Study on Non-linear Responses of Eccentric Structure

Size: px

Start display at page:

Download "Study on Non-linear Responses of Eccentric Structure"

Loraine Jacobs
6 years ago
Views:

Th 4 h World ofr o Erh Egrg or -7 8 Bg h Sd o No-lr Rpo of Er Srr Hdz WATANABE oh USUNI Ar TASAI 3 Grd Sd Dpr of Arhr ooh Nol Uvr ooh Jp Ao Profor Dpr of Arhr ooh Nol Uvr ooh Jp ABSTRAT : 3 Profor

1 Th 4 h World ofr o Erh Egrg or -7 8 Bg h Sd o No-lr Rpo of Er Srr Hdz WATANABE oh USUNI Ar TASAI 3 Grd Sd Dpr of Arhr ooh Nol Uvr ooh Jp Ao Profor Dpr of Arhr ooh Nol Uvr ooh Jp ABSTRAT : 3 Profor Dpr of Arhr ooh Nol Uvr ooh Jp El: d8@..p Th prpo of h rrh o ll h r of rgd h o-lr rg of r rr. I r o ll h vl ff rx h o-lr rg. of h w o ll h rx h vl lrzo hod propod T.. gh. Prvo d o h hod howvr fod o h vl gl-dgr-of-frdo (rfrrd o SDF hrfr) whh h r o lld drl. h ohr hd fw d hv rpord o l-dgr-of-frdo (rfrrd o DF hrfr). I r for h llo of h r of rgd h o-lr rg of r rr o dvlop h vl lrzo hod for DF. I h ppr h vl lrzo hod for h DF wr dvlopd o xd h ppll op of h hod rpord T.. gh whh o of h vl lrzo hod for SDF d d o h -r hod. Frhror d rpo l w odd wh o odl wh r rr o vl h vld of h propol hod. EWRDS: Er Srr r of Rgd Evl rzo l Dgr of Frdo D Rpo-r hod. INTRDUTIN Rl h p pr hod w dvlopd o vl h prfor of ldg. For xpl h Bldg Sdrd w of Jp o h hod o vl h prfor of ldg d o h vlo hod of h rpo d h l rgh. I h hod o-lr rpo of h rr vld o h o-lr rr wh h vl rr d o h vl lrzo hod. Th vl lrzo hod h vl ff lld wh h x rpo dpl d h vl dpg lld wh h o rv d h x rpo dpl. of h dvg of h hod h o-lr rpo of h rr od who odg hor rpo l. Th orol vro of h r rr d h dffr w h loo of h r of rgd d h r of grv. I h o-lr rg h r of rgd of h r rr hf ordg o h ff dgrdo of h rr. w o vl o-lr rpo of r rr o ovr h o-lr r rr o h vl r rr g h vl lrzo hod. Th vl r rr dfd h vl lr rr whh h h r of rgd h loo h o-lr rg. I ordr o ll h loo r o ll vl ff rx h o-lr rg g h vl lrzo hod. I ordr o ll vl ff rx h o-lr rg r o propo vl lrzo hod for h DF h vl lrzo hod for h SDF o lld h rx drl. Vro d hv rpord o h vl lrzo hod. Prvo d o h hod howvr fod o h vl SDF. Frhror fw d hv rpord o hod for h DF. Th h of h ppr o propo vl lrzo hod for h DF o fd h

2 Th 4 h World ofr o Erh Egrg or -7 8 Bg h loo of h r of rgd of h r rr h o-lr rg. I h ppr h vl lrzo hod for h DF wr dvlopd xdg h ppll op of h hod rpord T.. gh whh o of h vl lrzo hod for h SDF d d o h -r hod.. EQUIVAENT INEARIZATIN FR SINGE-DEGREE-F-FREED SSTES T.. gh dvlopd o of h vl lrzo for h SDF g h l-r hod. Hr h hod d h d ff hod (rfrrd o DS hrfr). Th hod ovr h d- rpo of h o-lr SDF. I h hod h vl ff d h vl dpg off r lld g h l-r hod o z h rdl of r for h dffr w lr rorg for d olr rorg for. Th h DS for h SDF whh hv -lr hr rv how Fgr wll drd. Q γ For ( ) whr h l ff of h γ h ff dgrdo ro h ld dforo h x dforo d Q h ld rgh. Th o of oo for h SDF gv E. (.). Th o-lr hr fo of h () gv E. (.) γ ( ) γ dforo Fgr olr rorg for hrr ( ) ( γ)( ) ( γ) ( γ)( ) ( ) ( γ) ( ) (.) d d d d whr h of h h dpg off of h h dforo of h h vlo of h h rlv lro of h d grod lro. Th vl lrzd o of oo for h SDF gv E. (.3) g h rror r. ( ) (.) (.3) whr h vl dpg off vl ff d ( ) h rror r dfd h dffr w vl lrzd rorg for ( ) d olr rorg for ( ). Th prpo of h DS for h SDF o ll d. I h DS for h SDF ( ). Aordg o dfo of h l-r hod h d lld zg h vl of oh d rhd xr vl r odo o z h vl of h fo.whr

