Fatigue life analysis of the plate structure with random vibro-acoustic loading

Transcription

1 INTER-NOISE 16 Ftigue life lysis of the plte struture with rdom vibro-ousti lodig Go Zhg 1 ; Hubig Jig 1 Istitute of Systems Egieerig, Chi Ademy of Egieerig Physis,Miyg Chi Istitute of Systems Egieerig, Chi Ademy of Egieerig Physis, Miyg, Chi ABSTRACT Vibro-ousti lodig is oe of the rdom lodigs, whih ts o the struture surfe. The vibro-ousti lod will exite the rdom vibrtio respose of the struture, whih will led to ftigue filure. I this ivestigtio, the rdom respose d ftigue filure of the typil plte struture with rdom vibrtio lodig is derived. The trsformtio reltio betwee ousti lodig d rdom vibrtio lodig is preseted. The ousti lodig is simulted with rdom vibrtio eviromet. The the power spetrum desity of the elertio is treted s the lodig oditio. The rdom vibrtio respose of typil plte struture is lulted with umeril method. Bsed o the lulted results of the rdom stress d ftigue lysis method, the evlutio of ftigue life for the struture is rried out d ompred with the riterio life to demostrte the relibility of the urret method. Keywords: 4 vibro-ousti lodig,ftigue life,fiite elemet lysis Subjets Number(s): 3.1 I-INCE Clssifitio of 1. INTRODUCTION Vibro-ousti lodig is importt eviromet tht wepo equipmet lwys experiees whe trsported d used, so Vibro-ousti lodig evirometl suitbility is sigifit pbility for wepo equipmet. I order to quit the struture property of the equipmet i the desig stge, methods of umeril lysis, experimet d so o be used to ssess it ftigue life uder vibrtio lods, whih provide support to optimize desig. Trditiolly, there re two methods to lyze struture s ftigue life uder vibrtio lodig (1,). Oe is time domi method bsed o dt sttistis, whih eeds to out the umbers of stress yles o dgerous poit of struture firstly, the sum the mout of dmge with umultive ftigue dmge method d ssess its ftigue life. However, it is ot effiiet eough beuse of its lrge mout of dt, d the ext time domi stress o dgerous poit is lso diffiult to get. Aother method is frequey domi method bsed o power spetrum desity, i this method the PSD (power spetrum desity) of the stress respods of dgerous poit is lulted through sttistis, d the ssess its ftigue life. Frequey domi method is low ost d oveiet, so it is more used i the egieerig. I this pper, the ousti lodig is simulted with rdom vibrtio eviromet. The the power spetrum desity of the elertio is treted s the lodig oditio. The rdom vibrtio respose of typil plte struture is lulted with umeril method. Bsed o the lulted results of the rdom stress d ftigue lysis method, the evlutio of ftigue life for the struture is rried out d ompred with the riterio life to demostrte the relibility of the urret method.. DEDUCTION OF FATIGUE LIFE The stress mplitude S d the umbers of lodig yles hve reltio bellow, whe the struture is uder sie ltertig lods(3, 4). 1 zg_13@163.om @qq.om 7635

2 INTER-NOISE 16 NS ( ) / S (1) I equtio.(1), d re both the mteril ostts. Aordig to Mier Lier Method, the umultio of ftigue dmge of the mteril uder sie ltertig stress whose mplitude is S.is s equtio.(). () D D / N M i i i i i I equtio.(), i is the yles umber of the stress S i, d N i is the yles umber of stress S whih me the mteril destroyed. D i is the dmge degree of S i, the mteril will be destroyed, whe D m rehed 1. I the proess of vibrtio, the frequey the stress whose mplitude is betwee S d S +ds emerges i time of T is (S ). ( S ) Tp( S ) ds (3) I equtio (3), the power spetrum desity of the stress o the dgerous poit is G(f), the spetrum momet is m f G( f ) df. I rrow bd rdom proess, ν is the umbers of slop th pss through.5 verge vlue, ( m / m ). I wide rdom proess, ν is the expeted vlue of stresspe,.5 p ( m4/ m), p(s ) is the probbility desity of the stress mplitude. The probbility dmge of the mteril uder rdom stress S is s bellow: ( S) ( S) T ds (4) N( S) N( S) Aordig to Mier Lier Method, the totl dmge of mteril uder rdom stress is D M : ps ( ) DM T ds (5) NS ( ) Whe D 1, the mteril will be destroyed, d its ftigue life T be lulted. M 1 T ps ( ) T ds NS ( ) S p( S ) ds I the sttiory Guss proess x(t) with zero verge vlue, its probbility pe p(t) is s bellow: p t ( ) exp( x ) (6) 1 1 (7) I rrow bd rdom proess, it ssumed tht, the stresspe is ord with Ryleigh distributio, d the stress mplitude d stresspe hve the sme probbility futio. 1 S ( ) S ps ( ) e (8) Itegrte the equtio (8) from zero to ifiity, it trsform to equtio (9): ps ( ) ds (1 ) / (9) NS ( ) I equtio (9), is root me squre vlue of stress, ( x) is gmm futio, (9) d equtio (6), the ftigue life be lulted:, merge equtio 7636

