Damping analysis in flexural vibration of sandwich beams with debonding

Transcription

1 Damping analysis in flxural vibration of sanwich bams with boning Iriss Mahamat Moustapha, Abrrahim El Mahi, Rachi El Gurjouma, Olivir Dazl To cit this vrsion: Iriss Mahamat Moustapha, Abrrahim El Mahi, Rachi El Gurjouma, Olivir Dazl. Damping analysis in flxural vibration of sanwich bams with boning. Société Français Acoustiqu. Acoustics 1, Apr 1, Nants, Franc. 1. <hal-81879> HAL I: hal Submitt on 3 Apr 1 HAL is a multi-isciplinary opn accss archiv for th posit an issmination of scintific rsarch ocumnts, whthr thy ar publish or not. Th ocumnts may com from taching an rsarch institutions in Franc or abroa, or from public or privat rsarch cntrs. L archiv ouvrt pluriisciplinair HAL, st stiné au épôt t à la iffusion ocumnts scintifiqus nivau rchrch, publiés ou non, émanant s établissmnts nsignmnt t rchrch français ou étrangrs, s laboratoirs publics ou privés.

2 Procings of th Acoustics 1 Nants Confrnc 3-7 April 1, Nants, Franc Damping analysis in flxural vibration of sanwich bams with boning I.M. Moustapha, A. El Mahi, R. El Gurjouma an O. Dazl Laboratoir acoustiqu l univrsité u Main, Bât. IAM - FR Scincs Avnu Olivir Mssian 785 L Mans Cx 9 iriss.moustapha.tu@univ-lmans.fr 411

3 3-7 April 1, Nants, Franc Procings of th Acoustics 1 Nants Confrnc Th papr prsnts, an analysis of th amping of sanwich composits with boning. Ths sanwich composits consist of two thin facs compos of glass fibrs an po rsin bon to light wight an wakr cor matrial of PVC foams. Natural frquncis an amping paramtrs ar invstigat using bam tst spcimns an an impuls tchniqu. Molling of th amping of a sanwich composit with boning is stablish consiring finit lmnt analysis which valuat th iffrnt nrgis issipat in th matrial irctions of th cor an th skins. Th ffcts of boning variabl lngths on th natural frquncis an th amping wr stui numrically an compar with xprimntal rsults. Th rsults show that th natural frquncis an amping ar snsibl to boning lngth. Ths proprtis offr th snsitiv inicators of amag of sanwich matrials uring liftim. 1 Introuction A sanwich structur consists of two thin, stiff an strong facs bon to thick, lightwight an wakr cor matrial using som ahsiv. Sanwich composits show xcllnt mchanical proprtis u to thir high spcific stiffnss an strngth to wight ratios. Th viscolastic cor has a high inhrnt amping capacity. In th flxural vibration of sanwich, th amp cor is constrain to shar. Th ffcts transvrs shar causs th flxural motion to b amp an nrgy to b issipat. In sanwich matrials a high part of th nrgy is issipat by th transvrs shar ffcts inuc in th sanwich cor. Assarar t al [1] us th iffrnt nrgis issipat in th matrial irctions of th cor an th layrs of th skins for amping moling of sanwich bam. For th fibr-rinforc composit, amping pns on fibr, layr orintation, stacking squnc []. Many rsarchrs us th concpt of a complx moulus. In this concpt, th imaginary part is associat with th nrgy issipation. Damag is mchanism which causs incras amping. Znkrt t al [3] us th finit lmnt mtho an xprimnt for analys th impact amag of sanwich. Rcntly Burlaynko t al [4] invstigat th influnc of siz, location an numbr of bon zons on ynamic charactristics of sanwich plats. Th boning rsults ahsiv graation, fcts of manufacturing, impact by forign objcts, or strss concntration u to localiz loaing [5-8]. Dboning introucs friction in th unboun rgion of th intrfac, th amping incrass with th siz of th boning. Bukt t al [9] stui th vibration bhaviour of flat an curv sanwich (with 15, 3, 45 an 6 opn angl) composit bams with fac/cor bon. Thy not that with prsnc of bon, th amping variation for sanwich bam with curvatur angl of 3 an 6 shows mor snsitiv rsults than that of sanwich bam with curvatur angl of 15 an 45. Suzuki t al [1] prsnt a finit lmnt analysis of th amping of laminat composits with lamination. Th moal strain nrgy mtho is also implmnt into this finit lmnt analysis. Th rsults obtain show that this analysis scribs fairly wll th xprimntal rsults. Th purpos of this articl is to vlop molling of amping of sanwich matrials with boning bas on a finit lmnt analysis. Th ffcts of variabl lngth boning on natural frquncis an amping paramtrs wr stui. Th rsults riv from this analysis ar compar to th xprimntal rsults. Finit lmnts moling.1 Strain nrgy Finit lmnts bas on th thory of plan strss ar us. Finit lmnt analysis givs th valus of th strsss σ, σ, σ an th strains ε, ε, ε in ach skins lowr (l), uppr (u) an cor (c) for ach finit lmnt (). Th nrgy stor in a givn finit lmnt can b xprss as a function th strain nrgis rlat to th iffrnt irctions as: = + + (1) With 1, xy = σ ε 1 σ, xy ε 1, xy = σ ε = () Whr th intgrations ar xtn ovr th ara of th finit lmnt. Th nrgy is th strain nrgy stor in tnsion comprssion along th x-irction of th matrials, is th strain nrgy stor in tnsion comprssion along th y-irction of th matrials an is th strain nrgy stor in-plan (plan (x, y)) shar. Th in-plan strain nrgy stor in lmnt is givn by Exprssions (3) an th total in-plan strain nrgis stor in th finit lmnt assmblag is thn obtain by summation on th lmnts as: =, lmnts = lmnts = lmnts, (3) Th strain nrgy stor in th sanwich composit structur can b xprss as a function of th in-plan strain nrgis rlat to th matrial irctions as: + +. = 4). Estimation of sanwich amping Th nrgy issipat by amping in th skins or in th cor of th sanwich matrial of th lmnt is riv from th strain nrgy stor in th skins or in th cor as []: Δ = ψ + ψ + ψ (5) p p p p p p p 41

