Optimisation of absorber parameters in the case of stochastic vibrations in a bridge with a deck platform for servicing pipelines

[1] Dallard P., Fitzpatrick T., Flint A., Low A., Smith R.R., Willford M., Roche M., 2001. London Millennium Bridge: Pedestrian-Induced Lateral Vibration, Journal of Bridge Engineering 6(6), 412 – 417. DallardP. FitzpatrickT. FlintA. LowA. SmithR.R. WillfordM. RocheM. 2001 London Millennium Bridge: Pedestrian-Induced Lateral Vibration Journal of Bridge Engineering 6 6 412 417 10.1061/(ASCE)1084-0702(2001)6:6(412) Search in Google Scholar

[2] Yau J.D., Yang Y.B., 2004. Vibration reduction for cable-stayed bridges traveled by high-speed trains, Finite Elements in Analysis and Design 40, 341 – 359. YauJ.D. YangY.B. 2004 Vibration reduction for cable-stayed bridges traveled by high-speed trains Finite Elements in Analysis and Design 40 341 359 10.1016/S0168-874X(03)00051-9 Search in Google Scholar

[3] Majcher K., Wójcicki Z., 2014. Kinematically excited parametric vibration of a tall building model with a TMD. Pt. 1, Numerical analyses. Archives of Civil and Mechanical Engineering 14(1), 204–217. MajcherK. WójcickiZ. 2014 Kinematically excited parametric vibration of a tall building model with a TMD. Pt. 1, Numerical analyses Archives of Civil and Mechanical Engineering 14 1 204 217 10.1016/j.acme.2013.09.004 Search in Google Scholar

[4] Herbut A., Rybak J., Brząkała W., 2020. On a Sensor Placement Methodology for Monitoring the Vibrations of Horizontally Excited Ground Sensors 20(7), 1938; https://doi.org/10.3390/s20071938. HerbutA. RybakJ. BrząkałaW. 2020 On a Sensor Placement Methodology for Monitoring the Vibrations of Horizontally Excited Ground Sensors 20 7 1938 https://doi.org/10.3390/s20071938. 10.3390/s20071938718079432235664 Search in Google Scholar

[5] Den Hartog J.P., 1985. Mechanical Vibrations, 4^th ed., Dover, New York. Den HartogJ.P. 1985 Mechanical Vibrations 4th ed. Dover New York Search in Google Scholar

[6] Korenev B. G., Reznikov L.M., 1993. Dynamic vibration absorbers, John Wiley. KorenevB. G. ReznikovL.M. 1993 Dynamic vibration absorbers John Wiley Search in Google Scholar

[7] Soong T.T., Dargush G.F., 1997. Passive Energy dissipation systems in structural Engineering, Wiley, New York. SoongT.T. DargushG.F. 1997 Passive Energy dissipation systems in structural Engineering Wiley New York 10.1201/9781439834350.ch27 Search in Google Scholar

[8] Jacquot R. Q., Hoppe D. H., 1973. Optimum random vibration absorbers, Journal of the Engineering Mechanics Division, ASCE 99, 612–616. JacquotR. Q. HoppeD. H. 1973 Optimum random vibration absorbers Journal of the Engineering Mechanics Division, ASCE 99 612 616 10.1061/JMCEA3.0001771 Search in Google Scholar

[9] Cheung Y.L., Wong W.O., 2013. Optimization of a hybrid vibration absorber for vibration control of structures under force excitation, Journal of Sound and Vibration, 332, 494–509. CheungY.L. WongW.O. 2013 Optimization of a hybrid vibration absorber for vibration control of structures under force excitation Journal of Sound and Vibration 332 494 509 10.1016/j.jsv.2012.09.014 Search in Google Scholar

[10] Sinha A., 2009, Optimal damped vibration absorber for narrow band random excitations a mixed H₂/H_∞ optimization, Probabilistic Engineering Mechanics 24, 251–254. SinhaA. 2009 Optimal damped vibration absorber for narrow band random excitations a mixed H₂/H_∞ optimization Probabilistic Engineering Mechanics 24 251 254 10.1016/j.probengmech.2008.06.005 Search in Google Scholar

[11] Tigli O.F., 2012. Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads, Journal of Sound and Vibration 331, 3035–3049. TigliO.F. 2012 Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads Journal of Sound and Vibration 331 3035 3049 10.1016/j.jsv.2012.02.017 Search in Google Scholar

[12] Sieniawska R., Sniady P., Zukowski S., 1996. Optimization of stochastic vibrations absorbers with respect to structure's reliability, Structural Dynamics-EURODYN, Florence, 583–589. SieniawskaR. SniadyP. ZukowskiS. 1996 Optimization of stochastic vibrations absorbers with respect to structure's reliability Structural Dynamics-EURODYN Florence 583 589 Search in Google Scholar

[13] Hua Y., Wong W., Cheng L., 2018. Optimal design of a beam-based dynamic vibration absorber using fixed-points theory, Journal of Sound and Vibration 421, 111–131. HuaY. WongW. ChengL. 2018 Optimal design of a beam-based dynamic vibration absorber using fixed-points theory Journal of Sound and Vibration 421 111 131 10.1016/j.jsv.2018.01.058 Search in Google Scholar

