DYNAMIC RESPONSE CONTROL FOR A MASS-SPRING- VISCOUS DAMPER SYSTEM BY USE OF AN ADDITIONAL ELECTRO-MECHANICAL IMPEDANCE

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1 U.P.B. Si. Bull., Sis D, Vol. 75, Iss. 4, 3 ISSN DYNAMI ESPONSE ONTO O A MASS-SPING- VISOUS DAMPE SYSTEM BY USE O AN ADDITIONA EETO-MEHANIA IMPEDANE Mihl And MÎŢIU, Dnil OMEAGA Th pp psns n invsigion onning h possiiliis o onol h hvio of dyni viion so onsising of ss-sping-visous dp wih ps //, y inging in is suu n lo-dyni uo nd n lil ipdn. Th pinipls nd h hods y whih, hough hngs of hnil nd/o li ps, n ffiv onol of h dyni spons of h sys n hivd sudid nd h suls psnd. Kywods: dyni so, lo-dyni uo, dyni onol.. Inoduion A his on h ondud woldwid shs nd sudis ld o h wy in whih h dyni spons of hnil o lohnil syss o h viion o nl siuli n onolld. Mos of h n o dl wih h hods h us, inly, so lo-hnil oponns of ddiionl syss h ingd ino h sys o onolld. Thus, ypil ppoh of h dyni spons onol of sys is psnd y h wy, in whih h opny EDAT TEHNOOGIES [] d "s suus" h diinish h ff of indud viion fo n o whos ss us isold in s of nl viion influns. Nw hods nd pinipls fo h onol of dyni spons of hnil o lo-hnil opl syss sudid y h opny ONEA (Offi Nionl d Euds hhs Aéospils) []. Th psn pp oninus h pvious sh in h fild of onol syss nd pfon uning of iv nd/o si-iv syss fo h isolion of viion ffs [4], [5]. Th pp psns h hoil sps of onol possiiliis gding h hvio of dyni so sys onsising of sping-ss-visous PhD. sudn, Dpn of Mhonis nd Pision Mhnis, uly of Mhnis nd Mhonis Enginning, Univsiy POITEHNIA of Buhs, oni, -il: ihl.iiu@yhoo.o. d, uly of Mhnis nd Mhonis Enginning, Univsiy POITEHNIA of Buhs, oni, -il:og_dnil@yhoo.o

2 5 Mihl Mîţiu, Dnil ogă dp wih p //, y inging in is suu n lo-dyni uo nd n lil ipdn.. Th si ss-sping-visous dp wih p // To y ou h poposd sudy ss-sping-visous dp sys, wih p //, is onsidd (ig. ), und h ion of nl fos h h ss o ov. ig. Th shi dig of h ss-sping- visous dp sys: - ss o isold, - sping onsn, - onsn of visous dping, X oving of s sys, X displn of ss, X - liv ss-s displn.. To onol h dyni spons of h sys (h spons o h ion of nl fos on h sys o h spons o s iion), n us h following hods: hnging h sys ps (//) y di ion on h hnil oponns (hod diffiul o pply in pi); inoduion of hnil ipdn in h sys ( dyni so)[3]; i is n si-o-ipln hod u dos no llow dusn duing opion of h sys; indi hng of h sys ps (//) y ion on h lil oponns onnd o h inls of n lodyni uo, ound in plll wih h visous dp nd sping (wy si o pply in pi, u wih liiions) [4], [5]; n ipovn of h dyni so spons, h hod nlyzd in his il. In his pp is psnd h hoil sudy pfod on h hod nd h ffivnss of h onol of dyni spons of h sys ( / / ) y plugging in n ddiionl hnil ipdn hivd only wih lns suh s hos h fo h si sys (ddiionl sss, spings nd visous dps) h up dyni so nd opd wih noh onol hod, whih inodus in h sys nw dyni so sd on n lodyni uo wih ddd nd nl li iui, whih nls dyni spons onol hough hng of lil ps.