3 Th 4 h World ofr o Erh Egrg or -7 8 Bg h rpr h r of h rror r ( ) o how h followg o.. Th prl dffrl of d (.4) Th grod lro d h hro grod oo E. (.5). Th d- rpo ol odrd. E. (.6) pproxd fro E. (.3) g h po h gord. o p ( ) (.5) ( ) o( p φ) (.6) whr h pld p h glr fr of h hro grod oo d φ h ph dffr w h hro grod oo d h d- rpo. Fro E. (.3) E. (.4) d E. (.6) gv E. (.7). Slrl gv E. (.8). ( γ) * * ( γ) θ γπ θ o θ π μ (.7) 4 ( γ) pμπ μ (.8) whr μ h dl for (/ ). Fro E. (.7) h vl ff how h fo of μ. Fro E. (.8) h vl dpg off h fo of μ d p. 3. EQUIVAENT INEARIZATIN ETHD FR UTI-DEGREE-F-FREED I h hpr ol of h l-dgr-of-frdo Evl rzo hod (rfrrd o E hrfr) d ol of h Splfd l-dgr-of-frdo Evl rzo hod (rfrrd o SE hrfr) wll drd. Th E w dvlopd g h DS for h DF whh d o h DS for h SDF propod T.. gh. Th SE w dvlopd o plf h E. 3.. odlg h Srr Th E ovr ll of rr whh r llowl o odl lpd. Th rr r odld follow. Th rr h dgr-of-frdo d l prg. Th dpl vor {} d rx [] wr E. (3.) d E. (3.) rpvl. { } { } T [ ] (3.) Hr odl of ll of h l prg -lr p how Fgr. Th ff rx h l rg gv E. (3.3) g wo for ( ) d ( ). (3.)

4 Th 4 h World ofr o Erh Egrg or -7 8 Bg h (3.3) ( ) ( ) ( ) ( ) ( ) ( ) ( ) whr γ d Q for h l prg d wr dfd γ d Q rpvl how Fgr. Th () o-lr hr fo of h l prg d. Th dpg rx d proporol o h l ff rx. Th h dpg rx oh l d l rg wr E. (3.4). (3.4) 3.. Th DS for l-dgr-of-frdo S I h o h DS for h rr odld h prvo o drd d o h DS for h SDF. Th vl ff rx [ ] d h vl dpg [ ] r dfd E. (3.5). Thrfor h olr o of oo gv E. (3.6). (3.5) {} { } { } { } Φ Q (3.6) (3.7) { } T Q whr h grod lro { h grod lro vor d { h o-l } Φ } Q r rorg for vor xprd E. (3.7). Th vl lrzd o of oo o h rr gv E. (3.8). { } {} { } { } { } { } ( ) { } Φ (3.8) whr h rror vor d xprd E. (3.9). {}{}{} ( ) {}{}{} ( ) ( ) ( ) ( ) { } {} {} {} { } Q T (3.9) Aordg o dfo of h l-r hod h l of oh [ ] d [ ] rhd xr vl

5 Th 4 h World ofr o Erh Egrg or -7 8 Bg h r odo o z h vl of h fo h l {}.Whr {} rpr h r of h rror vor. Th prl dffrl of h l {}{}{} ( ) {} h l of oh [ ] d [ ] o how h followg o. ( ) (3.) Th grod lro d hro grod oo E. (3.). Th d- rpo ol odrd. E. (3.) pproxd fro E. (3.8) g h po h {} gord. p o ) ( (3.) { } ( ) ( ) ( ) { } T φ p φ p φ p o o o ) ( (3.) whr x pld p glr fr of h hro grod oo h x dforo h dgr of frdo d φ h ph dffr h dgr of frdo w h hro grod oo d h d- rpo. Fro E. (3.9) E. (3.) d E. (3.) [ ]d [ ] r gv E. (3.3) d E. (3.4). (3.3) (3.4) [ ] ( ) ( ) * * θ γ γπ θ γ π μ θ o * (3.5) ( ) μ γ μπ p 4 (3.6) whr vl ff of h prg xprd E. (3.5) vl dpg off of h prg xprd E. (3.6) γ h ff dgrdo ro of h prg μ dl for of h prg ( / ) d x dforo h prg xprd E. (3.7).

6 Th 4 h World ofr o Erh Egrg or -7 8 Bg h ( φ φ ) o (3.7) E. (3.3) rpr h vl ff rx [ ] whh lld rplg of E. (3.3) (). Slrl E. (3.4) rpr Th vl dpg rx [ ] whh lld rplg of E. (3.3) (). Thrfor h DS for h DF h vl ff rx d h vl dpg rx lld g vl ff d vl dpg off lld for h prg. Th h r of rgd h o-lr rg of r rr lld E. (3.8) g h vl ff for h dro d h or. lx x x l (3.8) x whr x d vl ff of x d dro for h or l x d l r x-oord d -oord of h prg for h or d x d r r of x d dro for h or l of h E I h o h E whh d o rdo vro propod. Aordg o h rpor Sh wh SDF vr drg rh h vl ff lld pproxl h lop of h x dpl po o h org. Ad h vl dpg for h lld ll E. (3.9). h. h (3.9) μ whr μ dl for of l prg d h h l dpg for. Th hod d h gorl ff hod (rfrrd o GS hrfr). Th DS for DF dopd h hor of h GS h E. Th h vl ff of h prg lld E. (3.) d h vl dpg off of h prg lld E. (3.). Howvr h E o lld E. (3.7) φ o d h rdo vro. Thrfor h E lld orvg h dforo of h l prg drl. ( γ) γ μ.4 (3.) μ 3.4. l of h SE I h o h SE w dvlopd o plf h E. I h SE lld h how E. (3.). I d h olr rpo of h rr how fdl od h φ d φ orrpod o h ohr h dgr of frdo vr h ph. Th E. (3.) lld rplg h φ l h φ E. (3.7) (3.) 4. NUERIA ANASES N THE EENTRI STRUTURE I ordr o vld of h E d SE propod h prvo hpr d rpo l

