Observer based adaptive tuned mass damper with a controllable MR damper

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1 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 Porto, Portugl, 30 June - July 014 A. Cunh, E. Cetno, P. Ribeiro, G. Müller (ed.) ISSN: ; ISBN: Oberver bed dptive tuned m dmper with controllble MR dmper Mehmet Ali Eroglu 1, Neil Sim 1 1 Deprtment of Mechnicl Eng., Fculty of Engineering, Univerity of Sheffield, S1 3JD Sheffield, UK emil: mehmetlieroglu@gmil.com, n.im@heffield.c.uk ABSTRACT: Thi pper preent n oberver bed lineried control of emi-ctive tuned m dmper (OSTMD) with controllble mgnetorheologicl (MR) dmper. The propoed model replce pive dmping element with controllble emi-ctive dmper to emulte controllble tiffne nd controllble dmping, which ditinguihe it from the clicl pive tuned m dmper (TMD). A reult, the frequency of the tuned m dmper could be tuned in rel time to chnging frequencie of the min tructure. Mny emi-ctive control lgorithm meured the dmper force with lod-cell, nd the piton diplcement of the dmper, e.g. with liner vrible differentil trnformer (LVDT). However, the implementtion of force trnducer nd LVDT enor re difficult, nd penive in prctice. They lo incree the complity of ytem. In thi tudy, by propoing non-liner oberver, thee dt re etimted by uing two imple, low cot ccelerometer which re plced on the tructurl m nd on the tuned m. The oberver gin mtrix i evluted by uing pole plcement method bed on Luenberger theory. Both the dmping nd the nturl frequency re tuned ccording to clicl theory. The propoed theory i vlidted by numericl nd perimentl teting under the brodbnd cittion nd the reult re compred to pive tuned m dmper which i preciely tuned to the min tructure. The comprion how tht, the oberver bed lineried emi-ctive tuned m dmper with controlled MR dmper i ble to reduce the vibrtion mplitude much the optiml pive tuned m dmper. KEY WORDS: Semi-ctive tuned m dmper; Oberver. 1 INTRODUCTION Exceive vibrtion h been common problem throughout engineering hitory which cn reult from vriety of ource; humn body motion, rotting, ocillting nd impcting mchine, wind flow, erthquke induced vibrtion, rod trffic, rilwy trffic, contruction work etc. [1]. Often the mot effective nd economic wy to reduce vibrtion i to pply n dditionl dynmic ytem t dicrete point on the iting tructure, to chnge the ytem dynmic in deired wy []. Simple m-pring-dmper ytem ttched to elected point of the vibrting tructure ( een in Figure 1- ()), re one mple. They re clled tuned m dmper (TMD), tuned vibrtion borber [3], or vibrtion neutrlier []. Hitoriclly, the firt time tuned m dmper were ued to reduce the rolling motion of hip by Frhm in 1911 [4]. Lter, TMD were implemented to reduce the mplitude of the ingle degree of freedom ytem by Ormondroyd nd Den Hrtog [5], nd Brock [6]. Den Hrtog developed cloed form preion of optimum dmper prmeter which re frequency rtio nd dmping rtio of the TMD [7]. Thee preion re only for un-dmped min ytem with ingle degree of freedom. Lter, dmping in the min ytem w included by everl reercher [8-9]. To ummrie, imple optimum olution to ceive vibrtion problem uing pive tuned m dmper hve been widely invetigted nd implemented on rel tructure [10]. k k m m c c F k k m m c MR Dmper emulting the controllble pring tiffne nd controllble vicou dmping. () (b) Figure 1. Lumped prmeter model of tuned m dmper ytem. () Clicl pive TMD, (b) dptive TMD with n MR dmper, modified from [11]. However, ll thee propoed tuning method for optiml pive TMD ytem umed tht the nturl frequency nd tructurl m re known nd do not chnge. If the modl propertie of the min tructure re chnged (e.g. due to environmentl effec fter the TMD h been intlled, the performnce cn be ignificntly reduced [1-13]. Thee environmentl effect could be the time-vrying py lod, etimtion error or temperture chnge. All thee problem will reult in the de-tuning of the pre-tuned m dmper. A olution to thi generic de-tuning problem, mny dptive TMD control concept hve been propoed to develop new 1601

