Primer Adapted Dynamic Analysis in vibration problems
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1 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 69 Prmer Adted Dym Alyss rto rolems Ggdr TG* Blkeswr Sg kel Sk Adl reem Syed dssr el & Idstrl Egeerg Seto Sll ollege of Teology Sltte of Om *orresodg tor: tgggsd@ygmlom ABSTRAT Te Prmer Adted Dym Alyss (PADA) of dyml systems s solto roedre to rre t te sytess of elerto etors eloty etors d dslemet etors slemeted y te geerto of dym roertes te form of Nll-ge etors d Nll-ge mtr PADA metod tlzes te Hegde s Prmer Vle teorem d modfed Prmer Vle teorem to sole fored d free rto rolems resetely Te seod order degree of freedom dym eqto s frst frted to rtl otl eqto d defte ostrt eqto Usg te o-effet of tese eqtos te rmer dters re estmted y smle rtmet mltos w rodes solto to dym rles d rtl fore etor Te er s orgl effort te dreto of te oted erfeto w domtes oer te ro erfeto of omle deelomets of estee of tedos d omttolly dfflt metodologes osmg lrger se d tme Te rel tme to w s felt y te ssg r of PADA rogrm w estmtes te tme tke to sole te dsssed rolem glgtg te merl sgfe eywords: rmer dtor rmer le teorem dym lyss rto teory I INTRODUTION I te rto teory ref [] seod order dyml system tts eqlrm y te le of srg fore dmer fore d te ert fore for ge led fore ledg to te formto of rterst eqto Imerle mers of solto teqes re dsssed for te solto of te sme to rre t te dslemet etor As s edet tt otos systems osses fte mer of rto degrees of freedom t s y te dsretzto te DO re mde fte Bt wt fer dso te sze of te rolem reses d ee tkes more tme to sole d towrds redto tme tke tere d ee ttemts to deelo lgortms s see ref [] dg towrds erfeto my tme omromsg te ry of te solto Ades te omttol mtemts d ts lto to egeerg d setf reseres e tke dfferet se wt det of omters Howeer toed ss left fr ed tt rode reoltory solto o rel-tme ss; mke mt to srge ed of ll te reset teqes y te mrel of smlty reseess d erfeto w s ee te orgl offer of ts er med s Prmer Adted Dym Alyss (PADA) I te referee [] to rre t te trsfer fto e rto of ott d t of te dym system Lle trsform d Ierse Lle trsform re mde se Bt PADA rodes te solto dretly to get te relto etwee ott d t ftos wt te d of rmer dtory olg smle rtmet oertos ts llto w te mtemts sold et to e rel-tme solto Te Prmer Adoted Dym Alyss (PADA) frst frtes te rterst eqto to defte otl eqto d rtl otl eqto w e te form of ostrt fto (ezyme eqto) d ojete fto (rmry eqto) resetely Vrtl otl eqto rodes solto to rles sg rmer le teorem (see Aed) s fto of rmer dtor se of fored rto rolem or free rto rolem te odfed rmer le teorem s mde se to rre t te solto to rles terms of rmer dtor rter rmer dtor s estmted y ssttto of te rle to defte otl eqto osdered to e te ezyme eqto s referred ref [] It PADA s frter oted to fd te rtl fore etors wwwjsretorg
2 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 7 Nll-ge etor d te ll-ge mtr determed y te PADA roedre to defe te dym roertes of te system Te rmer le teorem odfed rmer de teorem (refly desred Aed) d te PADA roedre mke se of smle rtmet oertos Wt te d of referee [] te dym eqto for te seod order degree system wt srg mss-dmers s formlted wt te geerto of mss dmg d stffess mtres seto () Te solto to rles of elerto etor eloty etor d te osto etor d te rtl fore etor s ge seto () Ts seto resets te geerto of dym roertes te form of ll-ge etors d llge mtr I seto () emle of fored rto of seod order d degree tree s e demostrted merlly to e feel for te mer d omttol ese Te er s refly olded seto (5) Te rmer le teorem d modfer rmer le teorem re reseted ref Aed for referee j stffesstr T A elerto etor T V eloty etor T X dslemet etor Geerl srg mss- dmer system: II ORULATION Te rterst eqto s ted referee [] for te dyml system of degree of freedom of seod order wt srg-mss-dmer s deted gre() s ge s [ j ] [A ] + [ j ] [V ] + [ j ] [X ] = () Were j mss mtr j dmg g: Srg-ss-dmer system By Newto s eqto of oto te eqlrm eqto s formlted y te le of srg Dmg ert Aled fore fore fore fore Hee te eqlrm eqto s X + X+ X = Ts s eqlet to te dym eqto () wwwjsretorg
