Time Domain Response of Multidegree-of-Freedom Systems with Fuzzy Characteristics to Seismic Action

Size: px

Start display at page:

Download "Time Domain Response of Multidegree-of-Freedom Systems with Fuzzy Characteristics to Seismic Action"

Silvester Washington
5 years ago
Views:

1 CAS Itratoal Spos o Strctral ad arthqak r Octobr ddl ast chcal Uvrst Akara rk Doa Rspos of ltdr-of-frdo Ssts wth Fzz Charactrstcs to Ssc Acto AA aszad Odokz aıs Uvrst Faclt of r Dpartt of Cvl r 9 Sas/rk; azr@odtr ABSRAC: Strctr wth ft dac dr of frdo ad fzz otrcal ad phscal paratrs ar aalzd dr arthqak acto brshp fctos of qalt charactrstcs hav b stablshd dflctos of th fzz rslts as rats of th dtrstc ar statd wth prcts saft crtro ad ts stat s v prtal tst s ad b s orthooal arra ach s thod For ach α ct lvl th qatos of oto s solvd s stp b stp trato th t doa b th Nrcal Wlso-θ s thodso opratos wth fzz paratrs ar provdd b s tso prcpl Zadh96 Nrcal apls ar v ad th rslts ar plad words : arthqak acto; fzz st; ach thod; ft lt aalss ÖZ: Blaık otrk v fzk paratrlr sahp sol dak srbstlk drcl dsd apıı dpr tks aalz apılıştır araktr clklr ülk foksoları krlş dtrstk soçlara orala sapaları üzdlrl dğrldrlştrt krtr v dğrldrls vrlştr D plalaası ortooal ala ach tod l apılıştır Hr br α-ks ç harkt dkllr zaa-taı alaıda saısal Wlso-θ tod l çözülüştür Blaık paratrlr üzrd br sıra şllr şl prsb Zadh96 daaarak apılıştır Saısal örklr vrlştr soçlar açıklaıştır Itrodcto As s kow th aalss dr ssc acto of spcal strctrs csstats th s of actal rcords or slatd acclrato of rod I ths aalss o of crcal pots s th stato of sstvt of racto of a strctr wth rspct to th crtats otrcal ad phscal paratrs hht of a floor ass rdt dap tc I th applcatos crtats ar classfd as b rado ad fzz I th sbttd work a drcto of ach dac dr of frdo ddf ass hht of a floor odl of lastct s accptd b fzz qatts wth tralar brshp fcto ad ar rplacd b th α - cts hs for vr α -ct s costrctd th qato of oto Dspt of th avalablt of vstatos o

2 fzz qatos Bckl99 practcal thods for th applcatos s rathr ltd I so stas rcal ralzato of a cosdrd ad probl s of trval arthtcs for vr α -ct basd o a prcpl of paso Zadh s vr dffclt to b ralzd bcas bordrs of ractos tart paratrs of th sst ar dfd I ths std th arkd dffclts of trasforato coctd to th trval aalss hav b ovrco for vr α -ct b applcato th ach thod hs factors o whos varablt th sst s sstv to s rplacd for ach α -ct ad for ach sta of a prt cobato of costrctd qato that s solvd b a rcal Wlso θ thod brshp fctos for th sst strctr ractos dvato wth rspctd to th dtrstc vals cobato br qvalt to sst crtcal stat ad qvalt t dr th ffctv arthqak trval hav b obtad Rlatd to ths std rado vbrato of th sst wth fzz paratrs o ddf sst applcato has b vstatd Wa99 ; vctor ad val probls for th lt dr of frdo ssts wth fzz paratrs has b vstatd Ch997 ad Blld999 rspctvl Ivstato of sst ractos copl fzz loc wth statstcs has b vstatd Wada Fosctt stato of th rlblat of th strctr fodato rod wth stochastc charactrstcs ssts dr ssc acto has b vstatd asov999 Forlato or sstv fzz paratrs of ractos of strctr al hht of floor lastct odl of cols ass th drcto of -th ddf ar accptd to hav two lvl tralar brshp fctos µ µ f or f R µ f f f f R α f f R R α αr R Fr Fzz br wth tralar brshp fcto ad ts α-ct Aftr that paratrs ar fzzfd s fll factoral ad orthooal arr tst pla for ach α-ct lvl th rdt of stor s prphr rlatd wth ad factors; ol for th brcatd stors ddf tracto of th rdt factors ar accptd µ A fzz rlato f AB fro fzz st µ X to a fzz st Y s a fzz sbst of th Cartsa prodct XY whch s a app fro X to Y A fzz rlato f AB s prssd as Zadh s tso prcpl :