2 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 deign nd concept by controlling the propertie of the TMD in rel time to mtch the chnging propertie of tructure. Such concept nd their control were ummried by Fico nd Adeli [14]. Due to high power requirement, pene nd fil-fety problem of the ctive ytem, dptive tuned m dmper ytem re deigned motly bed on emi-ctive pproche [15]. After even decde of firt pive TMD dmper implementtion, Hrovt et l. introduced the concept of emi-ctive TMD for wind-induced vibrtion in high rie building [16]. Semi-ctive dmper require impler hrdwre nd hve lower power requirement thn ctive ytem, thu reducing opertionl cot. Thee device cn provide vrible dmping nd/or tiffne nd hve been ued for vibrtion reduction of mechnicl nd civil engineering tructure. Semi-ctive tuned m dmper concept hve conidered tuned m, tuned pive pring, or controlled emi-ctive dmper. A vriety of emi-ctive dmper hve been propoed, uch piezo tck [17], ctive mrt mteril (hpe memory lloy) [18], piezoelectric mteril [19], controllble friction device [0], nd mgnetorheologicl (MR) dmper [1-]. Weber et. l. preented emi-ctive pproch where rottionl MR dmper w ued to emulte both controllble dmping nd tiffne force under hrmonic cittion [15]. In ddition to thi, the me uthor tended thi numericl work by perimentl implementtion of propoed theory on lbortory footbridge, uing ccelerometer nd force trnducer to implement force trcking control [11]. They were ble to reduce the vibrtion mplitude between 38% to 63% reltive to pive TMD ytem, but they did not invetigte the performnce of propoed ytem under rndom or brodbnd cittion which i more-likely to be relitic ce. In ddition the ue of force trnducer lo incree the complity of the ytem. In thi tudy, thee two drwbck hve been plored uing n oberver bed lineried emi-ctive tuned m dmper ytem. The lumped prmeter/block digrm model of thi ytem i hown in Figure. Figure. Oberver be emi ctive tuned m dmper control cheme. Thi pper offer decription of the propoed oberver bed lineried control of emi-ctive tuned m dmper (OSTMD), long with dynmic nlyi of the optiml pive tuned m dmper (OPTMD) tht i bed upon numericl imultion (optiml tuning). Before introducing OSTMD, thi pper decribe clicl pive tuned m dmper to help ditinguih the two ytem. Ltly, thi pper ummrize the dynmic performnce of the oberver be tuned ytem nd ugget the bet control method for the propoed oberver bed emi-ctive ytem, bed upon the numericl reult. NUMERICAL MODELLING AND OPTIMAL TUNING A clicl model of force-cited ( F ) pive TMD configurtion i hown in Figure 1-(). The min tructure i coupled with clicl pive vibrtion borber, nd the m of the tructure nd borber re defined by m nd m with their correponding diplcement x nd x, repectively. The borber pring (k ) nd dmper (c ) re mounted on the tructure. The tiffne nd dmping of the tructure re repreented by k nd c, repectively. The eqution of motion of the force-cited pive TMD in mtrix form i; m 0 & c c c + k k k x = F (1) 0 m & c c k k x 0 The tedy tte olution of eqution 1 cn