4 Procings of th Acoustics 1 Nants Confrnc Introucing th spcific amping cofficints of th skins or of th cor. Ths cofficints ar rlat to th matrial irctions of th skins (p=l or u) or of th cor (p=c): ψ p ψ p an ar th amping cofficints in tnsioncomprssion in th x-irction an y-irction of th skins or of th cor, rspctivly; is th in-plan coupling ψ cofficint. Th amping nrgy issipat in th lmnt is nxt obtain by summation on th cor an on th skins of lmnt as: Δ = Δc + Δ s (6) Whr s is skin an c cor, th total nrgy Δ issipat in th finit lmnt assmblag is thn obtain by summation on th lmnts: p Δ = Δ (7) lmnts Finally, th amping of th finit lmnt assmblag is charactriz by th amping cofficint of th assmblag riv from rlation [11]: 3 Matrials Δ = ψ (8) Sanwich matrials wr construct with glass fibr laminats as skins an with PVC clos-cll foams as cor. Th glass fibr laminats of th skins ar cross-ply laminats consisting of uniirctional layrs of E-glass fibrs in an po matrix, arrang in th squnc [ /9 ] s. Th uniirctional layrs wr fabricat with uniirctional cloth of wight 3 g m with glass fibrs align in a singl irction. Th PVC clos-cll foams wr suppli in panls of thicknss mm. Two foams wr consir iffring in thir nsitis: 6 kg m 3 an 1 kg m 3. Sanwich matrials wr construct with ths foams an with cross-ply glass-fibr laminats prpar by han lay-up procss that las to a nominal thicknss of 3 mm for th sanwich skins. Sanwich plats of iffrnt imnsions wr cur at room tmpratur with prssur using vacuum mouling procss, an thn post-cur in an ovn. Th spcimns hav bn cut up with a iamon isc, from sanwich plats. Dimnsions of th spcimns ar shown in tabl 1. Cor thicknss a (mm) Tabl 1: Dimnsions of sanwich spcimn Skin thicknss p (mm) Lngth of spcimn L (mm) With of spcimn b (mm) Exprimntal procur Th amping charactristics of th sanwich bam without or with boning obtain by subjcting bams to flxural vibrations. Th quipmnt us is shown in Figur 1.a. Th tst spcimn is support horizontally as a cantilvr bam in a clamping block. An impuls hammr is us to inuc th xcitation of th flxural vibrations of th bam nar th clamping block (Figur 1.b) an th bam rspons is tct nar th fr n of th bam by using a lasr vibromtr. Nxt, th xcitation an th rspons signals ar igitaliz an procss by a ynamic analyzr of signals. This analyzr associat with a PC computr prforms th acquisition of signals, controls th acquisition conitions an nxt prforms th analysis of th signals acquir (Fourir transform, frquncy rspons, mo shaps, tc.). Th flxural bam rsponss wr intifi in th frquncy omain using analysis an fitting th xprimntal frquncy rsponss using Matlab toolbox. Thn, th intification procur allows us to obtain th valus of th natural frquncis f i an th moal loss factorsη i, rlat to th spcific amping cofficint by th rlation ψ = πη. Lasr Vibomtr OFV3 R x Msuring point i i (a) Clamping box Dynamic Analysr Siglab 6 Signal Conitionnr OFV 3 Impact point Figur 1: Analysis of bam vibrations; a) Exprimntal quipmnt, b) Impact an masuring points 5 Finit lmnts procur 3-7 April 1, Nants, Franc Bam Impact hammr Th finit lmnt mtho is us to comput moal natural frquncis, strss an strain for sanwich bam without or with boning. Th boning is btwn th skin an th cor of sanwich bam, it is moll as a voi btwn thm. Th bon surfacs ar not in contact. Th propagation of boning was not allow uring vibration. Th finit lmnt simulations wr conuct using ABAQS 6.1. Th ruc intgrat continuum plan strss lmnt (CPS4R) is us for msh, CPS4R is a four no lmnt. This lmnt bas on th thory of plan strss. Th matrial for th skin of a sanwich is consir anisotropic an th cors wr consir as homognous isotropic matrials. Th matrial proprtis 413

