Vibration Analysis of a Thick Ring Interacting with the Disk Treated as an Elastic Foundation

Transcription

1 Virios i Pysil ysems Vol. () Virio lysis o Ti ig erig wi e Dis Tree s lsi Foio isłw NOG Fly o Meil gieerig erois, zeszów iversiy o Teology l. Powsńów Wrszwy, zeszów, Pol og@rz.e.l Tesz MKOWK Fly o Meil gieerig erois, zeszów iversiy o Teology l. Powsńów Wrszwy, zeszów, Pol mrow@rz.e.l sr is sy e i le lexrl virio o i rig ierig wi Wiler oio is lyse o e sis o e lyil meril meo. Te ee o rory ieri ser eormio is ile. Te orml reqeies rl moe ses o e sysem virio re eermie. ieve resls re issse omre wi exerimel. F moels re ormle y sig NY oe. Keywors: i le virio, Timoseo s eory, i rig wi oio. roio Te rolems o i le lexrl virio o irlr rigs wi weel le s elsi oio i liio i severl ril rolems []. Te mel irlr rigs virio eory is resee i [5]. e rile [] ors lyse ree virio o rig ger y sig i rig eory. Free virio o Timoseo em e o lier elsi oio re ivesige i e er []. Te iroory sies rele o e sysems o e rigs wi weel le s e elsi oio re oe i [3, ]. er [] e seil ree rmeer elsi oio is roose. ove er e ree i le lexrl virio o irlr rig wi weel le s seil ree rmeer elsi oio is lyze sig e lssil i rig eory, e iie eleme (F) eiqe. Te roere o eermiig e ssie mss esiy o rig wi mssless oio is resee. Oie resls o llio re issse omre wi exerimel. xerimel ivesigio re oe y sig wo ojes wi e rirry ose geomery.. Teoreil ormlio Te meil moel o e sysem er sy osiss o irlr rig wi weel le s seil ree rmeer, lier, elsi oio. is ssme rig is omogeeos, erely elsi i s reglr, os ross seiol re. is iiolly ssme e eerlie o e rig s ris eleme o e rig, ixe y gle, isles i e ril irmereil ireio, rese-

2 8 ively (see Fig. ). Te smll islemes i ese ireios re eoe s (,) w(,), reseively, is ime. orig wi e eory, issse i [], e oio is reresee y e seil ree rmeer Wiler moel. Te oeiies, rerese e ril e geil siess er leg i, e rig ross-seio gle roio siess mols, reseively. rig oio w Figre. Virig sysem er sy Mig se o e lssil eory o virig i rigs [5], e ril iereil eqios o moio or e ree i le lexrl virio e omie io oly oe eqio i erms o e ril eleio (,) s G G G G G G G G G G G G () were eoes Yog s mols o elsiiy, G is e Kiro mols, is e re mome o ieri o e rim ross seio, is e mss esiy, is e ross seio re, is e ser orreio or. Te geerl solio o eqio () is ssme o e rmoi, i.e. ( ) ( ) i e, ()

3 Virios i Pysil ysems Vol. () 9 were is e rl reqey i is e imgiry i. siig solio () io eqio () gives e ollowig exressio ( ) (3) were, G,, G, G () Te solio o eqio (3) is ssme i e orm ( ) ( ) 3 si j j C j ϕ, K 3,, (5) were C j ϕ j re oss. We eqio (5) is ssie io eqio (3), i yiels e ollowig reqey eqio. ( ) ( ) () qio () is qri eqio i ee wo reqey vles re ssoie wi e vle o. Te smller vle o orresos o e lexrl moe, e iger vle orresos o e iess ser moe. eqio () ms e ieger wi vle greer. 3. Te iie eleme moels is seio e F moels o e sysem er osierio re ormle o isreize e oios moel give y e eqio (). To i e eigeirs (eigevle, eigeveor) rele o e rl reqeies rl moe ses o e rig wi elsi oio, e lo Lzos meo is emloye [5]. Te esseil rolem o