7 Th 4 h World ofr o Erh Egrg or -7 8 Bg h wr odd wh r rr. D rpo l wr odd wh SDF g h GS o opr h r wh h GS for SDF. I h ppr h r of h hod w vld fog o h r of h dpl of h dgr of frdo. 4.. All odl of h Er Srr Th rr h d r o-or o-x-r rr. Th ll odl of h r rr how Fgr. Th rr h for l prg hr dgr of frdo lrl rvr d rool dro d rgd floor. Th hr of h l prg -lr p..5.5 θ x Z. θ :. X Fgr All odl of Er Srr I h d hor l wr odd g wo hod for hdrd ll odl. Th prr of h odl r prod of X dro T x dpg for h ld rgh Q d r of dro how Tl. Th ld rgh Q lld rdo prg of h x rgh of xploror lr l. Tl Dl of prr prod of X dro () T x dpg for h ld rgh Q 4% 5% 6% 7% 8% 9% r of dro () Pro of h Al d Al Apo Pro of h l follow: () od olr hor l o o h olr x dpl h dgr of frdo p h rpo of h olr l. () ll h vl ff rx d h vl dpg rx h of h E d h SE g h p whh od h pro (). (3) od lr hor l o o h vl lr x dpl h dgr of frdo h rpo of h lr l g h vl ff rx d h vl dpg rx whh lld h pro (). (4) ll h r of h hod h dol vl / p h h dgr of frdo. For rh lro hor rord (El ro NS Hhoh EW o NS o) wr pd. P grd lro of ll rh d wr orlzd gl d wr pd ol h X dro. Dpg d proporol o h l ff rx. Th vrg lro hod w d for h grl Rl Th fr dro l of h r o X dgr of frdo how Fgr 3 (). Th fr dro l of h r o θ dgr of frdo how Fgr 3 (). Vrl x Fgr 3 how h fr. Horzol x Fgr 3 how h r ( / p ); for h hod whr

8 Th 4 h World ofr o Erh Egrg or -7 8 Bg h / p. rpr h o r po. 8% 8% SDF SE E SDF SE E 6% 6% Fr 4% Fr 4% % % % / p % / p () X dgr of frdo Fgr 3 Fr l () θ dgr of frdo I fro Fgr 3 () h h r of h E d h SE lo h wh h of h SDF. Th r of h SE howvr or r h h of h E d h SDF Fgr 3 (). Th d o h f h lld E. (3.7) h SE. Th h SE lld E. (3.7) for h po h olr rpo of h rr how h fdl od. Howvr h po r r rr h rr do o gor h hghr od of rr. 5. NUSINS Th E d h SE whh Evl lrzo hod for h DF wr propod g h l-r hod for h llo of h r of rgd h o-lr rg of r rr. Th h rl l wr odd wh h r rr o vl h vld of h E d Th SE. Rl fro h d r follow; Th E w propod o xpd h ppll op of h DS dvlopd T.. gh. I h E h vl ff rx lld rplg h l ff vl ff h prg h lr ff rx. Slrl h vl dpg rx lld rplg h l ff vl dpg off h prg h lr ff rx. Th r of rgd h o-lr rg of r rr lld g h E. Th r of h E lo h wh h of h GS for h SDF whh h lhd vl lrzo hod. Th r of h SE or r h h of h GS for h SDF o θ dgr of frdo hghr od of h rr gord h SE. REFERENES gh T.. (96). Sodl Exo of S wh Blr Hr. Jorl of Appld h Sh A. d.a. Soz (976). S Srr hod for S Dg R/. Pro. ASE. :ST Sh A. (975). A d o olr d rpo of vl lrzo hod. Toho Uvr Arhr Rpor. Vol ( Jp) Sh A. (3). rr S rrl Al. or Plhg. ( Jp)

Special Curves of 4D Galilean Space

Special Curves of 4D Galilean Space Irol Jourl of Mhml Egrg d S ISSN : 77-698 Volum Issu Mrh hp://www.jms.om/ hps://ss.googl.om/s/jmsjourl/ Spl Curvs of D ll Sp Mhm Bkş Mhmu Ergü Alpr Osm Öğrmş Fır Uvrsy Fuly of S Dprm of Mhms 9 Elzığ Türky