be obtined; X m + c+ k = () F m + c + k )( m + ( c + c ) + k + k ) ( c + k ) t ( X c+ k = (3) F ( m + c+ k)( m + ( c + c ) + k + k) ( c+ k) By defining the following prmeter μ = m m, M rtio (Aborber m/min m) δ = F k, Sttic deflection of the ytem ω = 0.5 ( k m ) ω = ( k m) ς = c 0.5 ( mω ) ( mω, Nturl frequency of the min tructure, Nturl frequency of the borber, Dmping rtio of min tructure ς = c ), Dmping rtio of borber g = ω ω, Rtio of nturl frequencie r = ω ω, Forced frequency rtio η = c ( m ω ), Lo fctor of borber η = c ( mω ), Lo fctor of min tructure the finl trnmiibility eqution for the forced-cited ytem become; X ( g r + ς grj) = δt ( r + ς rj+ ς μgrj+ 1+ μg ) + ( r + ς grj+ g ) μ( ςgrj+ g ) (4) X ( g + ς grj) = δt ( r + ς rj+ ς μgrj+ 1+ μg ) + ( r + ς grj+ g ) μ( ςgrj+ g ) (5) The trnmiibility Eqution 5 provide the men of tuning TMD uing Med [6] decription. The trget of the technique i to minimize the mximum trnmiibility. 3 SEMI-ACTIVE TMD DESIGN The propoed oberver be emi-ctive tuned m dmper (TMD) model replce pive dmping element with controllble emi-ctive dmper to emulte controllble tiffne nd controllble dmping, which ditinguihe it 160

3 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 from the clicl pive ytem. Figure 1-() how conventionl pive TMD model, nd the propoed emictive tuned m dmper model i hown in Figure 1-(b). A controllble dmper, uch n MR dmper, i the key element for the propoed ytem. It cn provide wide dynmic force rnge, cn offer rel-time control environment t low power, nd cn be quite cot-effective. The unified model of MR dmper [3] i choen for thi numericl tudy, due to not only it i flibility in the choice of the model dmping function, but lo the performnce of the unified model h been proved by perimentl teting of Lord Corportion RD hort troke MR dmper by Btterbee nd Sim [4] under the brodbnd mechnicl cittion. Incorporting thi vertile dmper into the propoed model will ignificntly enhnce it performnce, combining the benefit of both pive nd ctive ytem. The new ytem i nticipted to urp the performnce of clicl pive TMD in reducing the mximum vibrtion level of the primry tructure nd robutly dpt to the primry ytem prmeter chnge. Figure 3 w ued to derive the dynmic eqution of motion for the emi-ctive model: m 0 & + + c 0 + k k k x + 1 F F = (6) MR 0 m & 0 0 k k x 1 0 Where F MR i the force produced by the emi-ctive mgnetorheologicl dmper. Eqution 6 will be ued in the development of the numericl model of the emi-ctive TMD. Figure 3. Lumped-prmeter model of propoed emi-ctive tuned m dmper model, where emi-ctive element i the mgnetorheologicl dmper. 4 OBSERVER DESIGN The liner nd non-liner oberver deign re dicued in Chpter 3 nd the me deign theory will be ued to develop non-liner oberver for emi-ctive tuned m dmper ytem. In thi tudy the min focu w to evlute the performnce of the oberver be feedbck linerition of the MR dmper ce tudy. Therefore, the purpoe of the oberver w to be ble to etimte the bolute velocitie of the borber m nd tructurl m for the propoed control lgorithm, nd etimtion of the MR dmper force for feedbck linerition. Referring to Figure 3 the eqution of motion 6 w ued to deign the bic tte mtrice, where the tte pce model of the ytem i; ( = Ax( + Bu + Gw( (7) y( = C x( + Du + Hw( The tte vector i choen x = [ x ] ' 1 x x3 x4, where x1 = x x, x = x, x 3 =, nd x 4 =. Here y i the mtrix of meured ccelertion of borber m nd tructurl m, y = [&& x ] ' & x, w ( ) = F( ) i the ytem diturbnce nd ytem control input i u = FMR. Thu the ytem tte pce repreenttion