4 is seio is rere e F moel o e sysem wi roer vle o e rig ssie mss esiy z mssless elsi oio, reseively. Two ojes re osiere. lyse sysems ve e geomery s i is sow i Figre. For e oje, e F moel is relize s ollows. Te rig r is moele s e soli oy e oio r is moele s e mssles soli oy. Te e oe ererl eleme (soli87) wi ree egrees o reeom i e oe is se o solve e rolem. For e se, e roer vle o e rig ssie mss esiy z is selee rig llios o miimise e reqey error eie y [, 3] ( ) % ε (7) were is e rl reqeies o e moel is e e rl reqeies o e oje, reseively. ) l r ) l w øw øz øl erig Figre. () geomeril imesios, () moel o e sysem Te rere moels ile 97 (or e irs oje) 37 (or e seo oje) soli elemes, reseively.. Nmeril lysis Nmeril lysis resls o e irlr rig wi weel le ree virio re oie sig e moels sggese erlier. For ll resls resee ere, e irs seve rl reqeies moe ses re issse. No. o oje Tle. Prmeers rerizig e sysems o rigs wi oio z w [g/m 3 ] l r l w [P] Tle islys e rmeers rerizig e ojes er ivesigio. is le, is e e o e rig; ν is e Poisso rio e res o geomeril imesios re eie s sow i Figre. irs e omios re oe o evle e rig ssie mss esiy z o e F moels rele o e orresoig ν

5 Virios i Pysil ysems Vol. () ojes. isory resls re oie or e ollowig vles o z. o, or e F moel rele o e irs oje z [g/m 3 ] or e F moel reerre o e seo oje z [g/m 3 ]. For o ses, e sme vles o z re ile i e lyil solios. Moreover e roer vles o siess mols, i e orresoig lyil moels re selee rig meril simlios. Te resls o llio o e rl reqeies re sow i Tle. Tle. esls o omio rele o e sysems No. [N/m ] [N/m ] [N/m] rl reqeies o e osiere moels [Hz] (lyil solios) rl reqeies o e osiere moels [Hz] (F solios) e Figre 3 wo moe ses omes rom e F moel o e irs oje re islye. ) ) Figre 3. Moe ses rele o e ollowig reqeies:(), () 3 (F solio) 5. xerimel veriiio is seio e resls rele o e exerimel veriiio o e osiere lyil meril moels re issse. LM mesreme evirome is se i e exerimel ivesigio. Te mesrig se osise o e PCB moel 8C3 ye mol mmer eqie wi ggig oi me o seel, eleromeer PCB moel 353B8, LM CD qisiio sysem, CM-V ye mesrig mole sore y LM Tes.L sowre. Te exerimel ivesigio is oe o ieiy rl reqeies orresoig moe ses rele o e i le lexrl virio o e osiere ojes. s meioe erlier, or e mesreme exerime, wo ojes wi e geomery sow i Figre Tle re me. Te vles o e exie rl reqeies re sow i Tle 3. Tese vles

6 re omre wi e vles o rl reqeies rom e F lyil moels, reseively. e sme Tle e vles o e reqey error rele o e issse moels re resee. ieve resls re sisory lei, e es i is oie or e lyil moel rele o e irs oje. Tle 3. esls o veriiios o e sysems No. o moels rl reqeies o e osiere ojes [Hz] (exerimel ) reqey error ε [%] (omriso o e lyil solios wi e exerimel ) reqey error ε [%] (omriso o e F solios wi e exerimel ) Colsios Bse o e lssil eory o virig rigs, omreesive sy o e ree i le lexrl virio lysis o i rigs wi weel le s ree rmeer Wiler elsi oio is ivesige. Te serio o vriles meo is lie o solve e eigevle rolem. Oie lyil solios re omre wi e orresoig F solio resls. Presee i e er eoreil meril ivesigio, re veriie sesslly rig exerimel sies. eerees Nog,. Bogz, Free virio o e Timoseo em ierig wi e Wiler oio, ymlj w Bi i ozwoj, () Nog,. Bogz, T. Mrowsi, Virio lysis o weels omose o rig weel le moele s e ree rmeers elsi oio, rig reviews i J. o Vi., ().. Nog, T. Mrowsi,. Bogz, Nrl reqeies o lexrl virio o rig wi weel le s e Wiler elsi oio, ymlj w Bi i ozwoj, 3 () Nog, T. Mrowsi, le lexrl virio o rig ierig wi e Wiler oio, Virio i Pysil ysem, vol. XXV () o, Virio o Coios ysems, Wiley, Hooe, 7. X. W,. Prer, Virio o rigs o geerl elsi oio, J. o Vi., 95 () 9-3.