5 3-7 April 1, Nants, Franc Procings of th Acoustics 1 Nants Confrnc us for numrical simulation ar shown in Tabl an 3. Th sanwich bam with boning in molling finit lmnt is shown in th figur. Tabl : Mchanical charactristics of th PVC Foam Dnsity of th foam (kg m -3 ) 6 1 Young moulus (MPa) 6 85 Poisson s ration.4.43 Shar moulus (MPa) 38 Tabl 3: Enginring constants of uniirctional glass fibr layrs Enrgy (J) x1 x1 3 Normaliz boning lngth (%) Figur 3: Enrgis stor as function boning lngth in th skin of sanwich bam with foam of 6 kg m -3 of nsity 8 E L (GPa) E T (GPa) ν LT G LT (GPa) Enrgy (J) 6 4 Normaliz boning lngth (%) Figur : Msh of sanwich bam with boning 6 Rsults an iscussion 6.1 Enrgy stor in th constitunt of sanwich Th bam ha on cntral boning btwn th cor an th fac sht of varying lngth (l) locat at th miplan, symmtrically about th mi-span of th bam. For xampl, th figur 3 shows th iffrnt strain nrgis in th skins of th sanwich bams for th first mo of th bning vibrations. Ths rsults wr obtain using a finit lmnts analysis for iffrnt normaliz boning lngth an for sanwich with foam of 6 kg m -3. Th rsults obtain show that th nrgis stor cras whn th boning lngth incrass. Th rsults so show that th longituinal strain nrgy is highr than th othr nrgis. From this rsults it is possibl to consir only th longituinal nrgy stor ( ) in th skin. Th figur 4 shows th volution of th nrgis stor in th foam cor as functions of th boning lngth for th first mo an for sanwich with foam of 6 kg m -3. Th shar nrgy stor ( ) cras an th longituinal nrgy stor ( ) incras whn th boning lngth incrass. Th nrgy is much lowr an can b nglct. Figur 4: Enrgis stor as function boning lngth in th cor of sanwich bam with foam of 6 kg m -3 of nsity 6. Effct of th boning lngth on th natural frquncy Th figur 5 shows th ffcts of th variabl boning lngth, in bon sanwich bams on natural frquncy of th sanwich bam. Th finit lmnt rsults an xprimntal rsults ar compar. Th masur funamntal natural frquncy of th unamag sanwich bam is 18 Hz for cor nsity of 6 kg m -3 an is 19 Hz for cor nsity of 1 kg m -3. Th finit lmnt natural frquncy is about 18 Hz for cor nsity of 6 kg m -3 an is 19 Hz for cor nsity of 1 kg m -3. For two typs of sanwich th natural frquncy of th bon sanwich bam cras rastically at 5% of normalis lngth of boning for two typs of sanwich. An incras in th xtnt of boning givs a gratr ruction in th natural frquncis of th sanwich bams. For two typs of sanwich thr is a critical boning (5%) xtnt byon which th ruction of th natural frquncis incrass isproportionatly. Th comparison shows a goo agrmnt btwn th xprimntal rsults an th rsults uc from moling until 5% of normalis boning lngth. 414