i; x k x = u + ( ) 1 0 w t m m 3 x 3 (8) x k k c 1 & 4 0 x4 m m m m m k x x m x && m = + u + w( x && k k c x 3 m m m m x m 4 The following dynmicl ytem 9 i conidered n oberver. ˆ = Axˆ + Bu + Lz + GFˆ yˆ = C xˆ + Du + HFˆ (9) F = m & x Fˆ MR + kxˆ + k( xˆ xˆ ) cxˆ & (10) Where z = y yˆ, xˆ i the oberver tte, ŷ i the oberver output, Fˆ i the etimted diturbnce force ignl (Eqution 10) nd L i the oberver gin mtrix. The error between the ctul tte x nd the oberved tte xˆ i defined e = x xˆ (11) Where the dynmic of the tte etimtion error i then given by; e& = ( A LC) e + ( G LH )( F ˆ F) (1) Here L i the 4x oberver gin mtrix. Severl numericl tet reult howed tht with proper oberver mtrix the etimted diturbnce force nd the ctul diturbnce force mtched ech other. The pole plcement method w ued to evlute the oberver gin mtrix [5]. 5 MAIN PRINCIPLES AND CONTROL CONCEPTS The propoed pproch ue the feedbck linerition control of n MR dmper which h been propoed by The Univerity of Sheffield [6]. But the gol of thi pper i to emulte controllble vicou dmping nd/or controllble pring tiffne of the equivlent optiml pive ytem. A een in Figure, thi deired dmper force i produced by control concept prt, which ue the etimted tte of the ytem. Two type of control concept re propoed, which re plined ; 1603

4 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN Control concept 1 The firt control concept i intended to imply linerie the non-liner dynmic of the MR dmper, o it behve liner vicou dmper with vrying liner dmping. With reference to Figure 4 the etimted deired et-point force i; F ˆ = c ( ˆ ˆ ) deired MR Dmper emulting the controllble vicou dmping. tructure ccording to Med formule without ny contrint []. The teting tep re: Step 1; tuning of the borber, where the pring tiffne nd dmping level of the borber re optimlly tuned, nd the deired force i driven by the control concept 1. Step ; de-tuning of the min tructure. In thi tep, the ervice lod of min tructure i chnged by dding or removing me to/from min tructure. The new w tructurl m become, m = m + md, where m d repreent chnge of the ervice lod (which could be negtive or poitive). Auming the tructurl tiffne doe not chnge, the ytem frequency rtio chnge, nd thi led to the detuned ytem, hown in Figure 5. MR Dmper emulting the controllble vicou dmping. Figure 4. Lumped prmeter model of tuned m dmper configurtion. () pive tuned vibrtion borber, (b) Semictive MR bed tuned vibrtion borber (concept 1). Fˆ deired i the etimted deired dmper force, Where c i the optiml borber dmping, nd x & ˆ xˆ & ) i the reltive ( piton velocity. In thi concept, the MR dmper jut emulte the optiml vicou dmping of the pive tuned m dmper ytem. 5. Control concept In the econd control concept, the MR dmper trie to emulte the optiml vicou dmping nd optiml pring tiffne of the pive tuned m dmper ytem. In thi concept, optiml controllble pring tiffne i the um of the emulted controllble tiffne nd pive pring tiffne of the propoed ytem ( een in Figure 1-(b)) due to prllel intlltion of the pive pring nd controllble MR dmper. Thi will enble frequency tuning of the TMD ytem by ttempting to emulte the controllble poitive or negtive pring tiffne, nd controllble dmping force. Referring to Figure 1 -(b), the etimted deired et-point force i given by; Fˆ deired = c, optiml ( ˆ ˆ) + kdded ( xˆ xˆ ) Where xˆ xˆ ) i the reltive piton diplcement, nd ( k dded i the controllble tiffne which w umed to be zero for control concept 1. But, for the control concept, k dded = k, opt k Thee two control concept re invetigted