3 Dyni spons onol fo ss-sping-visous dp sys... 5 Th os sipl s, ls fo hoil poin of viw, is psnd y h inoduion in h sys of n ddiionl ipdn psnd y h ss supl. To oin V, und h ion of nl fos on h ss, i is nsy o hv supl. This siuion n hivd only y dding ddiionl dvis o s n infini wigh, ls fo piul fvny o pulsion, ion quivln o h ddiion of n ddiionl ipdn () wih ( ). 3. Th dyni spons onol using opl hnil ipdn Th ddiionl hnil ipdn n hivd wih sipl hnil sys onsising of ss-sping-visous dp wih ps / /, oonly lld dyni so (ig. ). ig. Th onol of h dyni spons fo hnil sys wih sys sd on ddiionl hnil sys gning ddiionl hnil ipdn supli. Addiionl sys is hizd y ss, sping onsn nd dping onsn of h visous dp. Th ddiionl sys n qud wih n quivln ss wih opl vlu [3] (fig. 3): h () Th following noions d: ; n ; β n ; ξ n ; ()

4 5 Mihl Mîţiu, Dnil ogă ig. 3 Equivln of h sys hizd y ps / / wih opl ss h If susiuions d, h following lion is oind: ξ β h (3) ( β ) ξ β I us n ino oun h f h: h θ θ od ul h h (4) l igin h odul Th gph of h funion od ul( β ), suling fo h siulion d y using h Ml ppliion is shown in h figu 4. ig. 4 Gph funion h dsis h lion wn h io wn h odul of h quivln ss nd h ddiionl ss nd h io / n. To oin h ondiion of infini ss, quis null dping in h dyni so sys suu:, i ζ, whih lds o: h (5) β

5 Dyni spons onol fo ss-sping-visous dp sys Th only soluion o g n ddiionl infini ss fo in iil fquny is o slish null dping fo h suu of h dyni so h s i wih h dvlopn of sonn fquny of h dyni so qul o h iil fquny of dyni iion. P dusn fo h sys hizd y h ps / /, in od o nsu opiu woing fquny dpion of h dyni so o h in fquny is diffiul, oh fo hoil poin of viw s wll s pil, spilly if i is dsil h his dusn is pfod duing sys opion. Anoh possiiliy of dusn nd opiizion of h sys's opion is psnd y h dusn of sys ipdn, oind y h inoduion of lo-dyni uo in plll wih h si sping nd visous dp nd n nl lil iui onnd o h inls of h lo-dyni uo. This iui n usd o onol lo-hnil ps of h sys (Mhih,) [4], [5]. This hod is sois o diffiul o oplish du o h ovll ondiions nd h nssiy of fiing h uo o h ss nd lso h s of h sys. Th hn of hnil so o h sys is o onvnin us i is fid only on oil ss. Th niond disdvng of hnil so (diffiuly dusn duing opion fo vil iil fquny) n ovo y oining wo ids: h inoduion of hnil so in h sys nd h us of n lodyni uo fo indi gulion of hnil ps of dyni so. 4. guling h opion of h sys // hough h inoduion of n lo-dyni uo in plll wih h sping nd visous dp On onsidd h s-up psnd in h following figu, in whih h lo-dyni fo ws nod wih d. ig. 5 Inoduion of n lo-dyni uo in plll wih h sping nd visous dp.

6 54 Mihl Mîţiu, Dnil ogă If is h fo h s on suppo (fn), h following lion is oind: d (6) Th quion of oion fo h ss is in his s: d (7) Th lo-dyni fo is: d V U l B i l B (8) Tol fo ing on h fn os: (9) In h ov lions, h psns h oniuion of h hnil sys nd h psns h oniuion of lo-hnil. o will hv h pssion: () Th quivln ss h of h dyni so nd of h lil sys n pssd using h lionship: h () If h nl ipdn is psnd y sisn : () hn is ff is siil o h hng of h dping onsn of h visous dp: * (3)

