/j.jsv.2012.04.023 Harith NSH, Tongkul F, Adnan A (2023) Seismic hazard curve as dynamic parameters in earthquake building design for Sabah, Malaysia. Buildings 13(2) Zacchei E, Molina J-L (2018) Damage estimation on concrete gravity dams through artificial accelerograms. MATEC Web Conf 211:14001. https://doi.org/10.1051/matecconf/201821114001 Novak MS, Lazarevic D, Atalic J, Uros M (2019) Influence of multiple-support excitation on seismic response of reinforced concrete arch bridges. Appl Sci 10:17. https://doi.org/10.3390/app10010017 Luo J, Wierschem NE, Hubbard SA, Fahnestock LA, Dane Quinn D, Michael McFarland D, Spencer BF, Vakakis AF, Bergman LA (2014) Large-scale experimental evaluation and numerical simulation of a system of nonlinear energy sinks for seismic mitigation. Eng Struct 77:34–48. https://doi.org/10.1016/j.engstruct.2014.07.020 Console R, Carluccio R, Papadimitriou E, Karakostas V (2015) Synthetic earthquake catalogs simulating seismic activity in the Corinth Gulf, Greece, fault system. J Geophys Res Solid Earth 120(1):326–343. https://doi.org/10.1002/2014JB011765 Oliva M, Barone G, Lo Iacono F, Navarra G (2020) Nonlinear energy sink and Eurocode 8: An optimal design approach based on elastic response spectra. Eng Struct 221:111020. https://doi.org/10.1016/j.engstruct.2020.111020 Poiata N, Miyake H (2017) Broadband ground motion simulation of the 2004 and 1977 Vrancea, Romania, earthquakes using empirical green’s function method. Pure Appl Geophys 174(9):3503–3519. https://doi.org/10.1007/s00024-017-1605-z Azira M, Guenfaf L (2018) Empirical multi-degree-of-freedom-generalized minimum variance control for buildings during earthquakes. J Low Freq Noise Vib Active Control 37(1):3–30. https://doi.org/10.1177/1461348418760878 Deodatis G (1996) Non-stationary stochastic vector processes: seismic ground motion applications. Probab Eng Mech 11(3):149–167. https://doi.org/10.1016/0266-8920(96)00007-0