by numericl nd perimentl teting. Tet re crried out in four tep with umption tht the borber m ( m ), borber tiffne ( k ), tructurl pring tiffne ( k ) nd tructurl dmping ( c ) do not chnge t ny tep of teting. Then, k, opt nd c, opt cn be djuted to the ctul frequency of the min Figure 5. Detuned lumped prmeter model of detuned m dmper configurtion. () pive detuned vibrtion borber, (b) Semi-ctive MR bed detuned vibrtion borber (tep ). In thi de-tuned ce, the dptive TMD with controllble MR dmper i lineried to emulte the pre-tuned vicou dmping of the optiml pive pre-tuned dmper ytem in concept 1. Step 3; retuning of the dmping. The nlyticl frequency retuning of the detuned borber i done ccording to Med optimition theory [] by uing the de-tuned tructurl m ( m w ) nd unchnged tructurl tiffne ( k ) een in Figure 5. MR Dmper emulting the controllble vicou dmping. Figure 5. Detuned lumped prmeter model of retuned m dmper configurtion. () pive retuned vibrtion borber, (b) Semi-ctive MR bed retuned vibrtion borber (tep 3). In thi tudy, it i umed tht, tructurl m of thi new detuned could be etimted by empiricl mode decompoition nd Hilbert trnform (EMD/HT) [7], or 1604

5 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 modified cro-correltion (MCC) method [13] in the rel-time control proce. So tht, the frequency of the borber ytem could be tuned to the ctul frequency of the min tructure by djuting k to k, nd c c, opt to opt. Thi retuned pive TMD ytem i clled idel dptive TMD nd pected to equlize the repone pek ccording to theory. In thi tep, jut vicou dmping w retuned o tht MR dmper only emulte the vicou dmping of the pive TMD nd etimted deired force w choen by control concept 1. Step 4; retuning of dmping nd tiffne. In thi tep retuning of the tiffne element of the pive TMD w done ccording to theory. The etimted deired force w choen by the control concept o tht the MR dmper i forced to emulte the retuned vicou dmping nd retuned pring tiffne of the new retuned idel dptive TMD een in Figure L = The min tructure with optiml pive TMD nd oberver bed dptive TMD with controllble MR dmper i imulted for vried de-tuned tructurl me w m = 0.5m,0.6m,...,1. 5m nd for ech m the tructure i cited with high-p filtered rndom white noie force ignl with bndwidth of 0-15 Hz of durtion 300 econd, for ech of the four tep. The firt ten econd of thi cittion force ignl i hown in Figure 7. MR Dmper emulting the controllble tiffne nd controllble vicou dmping. Figure 7. Firt ten econd of the cittion force ignl. Figure 6. Detuned lumped prmeter model of retuned m dmper configurtion. () pive retuned vibrtion borber, (b) Semi-ctive MR bed retuned vibrtion borber (tep 4). 6 NUMERICAL TESTING In thi tudy it i imed to implement the propoed oberver bed lineried control of n MR dmper ytem to the tuned m dmper problem, o tht MR dmper could emulte the controllble vicou nd pring tiffne of the pive TMD. Thi ection intend to numericlly invetigte thi cenrio. Prmeter of pive tuned m dmper ytem re given in Tble 1 with the m rtio of Tble 1. Prmeter of pive tuned m dmper. Prmeter Symbol Unit Vlue M of borber m kg 448 M of tructure m kg 1845 Aborber tiffne k Nm Structurl tiffne k Nm Aborber dmping c Nm Structurl dmping c Nm The tet reult will indicte the dmping potentil of the propoed theory. The entire ytem i olved in MATLAB/Simulink uing the ode4 (Runge Kut olver with fixed mpling frequency of Hz. The borber vicou dmper i replced by the numericl unified model of MR dmper where depending on the control concept; the MR dmper will trck the etimted deired force. 