Diagnosis of Free-Drop Shock Events Using On-Board Sensor Signals

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1 Dagoss o F-Dop Soc Evs Usg O-Boad Sso Sgals a W. Assoca Posso Dpam o cacal ad Aospac Egg Uvsy o Alabama Husvll Husvll A 5899 Sv aoa Tg Oo U.S. Amy Avao ad ssl Rsac Dvlopm ad Egg C Rdso Asal A 5898 ABSTRACT Idcao o soc mpac oc d o a sucual assmbly subjcd o a dop mpac s ssal o assssg gy codo o assmbly. O pacula mpoac a os sucus suc as mssls ad gudd muos a a uppd sopscad lcocs. Usg o-boad gad dyamc ssos s possbl o cod soy o dyamc spos o sucu dug s l cycl c accdal dops o sv mpacs occu. I s pap a aalycal modl as dvlopd o vsly v d soc mpac oc om o-boad dyamc sso sgals. A omulao o la dop mpac o a bam sucu as psd ad a ducd omulao o a sgl-dg-o-dom sysm as mplmd o valda aalycal scm. I as so a aalycal scm ca accualy v soc mpac oc d o sysm. Ioduco ay assmbld ucoal sucual sysms a o subjcd o accdal -dop soc loads dug sppg ad adlg paculaly aspoao o suc sysms volvs g lg macs. T cds o dop socs may o caus ay vsbl ac o suc vs o o o sucu. vlss som ccal compos ousd sd sucu ca b damagd ad caus sysm o maluco. Ts s paculaly suao may sopscad ucoal lcocs a pa o sysm. I s dsabl a usg gad o-boad dyamc soc ssos occuc o dop soc vs ca b dcd. Idcao o spaal ad mpoal maup o soc loads d o sysm ll abl a accua assssm o gy codo o sysm. Usg o-boad sso sgals o v locao ad m soy o mpac ocs as md as vs dcao poblm vbao sac commuy ad as b dly sudd o pas o dcads. T gal mod ollod amo o dcovoluo uo ocg uco as dcovolud om sysm spos. Sval appoacs av b mployd. T sgula valu dcomposo mod as usd by Ha ad Wcs o dm oc spcum ucy doma. T ucy doma appoac as also usd by Iou al. o pdc magud ad dco o a mpac oc. Sval soluo cus m doma av also b dvlopd o oc dcao poblm. Usg pmal daa Cag ad Su sablsd pmal G s u ad mpac oc as dmd by sgal dcovoluo om G s u. A gal m doma mod o dyg dyamc loads c pc-sly appomad by a la uco o couous sysms as dvlopd by Zu ad u. T spaal dsbuo ad m soy o mpac loads gally ca b dmd povdd load locao s o. A mods av also b poposd o dy locao o mpac oc. Doyl 5 usd pas omao om a spcal aalyss o m soy o a sso masum o dy locao o oc applcao. Usg mulpl ssos Co ad Cag 6 sablsd a sysm modl ad a spos compaao. By compag masud sso oupus smad sysm spos om modl locao ad oc soy o mpac ca b dmd. Rcly Wag ad Cu 7 appld opmzao pocdu o dy locao o oc applcao ad amplud o appld ocs o a smply suppod bam.

2 I s pap a omulao o vs poblm vg soc mpac oc om acclao daa as psd o a bam sucu ud la dop codo. To valda vs aalycal scm a ducd om o omulao dg a sgl-dg-o-dom sysm as mplmd. A cas sudy as coducd usg smulad acclao daa poducd by a o al-s mpuls uco. T suls so a vd mpac oc s dcal o appld mpac oc as pcd. Fomulao Cosd a lbl bam sucu lasd a a g o abov suac o ag. Assu o oao dug all ad a pcly la mpac o ag soc mpac oc ducd o bam ca b dd uom alog lg o bam. Fgu sos a scmac llusao o codo. T uao o moo o bam a -dop soc mpac ca b pssd as: suac. c A s a uo ocg uco d by soc mpuls c dpds o domably o ag y Fgu. Scmacs o -dop soc spos modl o a bam sucu. Usg mod summao mod dlco o bam ca b pssd as:. T sulg spaal uao ylds ollog om:. Basd o - bouday codos: ; ; ; bouday codos o spaal uao ca b sablsd as: ; ; ;. 5 Applyg bouday codos E. ca b solvd ad mod sap uco bcoms: µ s s 6 s s s - oo o ascdal uao ad µ. Usg mod sap uco mpoal uao ca b sablsd as: C K Q 7