[14] Basili M., De Angelis M., Pietrosanti D., 2019. Defective two adjacent single degree of freedom systems linked by spring-dashpot-inerter for vibration control, Engineering Structures 188, 480–492. BasiliM. De AngelisM. PietrosantiD. 2019 Defective two adjacent single degree of freedom systems linked by spring-dashpot-inerter for vibration control Engineering Structures 188 480 492 10.1016/j.engstruct.2019.03.030 Search in Google Scholar

[15] Zuo L., Nayfeh S. A., 2006. The two-degree-of-freedom tuned-mass damper for suppression of single-mode vibration under random and harmonic excitation, Journal of Vibration and Acoustics, Transections of the ASME, 128(2), 56–65. ZuoL. NayfehS. A. 2006 The two-degree-of-freedom tuned-mass damper for suppression of single-mode vibration under random and harmonic excitation Journal of Vibration and Acoustics, Transections of the ASME 128 2 56 65 10.1115/1.2128639 Search in Google Scholar

[16] Barredo E., Larios J.G.M., Mayen J., Flores-Hernandez A.A., Colin J., 2019. Optimal design for high-performance passive dynamic vibration absorbers under random vibration, Engineering Structures, 195, 469–489. BarredoE. LariosJ.G.M. MayenJ. Flores-HernandezA.A. ColinJ. 2019 Optimal design for high-performance passive dynamic vibration absorbers under random vibration Engineering Structures 195 469 489 10.1016/j.engstruct.2019.05.105 Search in Google Scholar

[17] Laurentiu M., Agathoklis G., 2014. Optimal design of novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems, Probabilistic Engineering mechanics, 38, 156–164. LaurentiuM. AgathoklisG. 2014 Optimal design of novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems Probabilistic Engineering mechanics 38 156 164 10.1016/j.probengmech.2014.03.007 Search in Google Scholar

[18] Jacquot R.G., 2001. Suppresion of random vibration in plates using vibration absorbers, Journal of Sound and Vibration, 248 (4), 585–596. JacquotR.G. 2001 Suppresion of random vibration in plates using vibration absorbers Journal of Sound and Vibration 248 4 585 596 10.1006/jsvi.2001.3558 Search in Google Scholar

[19] Shum K.M., 2015. Tuned vibration absorbers with nonlinear viscous damping for damped structures under random load, Journal of Sound and Vibrations, 346, 70–80. ShumK.M. 2015 Tuned vibration absorbers with nonlinear viscous damping for damped structures under random load Journal of Sound and Vibrations 346 70 80 10.1016/j.jsv.2015.02.003 Search in Google Scholar

[20] Javidialesaadi A., Wierschem N.E., 2018. Optimal design of rotational inertial double tuned mass dampers under random excitation, Engineering Structures, 165, 412–421. JavidialesaadiA. WierschemN.E. 2018 Optimal design of rotational inertial double tuned mass dampers under random excitation Engineering Structures 165 412 421 10.1016/j.engstruct.2018.03.033 Search in Google Scholar

[21] Yang F., Sedaghati R., Esmailzadeh E., 2021. Vibration suppression of Structures using tuned mass damper technology: A state-of-the-art review, Journal of Vibration and Control, https://doi.org/10.1177/1077546320984305. YangF. SedaghatiR. EsmailzadehE. 2021 Vibration suppression of Structures using tuned mass damper technology: A state-of-the-art review Journal of Vibration and Control https://doi.org/10.1177/1077546320984305. 10.1177/1077546320984305 Search in Google Scholar

[22] Frahm H., 1911. Device for damping vibrations of bodies, United States Patent, 3576–3580. FrahmH. 1911 Device for damping vibrations of bodies United States Patent, 3576–3580. Search in Google Scholar

[23] Ormondroyd J., Den Hartog J.P., 1928. The theory of the dynamic vibration absorber, Transactions of ASME, Journal of Applied Mechanics 50 (7), 9–22. OrmondroydJ. Den HartogJ.P. 1928 The theory of the dynamic vibration absorber, Transactions of ASME Journal of Applied Mechanics 50 7 9 22 Search in Google Scholar

[24] Anh N. D., Nguyen N. X., Hoa L. T., 2013. Design of three-element dynamic vibration absorber for damped linear structures, Journal of Sound and Vibration 332, 4482–4495. AnhN. D. NguyenN. X. HoaL. T. 2013 Design of three-element dynamic vibration absorber for damped linear structures Journal of Sound and Vibration 332 4482 4495 10.1016/j.jsv.2013.03.032 Search in Google Scholar

[25] Asami T., Nishihara O., Baz A.M., 2002. Analytical solutions to H_∞ and H₂ optimization of dynamic vibration absorbers attached to damped linear systems, Transactions of ASME Journal of Vibration and Acoustics;124(2), 284–295. AsamiT. NishiharaO. BazA.M. 2002 Analytical solutions to H_∞ and H₂ optimization of dynamic vibration absorbers attached to damped linear systems Transactions of ASME Journal of Vibration and Acoustics 124 2 284 295 10.1115/1.1456458 Search in Google Scholar