7 TEST RESULTS Frequency repone curve re ued to nlye the performnce of the ech control concept for numericl nd perimentl teting, which i evluted by uing tfetimte method of Simulink oftwre. The Figure 8 indicte tht the pive TMD i ble to equlie the pek t reonnce mplitude, ccording the Med theory (olid line, tep 1 tuning). But, the dmping performnce drmticlly decree with detuning of the ytem (dhed nd dh-dotted line, tep ). The oberver gin mtrix i thn evluted by uing pole plcement method uch tht; Figure 8. Frequency repone of the pive TMD, for optimlly tuned ce (tep 1, olid line) nd detuned ce (tep, dhed nd dh-dotted line). 1605

6 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 Alo it i cler tht from the Figure 8, if the detuning i done with increed tructurl m, the hot tructure i overdmped with n lmot un-dmped borber reonnce frequency; where if the detuning proce i done with decreed tructurl m, the reonnce frequency mplitude of the borber i over-dmped nd the tructurl reonnce i un-dmped. A pected, Figure 9 illutrte tht the mplitude reduction of the idel dptive TMD (with retuned dmping nd tiffne), depend on the frequency of the min tructure. of the borber, which h greter effect on the ytem repone. On the other hnd, if the ytem i detuned with decreed m, frequencie of hot tructure nd the borber move wy from ech other. Figure 11. Frequency repone of the dptive TMD with lineried MR dmper, for optimlly tuned ce (tep 1,olid line), nd re-tuned ce (tep 3, dhed nd dh-dotted line). Figure 9. Frequency repone of the idel dptive TMD, for tep 1 (olid line), nd tep 3 (dhed nd dh-dotted line). The frequency repone of the oberver bed dptive TMD with lineried MR dmper controlled ccording to concept 1 i hown in Figure 10. It i cler tht if the deired force gin i choen the vicou dmping c of the pive tuned m ytem, then it i pected to chieve the me mplitude reduction for tuned nd detuned ce of pive TMD. Compring Figure 8 nd Figure 10 clerly prove tht for the tep 1, the oberver bed dptive TMD with lineried MR dmper i ble to equlize the pek for tuned vlue (olid line). In ddition, lo for the tep (detuned ce), it i lo ble to follow the performnce of the pive TMD (dhed nd dh-dotted line). However, the im of thi tudy to invetigte tht whether the oberver bed lineried MR dmper cn emulte the controllble tiffne nd vicou dmping or not. To find thi out, the lt numericl tet tep 4 nd control concept re implemented, where the lineried MR dmper will emulte both dmping nd tiffne force. The reult re hown in Figure 1, where up to everl 100% mplitude reduction i chieved for the oberver bed dptive TMD with lineried MR dmper. Figure 1. Frequency repone of the dptive TMD with lineried MR dmper, for optimlly tuned ce (tep 1, olid line) nd re-tuned with controllble vicou dmping nd controllble tiffne ce (tep 4, dhed nd dh-dotted line). Figure 10. Frequency repone of the dptive TMD with lineried MR dmper, for optimlly tuned ce (tep 1,olid line), nd de-tuned ce (tep, dhed nd dh-dotted line). If the detuned ytem i retuned in tep 3 with control concept 1, then the oberver bed dptive TMD with lineried MR dmper improve the mplitude reduction compred to the pive TMD een in Figure 11. But, if the ytem i detuned with increed tructurl m the frequency of the detuned tructure get cloer to the frequency In concluion, thee numericl tet reult how tht the oberver bed linerition of n dptive TMD i ble to emulte the poitive or negtive tiffne in ddition to providing energy diiption in the TMD. REFERENCES 1. Bchmnn, H., Vibrtion problem in tructure: Prcticl guideline. 1995: Springer.. Med, D.J. nd D. Medor, Pive vibrtion control. 1998: Wiley Chicheter. 3. Koo, J. nd M. Ahmdin, A qulittive nlyi of groundhook tuned vibrtion borber for controlling tructurl vibrtion. Proceeding of 1606