3 X Y B A f AB f µ µ Fzz arthtc s basd o th Zadh s tso prcpl h coptatoal fatrs of th tso prcpl ca b achvd b s th α-ct rprstato of fzz brs For ach α-ct lvl fzz paratrs for th tst cobato br accord to th crtcal stato tracto btw two stors ddf qato of oto ar rra as: ; * * t F F c + + Whr c ar ass rdt ad dap atr of sst f th probl s ad to b solvd s th ft lt thod th ar prssd th for : Whr ar ass ad rdt of th ssts th -th ddf Wh v vctor wth dap rato lts for th ach ddf dap coffct atr s prssd as: ; a a c Whr frqc of strctr for -th vbrato od ; total ddf of sst F * F * - t t dac forc th -th ddf of th sst valatd dr rod acclrato Solto For ach α-ct of th fzz paratrs tst cobato br accptd to th crtcal posto of th stor tracto th qato of oto s solvd s stp b stp trato th t doa s th Wlso-θ s thodas a crtcal stato th tfor th aal ovrtr ot th bas of strctr -th tst t * t a ov s accptd I crtcal stato No* t * for ach α-ct of fzz paratrsrspos of th sst s prssd th for:

4 Whr th dsato :j as j-th col of a atr For th - br tst cobato dsplact vloct acclrato ssc forc F ovrtr ot ov ar prssd th for: F k br of d d f 7 br of tst cobato OV row 8 Rht ovr ad lft ov vals of th ovrtr ot ad brs of tst for ths vals No NoR ar fod for -th α-ct basd o tso prcpl: ov No ov ovr NoR a ov 9 Rspos of th strctrs dsplact vloct acclrato whch corrspod to tst brs No NoR for th lft ad rht vals for ach -th α-ct lvl ar valatd as th dsato : j as -th ad j-th cols of a atr : : ov : : No lft 678 lft ov : No R rht 678 Aftr - s t ralzato atrcs s prssd th for: st sc to d sc to s sc to α α α k br d d f F s br cols ov F : F : No* ov R rht row Accord to ths rslts th brshp fctos of th sst rspos ad ts dflctos rard dtrstc rspos ar calclatd asl

5 Nrcal Aalss h shar bld show th f wth ts phscal ad otrcal paratrs v blow s vstatd: J J J N / J 9 9 J J 69 9 ; 9 J 7 9 J R 868 J J 9 8 R J R 6 ; ; tr R ; ; Nwto R ; ; Frst 9 scods rcords for th ast-wst copot of 9 l Ctro arthqak s accptd as rod acclrato Itrato t stp: t paratr of θ thod bcos codtoall stabl s accptd a cha trval charactrstc ractos of th sst wth fzz paratrs stadart dvato fro ts avra% stadard dvato fro ts avra%stadard dvato fro ts avra%ar v ablcas A a cha trval charactrstc ractos of th sst wth fzz paratr stadard dvato fro ts avra% ; cas B th ol lastct odl stadard dvato fro ts avra%; cas C th ol stor asss stadard dvato fro ts avra%; cas D s v abls 6 7 rspctvl h sstvt of th strctr to chas th fzz paratrs for th ovrtr ot copar ABCD cass ar show blow: Dvato of Fzz ovrtr ot rard to dtrstc rslts for th lft ad rht dvato vals prct Fr stor shar bld st Cobato No for th ov ad ovr stat rspctvl Cas A%%% ; %7 ov % ; R Cas B% ; %9 ov %78 ; R Cas C% ; % 99 ov %7 ; R Cas D% ; %7 ov %8 ; R hat for ths tp strctr s a rarcabl fatr s or sstv to cha th stor hht cas B ''

LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES

LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES TRANSFORMATION OF FUNCTION OF A RANDOM VARIABLE UNIVARIATE TRANSFORMATIONS TRANSFORMATION OF RANDOM VARIABLES If s a rv wth cdf F th Y=g s also a rv. If w wrt