[26] Nishihara O., Asami T., 2002. Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors), Transactions of ASME Journal of Vibration and Acoustics 124(4), 576–582. NishiharaO. AsamiT. 2002 Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors) Transactions of ASME Journal of Vibration and Acoustics 124 4 576 582 10.1115/1.1500335 Search in Google Scholar

[27] Sims N. D., 2007. Vibration absorbers for chatter suppression: a new analytical tuning methodology, Journal of Sound and Vibration 301 (3), 592–607. SimsN. D. 2007 Vibration absorbers for chatter suppression: a new analytical tuning methodology Journal of Sound and Vibration 301 3 592 607 10.1016/j.jsv.2006.10.020 Search in Google Scholar

[28] Shen Y., Peng H., Li X., Yang S., 2017. Analytically optimal parameters of dynamic vibration absorber with negative stiffness, Mechanical Systems and Signal Processing 85, 193–203. ShenY. PengH. LiX. YangS. 2017 Analytically optimal parameters of dynamic vibration absorber with negative stiffness Mechanical Systems and Signal Processing 85 193 203 10.1016/j.ymssp.2016.08.018 Search in Google Scholar

[29] Issa J. S., 2013. Vibration absorbers for simply supported beams subjected to constant moving loads. Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics 226(4):398–404. IssaJ. S. 2013 Vibration absorbers for simply supported beams subjected to constant moving loads Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics 226 4 398 404 10.1177/1464419312450652 Search in Google Scholar

[30] Samani F. S., Pellicano F., Masoumi A., 2013. Performances of dynamic vibration absorbers for beams subjected to moving loads. Nonlinear Dynamics 72(1–2). SamaniF. S. PellicanoF. MasoumiA. 2013 Performances of dynamic vibration absorbers for beams subjected to moving loads Nonlinear Dynamics 72 1–2 10.1007/s11071-013-0853-4 Search in Google Scholar

[31] Crandall S.H. and Mark W.D., 1963. Random Vibration in Mechanical Systems. New York: Academic Press. CrandallS.H. MarkW.D. 1963 Random Vibration in Mechanical Systems New York Academic Press Search in Google Scholar

[32] Soong T.T., Grigoriu M., 1993. Random vibration of mechanical and structural systems, PTR Prentice-Hall, Inc. SoongT.T. GrigoriuM. 1993 Random vibration of mechanical and structural systems PTR Prentice-Hall, Inc Search in Google Scholar

[33] Lin Y.K., Cai G.Q., 1995. Probabilistic structural dynamics: Advanced theory and applications, McGraw-Hill. LinY.K. CaiG.Q. 1995 Probabilistic structural dynamics: Advanced theory and applications McGraw-Hill Search in Google Scholar

[34] Solnes J., 1997. Stochastic processes and random vibrations, John Wiley & Sons. SolnesJ. 1997 Stochastic processes and random vibrations John Wiley & Sons Search in Google Scholar

[35] Rystwej A., Śniady P., 2007. Dynamic response of an infinite beam and plate to a stochastic train of moving forces, Journal of Sound and Vibration, 299, 1033–1048. RystwejA. ŚniadyP. 2007 Dynamic response of an infinite beam and plate to a stochastic train of moving forces Journal of Sound and Vibration 299 1033 1048 10.1016/j.jsv.2006.08.009 Search in Google Scholar

[36] Śniady P., 1989. Dynamic response of linear structures to a random stream of pulses, Journal of Sound and Vibration, 131, 1, 91–102. ŚniadyP. 1989 Dynamic response of linear structures to a random stream of pulses Journal of Sound and Vibration 131 1 91 102 10.1016/0022-460X(89)90825-0 Search in Google Scholar

[37] Śniady P., 2000. Fundamentals of stochastic structure dynamics (in Polish), Oficyna Wydawnicza Politechniki Wrocławskiej. ŚniadyP. 2000 Fundamentals of stochastic structure dynamics (in Polish) Oficyna Wydawnicza Politechniki Wrocławskiej Search in Google Scholar

[38] Wolfram Mathematica 12. Wolfram Research ©Copyright 1988–2021. Wolfram Mathematica 12. Wolfram Research ©Copyright 1988–2021 Search in Google Scholar

[39] Podwórna M., Grosel J., Śniady P., 2021. Absorbers impact on the reliability of structures subjected to random vibrations, IOP Conference Series: Materials Science and Engineering 1015. PodwórnaM. GroselJ. ŚniadyP. 2021 Absorbers impact on the reliability of structures subjected to random vibrations IOP Conference Series: Materials Science and Engineering 1015 10.1088/1757-899X/1015/1/012003 Search in Google Scholar

[40] Warburton G.B., 1982. Optimum absorber parameters for various combinations of response and excitation parameters. Earthquake Engineering and Structural Dynamics 10, 381–401. WarburtonG.B. 1982 Optimum absorber parameters for various combinations of response and excitation parameters Earthquake Engineering and Structural Dynamics 10 381 401 10.1002/eqe.4290100304 Search in Google Scholar