7 Dyni spons onol fo ss-sping-visous dp sys If h nl ipdn is psnd y n ipdn : (4) hn is ff is siil o h hng of h lsi sping onsn : * (5) If n - plll iui is inodud h following lion is oind: (6) siuion in whih siulnously hng of h vlus nd ous. If h lil ipdn is (opn inl) hn sul: h (7) so h lil sys hs no influn. Th inoduion in h iui of h nl ipdn of ondns hs spil ff. Th quivln ss is in his s: h (8) nd fo: (9) Th fis osponds o h inoduion of sss * insd of : * () u on us ino oun lso h sond in h fo pssion, whih dos no llow only hng of h ddiionl ss of h dyni so y odifying h vlu of h pio onnd oss h uo. Adusing h pio vlu n hlp us o hiv h ondiion fo "infini ss" (l 9), lding o ipos h following ondiions: () Th ov lions indi h piy vlu fo h pio whih povids dyni so dusn fo spifi iion fquny,

8 56 Mihl Mîţiu, Dnil ogă wihou hving o dus hnil ps. Adusn is possil only if h vlu suling fo is posiiv, spivly h iil fquny ds h sonn fquny of dyni so. Th l s is h of n lil sisn nd n indun onnd in sis, du o oil of lodyni uo, o whih i is onnd, lso in sis, n nl ipdn. Th quivln ss pssion os: h () If n nl ipdn onsising of pio wih h li piy is onsidd, h vlu of h lil ipdn is: (3) nd so: h (4) Th ondiion h is fulfilld if only if h dnoino of h ov lionship is zo: (5) Th ov lionship n fulfilld only if: (6) Wih h noion: (7) on oins, y pling:

9 Dyni spons onol fo ss-sping-visous dp sys (8) o h ov lions h following ss n idnifid: s, whn, fo whih: (9) If, h soluion is only so β (dyni hnil so) nd h (lodyni uo wih h inls in i) nd. Th soluion is no onvnin us i nls h ff of lodyni uo nd inins only hnil so, nondusl. s, whn nd, fo whih: (3) o h fis quion i follows h so dpiion β, i.. puly hnil dusn nd fo h sond quion, i yilds h ondiion, quivln o n lodyni uo wih h inls in i. As in h pvious ss, h soluion is no onvnin us i nls h ff of lodyni uo nd inins only hnil so, non-dusl. s 3, whn nd, fo whih so, psning h lionship wn h oponn of h lil dping ond nd h hnil sys. s 4, whn nd, fo whih: ) ( (3) Sin in h sond quion ll s posiiv, hi su n no zo, whih shows h his s n no n ino oun.

10 58 Mihl Mîţiu, Dnil ogă As onsqun, fo h l sys wih n lodyni uo (wih lil sisn nd indun of oil), us dding n li pio o h inls povids h ondiion fo h dyni so if h innl sisn of h oil is uh dud nd h nl piy is dusd o sisfy h ondiion indid in s 3. Th sys n op in wo ods: on od puly hnil wih h hnil so und o h iil fquny nd hving h nl li iui opn nd h sond od wih losd nl li iui nd nl piy dusn (g y inoduing ddiionl pios in h iui, using lys) o dp h dyni so iil fquny viion. Modling nd siulion of h hvio fo hnil sys [6] on whih is fid hnil so whih onins n lodyni uo hving n nl li iui onnd o h inls nd dfind y n lil ipdn n hivd y: - quivln lil iuis fo h syss ing sudid nd h us of ddid sofw fo h siulion of h lil iuis (fig. 6); - odling of sys opion using Ml Siulin pg (fig. 7), sing fo h quions: s v d ( v v ) ( v v ) s s U (3) s v ( v v ) s i i ( s) i ( v v ) ( v v ) d s ig. 6 Th quivln iuis of h syss involvd in h onol of h dyni spons. On dnos wih v h vloiy of ss on wih h dyni so is fid nd wih v h solu vloiy of dyni so ss.