3 INTER-NOISE 16 T (1 ) (1) For wide rdom proess, the mteril s dmge D WB be obtied from medig D NB i rrow proess. D WB D (11) NB I equtio (11), hs the bellow reltio with oeffiiet d slop of S-N urve. Where = , b= , / p m / m m 4 (1 )(1 ) b (1) So, the ftigue life T of mteril uder wide rdom lodig be quired. T (1 ) 1, is irregulr oeffiiet (13) 3. FATIGUE LIFE ANALYSIS OF PLATE STRUCTURE Cirulr plte(5) is typil struture i wepo equipmet tht my be destroyed uder rdom vibrtio lodig or vibro-ousti lodig. Numeril simultio of the struture s respods uder rdom vibrtio lodig is rried out. Firstly, the dgerous poit is foud i the umeril modl. The the reltio betwee power spetrum desity of stress i dgerous poit is lulted, Thirdly, the root me squre, the spetrum momet m d expettio of stresspe ν re lulted through itegrtio. Te these prmeters ito equtio (1), the ftigue life of irulr plte will be gotte. The fiite elemet model is set up i the softwre s show i Figure.1, where the modulus of elstiity is e11, d Poisso s rtio is.3. The displemet of four poits roud the border is restrited. Figure 1 Fiite elemet modl 3.1 Model Alysis Modl lysis is the premise of spetrum lysis, the mi modls of the struture be quired through some softwre. Tble 1 shows the former five modls of the plte, lwys, the former two modls is wht is most foused o (6. 7). 7637

4 INTER-NOISE 16 Tble 1 The former five turl frequey of the plte modl Nturl frequee(hz) Figure PSD of rdom lodig 3. Spetrum Alysis I the proess of spetrum lysis, the urve of power spetrum desity show i Figure. is loded o the restrited poits of the plte. The displemet d stress be quired through the Post-proessig. Fig.3 shows the stress ephogrm, with stress probbility of 1σ whih mes tht uder the give lodig, the probbility the mximum stress or displemet less th the lulted result is 68%. From fig.3, the positio with mximum stress is er the restrited poit, with σ x =6.e6, σ y =6.9e6 d σ y =1.3e7. Aimed t this positio, the hgig reltio betwee stress d frequey is lulted s show i the urve i Figure 4. The, spetrum momet d the umbers of slop th pss through verge vlue be lulted through equtio (14) d equtio (15). If the rdom respods uder the give lodig is ssumed rrow rdom proess, ftigue life of the plte ould be obtied by tig the m d ν + from equtio (14) d equtio (15) ito equtio (1). Through the proess of lultio, the ftigue life of plte is bout 14 hours. m f G( f ) df (14).5 ( m/ m) (15) Figure 3 Stress ephogrm 7638

5 INTER-NOISE 16 Figure 4 Chgig reltio betwee stress d frequee Compred with the stdrdized life, the result lulted though the method bove is slightly smller. The most probble reso is tht there some differee betwee umeril modl d rel struture. I the rel struture, the displemet of the oetio positio is ot zero, whih is ssumed zero i the umeril modl, so the stress lulted beome lrger ledig to the ftigue life smller. Also, there re some other resos suh s lgorithm i the softwre d so o. All the sme, the lulted result by mes bove hs referee vlue for egieerig. 4. CONCLUSIONS Bsed o Mier Lier Method, d reltio betwee stress mplitude S d the tio times N by the lod, the preditio modl of struture s ftigue life uder rdom vibrtio is deduted, refereig doumet. Through softwre, the stress distributio of plte struture d the power spetrum desity of stress i dgerous poit re lulted. Tig the result from umeril lysis ito the preditio, its ftigue life is lulted d ompred with stdrdized life. The mes through umeril lysis d frequey domi method to predit struture s ftigue life is doble. ACKNOWLEDGEMENTS The uthors grtefully owledge the fiil support from the Ntiol Nturl Siee Foudtio of Chi (Grt No ) d the ey subjet Computtiol Solid Mehis of the Chi Ademy of Egieerig Physis. REFERENCES 1. Zeg. Chuhu, Zheg. Shiji. Method of ftigue life lysis d its pplitio[m]. Beijig: Ntiol Defese Idustry Press. 199:1~41. Yo. Qighg. Issue of elerted vibrtio test[j]. Stdrd d Qulity of Avitio, 1975(6):7~ H. Qighu. H. Fei. Alysis o vibrtio ftigue test for horizotl til of irrft[j]. Jourl of Struturl Stregth, 9():4~7. 4. Wg Migzhu. Reserh o life lysis method of struture vibrtio ftigue[d]. Njig: Njig Uiversity of Aeroutis d Astroutis. College of Aerospe Egieerig, 9: C. L. Chow, D. L. Li, Alytil solutio for fst ftigue ssessmet uder wide-bd rdom lodig[j]. Itertiol Jourl Ftigue, 1991(13):395~ T. T. Fu, D. Cebo, Preditio ftigue lives for bimodl stress spetrl desities, Itertiol Jourl Ftigue, ():11~1. 7. D. Besiutti, R. Tovo. Comprisio of spetrl methods for ftigue lysis of brod-bd Gussio rdom proess[j]. Probbilisti egieerig mehis, 6,1(4): 87~