7 Proceeding of the 9th Interntionl Conference on Structurl Dynmic, EURODYN 014 the Intitution of Mechnicl Engineer, Prt K: Journl of Multi-body Dynmic, (4): p FRAHM, H., Vibrtion of bodie. 1911, Google Ptent. 5. Ormondroyd, J., Theory of the dynmic vibrtion borber. Trnction of the ASME, : p Brock, J.E., A note on the dmped vibrtion borber. Journl of Applied Mechnic, (4): p. A den Hrtog, J.P., Mechnicl vibrtion. 1956: DoverPubliction. com. 8. Wrburton, G. nd E. Ayorinde, Optimum borber prmeter for imple ytem. Erthquke Engineering & Structurl Dynmic, (3): p IOI, T. nd K. IKEDA, On the dynmic vibrtion dmped borber of the vibrtion ytem. Bulletin of JSME, (151): p Hong, N., Y. Fujino, nd P. Wrnitchi, Optiml tuned m dmper for eimic ppliction nd prcticl deign formul. Engineering Structure, (3): p Weber, F. nd M. Mślnk, Frequency nd dmping dpttion of TMD with controlled MR dmper. Smrt Mteril nd Structure, 01. 1(5): p Occhiuzzi, A., M. Spizzuoco, nd F. Riccirdelli, Loding model nd repone control of footbridge cited by running pedetrin. Structurl Control nd Helth Monitoring, (3): p Hzr, B., et l., Re-tuning tuned m dmper uing mbient vibrtion meurement. Smrt Mteril nd Structure, (11): p Fico, N. nd H. Adeli, Smrt tructure: prt II hybrid control ytem nd control trtegie. Scienti Irnic, (3): p Weber, F., C. Boton, nd M. Mślnk, An dptive tuned m dmper bed on the emultion of poitive nd negtive tiffne with n MR dmper. Smrt Mteril nd Structure, (1): p Hrovt, D., P. Brk, nd M. Rbin, Semi-ctive veru pive or ctive tuned m dmper for tructurl control. Journl of Engineering Mechnic, (3): p Gell, D., G. Feltrin, nd M. Motvlli, Adptive tuned m dmper bed on pre-treble lef-pring. Journl of Intelligent Mteril Sytem nd Structure, (8): p Willim, K., G.-C. Chiu, nd R. Bernhrd, Dynmic modelling of hpe memory lloy dptive tuned vibrtion borber. Journl of ound nd vibrtion, (1): p Jing, G. nd L.M. Hngn. Semi-ctive TMD with piezoelectric friction dmper in floor vibrtion control. in Smrt Structure nd Mteril. 006: Interntionl Society for Optic nd Photonic. 0. Lin, C.C., G.L. Lin, nd J.F. Wng, Protection of eimic tructure uing emi ctive friction TMD. Erthquke Engineering & Structurl Dynmic, (6): p Koo, J.-H., M. Ahmdin, nd M. Setreh. Experimentl evlution of mgnetorheologicl dmper for emi-ctive tuned vibrtion borber. in Smrt Structure nd Mteril. 003: Interntionl Society for Optic nd Photonic.. Kng, J., H.S. Kim, nd D.G. Lee, Mitigtion of wind repone of tll building uing emi ctive tuned m dmper. The Structurl Deign of Tll nd Specil Building, (5): p Sim, N., N. Holme, nd R. Stnwy, A unified modelling nd model updting procedure for electrorheologicl nd mgnetorheologicl vibrtion dmper. Smrt Mteril nd Structure, (1): p Btterbee, D. nd N. Sim, Vibrtion ioltion with mrt fluid dmper: benchmrking tudy. Smrt Structure nd Sytem, (3): p Ogt, K. nd Y. Yng, Modern control engineering Sim, N., et l., Controllble vicou dmping: n perimentl tudy of n electrorheologicl long-troke dmper under proportionl feedbck control. Smrt Mteril nd Structure, (5): p Vrdrjn, N. nd S. Ngrjih, Wind repone control of building with vrible tiffne tuned m dmper uing empiricl mode decompoition/hilbert trnform. Journl of Engineering Mechnic, (4): p

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