11 Dyni spons onol fo ss-sping-visous dp sys ig. 7 Siulin siulion sh fo h sys, lodyni uo nd dyni so. In fig. 8 h dyni spons funion [7] of h sys // wih dyni so und o pulsion of d/s is psnd (h ps fo h dyni so,. g, ). ig. 8 Bod pliud dig fo n ny poin, n i poin v o, nd nl lil volg U. In ig. 9 h spons of h sys is psnd, onsiding h psn of h lodyni uo nd high sisn of oil. Th lil ps :.56 H, 4* -6, 8 Ω. Th ff of h lil iui is ngligil [8]. Wih h signifin duion of lil

12 6 Mihl Mîţiu, Dnil ogă sisn h ff of h lil iui, whih s li nw dyni so n sn (fig.). ig. 9 Bod pliud dig fo n ny poin, n i poin v o, 4, nl lil volg U nd.5 ig. Bod dig fo h sys, dyni so nd lodyni uo, wih. 5. onlusions Th us of dyni so o onol h dyni spons of hnil sys liv o fn hs n nown fo long i. Dyni so is usully onsidd s n ddiionl ss quivln wih opl vlu. I is dsignd o h ngy of viion of h fn nd o dissip o so his ngy in is hnil suu. Usully, h dsign of dyni so dpnds on ipdn of fn sys nd h fqunis whih signifin ion is dsid

13 Dyni spons onol fo ss-sping-visous dp sys... 6 (whih y diff fo h sonn fqunis of h suu o whih i is hd). Any hng in hnil ipdn of h fn o on h fquny who podus o iion nd dping of viion is dsid quis h hnging of on of h hnil ps of h dyni so (ss, siffnss, visous dping), ly diffiul o d duing sys opion. In h il i ws psnd o onvnin soluion y insing n lodyni uo in h dyni so suu nd hing o h uo inls n nl li iui. Thus, i is possil o oin hng of quivln hnil ps of h ssly: hni so lodyni uo lil iui y hnging h lil ps of h iui, uh si o hiv in s of onsuion nd possily o iplnd s n dpiv sys, onolld y ioonoll whih n nlyz h fn viion nd onol h hng of on piul p vlu o li iui oponn (wih h id of iuis onsising of nwos of lil oponns h o insd o ovd fo h lil iui). Th soluion hs liiions du o h nd fo lil sisn o ound zo fo h nl li iui inluding h oil. Pilly i is nssy fo h lil dyni so h s opion ondiion s fo hnil so: h nllion of innl ngy dissipion. A soluion y h inoduion of n iv sys l o inodu li ngy, y ing ion onnion wn p v nd h lil onol p U, onsidd null in his sudy. This is h su o fuu dvlopns. E E E N E S [] [] hp:// [3] yil M. His, HAIS Sho nd viion hndoo, ifh Ediion, dio MGw- Hill, Nw Yo, 5 [4] Mihl And Mîţiu, Niol Alndsu, Dnil ogă, unţiu l, Epinl sudy of n lohnil sys usd o onol h hnil oiliy, onin viw of Pision Mhnis, Opis & Mhonis n. 4 /, pp [5] Mihl And Mîţiu, Niol Alndsu, Modling nd siulion of siiv nd iv onol syss fo h isolion of viions, onin viw of Pision Mhnis, Opis & Mhonis n. 4 /, pp [6] Auo lii is, du Moiu-Gligo, Th siulion of viion nuion in h hnd- sis, U.P.B. Sinifi Bullin, Sis D, Vol. 75, Iss. 3, 3.

14 6 Mihl Mîţiu, Dnil ogă [7] Dnil J, Inn, Viion wih onol, John Wily & Sons, Th Aiu, Souhn G, his, Ws Suss, PO9 8SQ, Englnd, 6. [8] Andé Puon, sponsiv Syss fo Aiv Viion onol, NATO Sin Sis, vol 85. Kluw Adi Pulishs, P.O. Bo 7, 33 AA Dodh, Th Nhlnds,