3 Galzd Foc Galzd Dampg Galzd Sss Galzd ass " d Q c d c C d K d m µ omalzao spc o galzd mass ollog modal uao s obad: A µ 8 ad. T pacula soluo o abov uao ca b obad by covolug omogous m ad mpuls spos uco as: A p µ 9 s. T compl soluo o modal uao us ylds ollog om: s al codos o modal uay ca b dvd by } } } } c s modal ma. T dlco spos o bam subjcd o -dop soc mpac al codos o a la all.. ad } g } suls ollog psso: } s

4 g. T vlocy ad acclao us ca also b dvd om abov dsplacm uao. Ty av oms spcvly as: } s } s. To vsly oba ocg uco a pc-s la appomao as usd o dscb s uo uco. W m val uo ocg uco ca b laly appomad by: o. Subsug la appomao om o uo ocg uco o acclao uao E. ad covoluo m a pc-s aso acclao a m a locao o bam bcoms: } s d 5 Usg masud acclao daa soc mpuls ducd ocg uco us ca b vsly calculad om E. 5 ad o a umcal scm o cay ou pc-s covoluo m. Fo smplcy abov aalycal scm as s mplmd o a sgl-dg-o-dom SDOF sysm. Fo a SDOF spg-mass-damp sysm omulao ducs o a muc smpl om. T sulg acclao o sysm bcoms: s d m g 6 Cas Sudy To mplm aalycal pocdu dvlopd s sudy a s cas as coducd o SDOF sysm. T aalyss dd a objc o.5 g mass a spg a o.7 G/m ad dampg ao o. avg a dop om a g o m. T sulg soc mpac oc d o objc pmaly dpds o popy o ag suac. Wl acclao daa ca b pmally obad o valdag aalycal pocdu ducd mpac oc s assumd o b a al-s mpuls a magud o ad duao o 5 µs. Ud s codos smulad acclao o objc s calculad usg E. 5 s ducd om ad s so Fgu.

5 Acclao m/s Tm µs Fgu. Acclao ducd om a dop soc mpac. Usg smulad acclao as o daa o E. 6 ad Smpso umcal gao scm o covoluo m mpac oc as vsly calculad. Fgu sos vd mpac oc. As pcd s ocg uco obad om vs aalycal scm s dcal o appld mpac oc. 8 Impac Foc Tm µs Fgu. T vd mpac oc.

6 Cocluso Idcao o soc mpac oc d o a sucual assmbly subjcd o a dop mpac s dd o assssg gy codo o assmbly. A omulao o vs poblm o vg soc mpac oc om acclao daa o a bam sucu ud la dop codo as psd. To valda vs aalycal scm a ducd om o omulao dg a sgl-dg-o-dom sysm as mplmd. A cas sudy as coducd usg smulad acclao daa gad om a o al-s mpuls uco. As pcd vd mpac oc appad o b dcal o appld mpac oc. Rc. Ha. C. ad Wcs A.. Foc Dmao Slop ad Sa Rspos asum Pocdgs o 8 Iaoal odal Aalyss Coc 65-7 Kssmm F Iou H. Ida. Ksmoo K. Sbuya T. ad Kozum T. Ivs Aalyss o agud ad Dco o Impac Foc JSE Iaoal Joual Ss A Vol. 8 o. pp Cag C. ad Su C. T. D Tasvs Impac Foc o a Compos ama by Sgal Dcovoluo Epmal cacs 9 pp Zu J. ad u Z. A Tm Doma od o Idyg Dyamc oads o Couous Sysms Joual o Soud ad Vbao 8 pp Doyl J. A Epmal od o D ocao ad Tm o Iao o a Uo Dspsg Puls Epmal cacs 7 pp Co K. ad Cag F. K. Idcao o Impac Foc ad ocao Usg Dsbud Ssos AIAA Joual Wag B.-T. ad Cu C.-H. Dmao o Uo Impac Foc Acg o a Smply Suppod Bam cacal Sysms ad Sgal Pocssg

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