3 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 7 III SOLUTION BY PADA PROEDURE Te Prmer Adted Dym Alyss roedre frst frtes te dym eqto () to rtl Potl Eqto d defte ostrt eqto rter y te lto of Hedge s rmer le Teorem (ge Aed) Te solto to dslemet etor eloty etor d te elerto etor re oted s fto of rmer dtors tt re estmted from te defte ostrt eqto y ssttto Solto y PADA etod: Te rtl otl eqto s formlted s A + V + X = () Were = = = j j j or = J = V = = Vrtl ore Ad = Aled fore Te seleto of sg s so omlsed to e [ ] Te defte ostrt eqto tkes te followg form Were = m = m = m m m m m m m Te sg s seleted so s to get [ ] Ad = m m m or m = d = m Te estmto of rmer dtors () Were Te mer of rmer dtors s eql to te degrees of freedom of te system omtto of etors: Te geerto of etors s orde wt te rmer le teorem A V X Ad rtl fore = Also = [ j ] A + [ j ] V + [ j ] X A + V + X = () wwwjsretorg
4 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 7 Geerto of ll-ge etor d tr : Tere ests ll-ge etor X s tt [ j ] X = od = k j Te ll-ge mtr s j X j X for = stffesstr PADA roedre for free rto rolem I free rto rolem t my e osered tt = d eq () fls to el te sd solto s t rodes rmer dters to e zero s se s tkled y odfed rmer le teorem (ge Aed) y w / (5) P ( ) Te Solto for etors s ge y A V X d = Vrtl fore A refl oserto of eresso (5) sows tt we te deomtor of (5) s zero t leds to trl solto w o rtl sgfe Te ll-ge o-effet d ll-ge mtr e omted te sme wy s dsssed erler te fored rto rolem IV EXAPLE So s to merlly demostrte te PADA roedre seod order tree degrees of freedom system wt srg-mss-dmer rrgemet wt reset to fgre s soled for ot fored d free rto Dt roded = = = = = = d = = = d te led fore = Te mss dmg d stffess mtres re j j j Te rtl otl eqto from PADA roedre s to e formed s tt [ ] Hee = - + goers te formto Te rtl otl eqto s A V Te defte ostrt eqto e formlted y te ssmto of so tt A V X Te estmto of rmer dtors wwwjsretorg
5 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 7 Te etors re A 6 7 V X V V V 5 Wt (Assmto) Vrtl fores = & ( ) for = (Ie ) j k j j 7 8 ( ) ( ) ( ) It my e erfed V V V 6 d Geerto of Nll-ge etors / / / 7 6 Vrtl fores O ssttto to defte ostrt eqto 7 6 Nll-ge mtr 8 N 77 wwwjsretorg
6 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 7 Te ge rolem s soled for free rto s tt te defte ostrt eqto s of te form [ -] A + [- -] V + [- -] X = d te rtl otl eqto s [ ] A + [ - ] V + [ - ] X = By modfed rmer le teorem te dter s estmted s ( ) ( ) Te etors re A V X 5 Verfto 5 / 5 () () () 5 6 IV ONLUSION Te dtge of rmer Adted Dym Alyss (PADA) roedre s dered y te smlty of geerto of soltos to dym rles d roertes etrted y te dret lto of smle rtmet oertos Te oted erfeto s eted y te rte d fster reslt rodg lty of te PADA teqe Te Setsts d egeers fd ts sefl e-mrkg s te metod tt rode et solto to smller rolems y mered llto s s edet te demostrted emle Te sge of Hedge s rmer le teorems PADA ro sgfes te elorto of left ot strek te strem of st omttol d teologl det Ts s to te te setf ommty to et d ly te PADA to ge orzotl sred gg le te omttol jorey ANOWLEDGEENT We re tkfl to r N Sell HOS of el Egeerg Dr Sd ommed Al-sk Hed Dertmet of Egeerg d Dr rym AlAwd De Sll ollege of Teology for ter lle srto eorgemet d rodg eessry fltes for te stdy REERENES [] Tomso WT Teory of Vrto wt lto d ed PHI - New Del (98) wwwjsretorg
7 wwwjsretorg 75 Itertol Jorl of Setf Reser Egeerg & Teology (IJSRET) ISSN Volme 5 Isse r 6 [] Ogt oder otrol Egeerg Perso edto () [] Ges S Hegde orwrd Oerto rmer sytess EA Proeedgs of tertol oferee Tem Te 6 IIS Bglore Aed Prmer le teorem: Ge te goerg eqto Ad te ezyme eqto d Te roots re ge s follows By ssttto of roots to ostrt eqto d lger mlto te rmer key s ge y d odfed rmer le teorem Te ge ojete fto s te goerg eqto d te ostrt eqto s te ezyme eqto f d f or f Te rmer key s estmted y ssttto of te roots to ostrt eqto d y smle mlto /
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