6 Procings of th Acoustics 1 Nants Confrnc 3-7 April 1, Nants, Franc,8 Frquncy (Hz) Exprimntal rsults Finit lmnt analysis Loss factor η (%),6,4, Frquncy (Hz) Normaliz boning lngth (%) (a) Exprimntal rsults Finit lmnt analysis Normaliz boning lngth (%) Figur 5: Comparison btwn rsults uc from xprimnt an moling for th natural frquncy vrsus th boning lngth for th composit sanwich bams with two iffrnt foam nsitis: a) 6 kg m -3 an b) 1 kg m Loss factor amping of sanwich Moling prform taking into account th variation of th amping cofficint (or loss factor) of th various constitunts of th sanwich matrials as a function of frquncy. Th loss factor of th various constitunts of th sanwich matrials (skin an cor) is invstigat by El Mahi t al. [] an Assarar [13], th loss factor as function th frquncy ar shown in figur 6 an 7. Th figur 8 shows th loss factor amping volution vrsus th normaliz boning lngth. Ths rsults ar uc from th xprimntal invstigation an finit lmnt analysis. Th amping loss factor valus incras with incrasing boning, bcaus bon introucs mor friction in th sanwich bam. Th variation of amping ratios is consirably highr in cas of th spcimns with foam nsity of 6 kg m -3 (figur 8.a). For two iffrnt sanwich, th comparison shows a goo agrmnt btwn th xprimntal rsults an th rsults uc from molling until 5% normaliz boning lngth. Th analysis finit lmnt tns to giv highr loss factor amping compar to by th xprimntal invstigation., Frquncy (Hz) Figur 6: Th loss factors as function of th frquncy for longituinal irction of th skin [] Loss factor η (%) kg m -3 1 kg m Frquncy (Hz) Figur 7: Th loss factors as functions of th frquncy for th two nsitis of th foams: 6 an 1 kg m -3 [13] Loss factor (%) Loss factor (%) 3,,5, 1,5 1,,5 Exprimntal rsults Finit lmnt analysis, Normaliz boning lngth (%),5, 1,5 1,,5 (a) Exprimntal rsults Finit lmnt analysis, Normaliz boning lngth (%) Figur 8: Th ffct of boning lngth on th loss factor amping of th sanwich bam with foam cor of nsity: a) 6 kg m -3 an b) 1 kg m

7 3-7 April 1, Nants, Franc 7 Conclusions An valuation of th amping of sanwich matrials fabricat with a foam cor an laminat skins was prsnt bas on th thory of plan strss an a finit lmnt analysis in vibrations of a composit sanwich. Th analysis rivs th strain nrgis stor in th matrial irctions of th foam cor an in th matrial irctions of th skins. Damping charactristics of sanwich for iffrnt boning lngth wr valuat xprimntally using bam spcimns subjct to an impuls input. Damping moling is vlop using a finit lmnt analysis which valuat th iffrnt nrgis issipat in th matrial irctions of th cor an th skins. Th comparison shows a goo agrmnt btwn th xprimntal rsults an th rsults uc from molling until 5% of lvl boning. This agrmnt unrlins that th moling consir is wll suit to scrib th amping of sanwich matrials with variabl lngth boning. Procings of th Acoustics 1 Nants Confrnc [11] E. E. ngar, E. M. Krwin, Loss factors of viscolastic systms in trms of nrgy concpts, Journal of Acoustical Socity of Amrica, 34(7), (196). [1] M. Assarar, Etu xpérimntal t moélisation u comportmnt ynamiqu s composits stratifiés t sanwichs, PhD thsis, 7, L Mans Rfrncs [1] M. Assarar, A. El Mahi, J.M. Brthlot, Damping Analysis of Sanwich Composit Matrials, Journal of Composit of matrials, 43(13), (9). [] A. El Mahi, M. Assarar, Y. Sfrani, J.M. Brthlot, Damping analysis of orthotropic composit matrials an laminats, Composit: Part B, 39(7-8), (8). [3] D. Znkrt, A. Shipsha, P. Bull, B. Hayman, Damag tolranc assssmnt of composit sanwich panls with localis amag, Composits Scinc an Tchnology, 65(15-16), (5). [4] V.N. Burlaynko, T. Saowski, Dynamic bhaviour of sanwich plats containing singl/multipl boning, Computational Matrials Scinc, 5(4), (11). [5] A. El Mahi, M. K. Farooq, S. Sahraoui, A. Bzazi, Molling th flxural bhaviour of sanwich composit matrials unr cyclic fatigu, Matrials an Dsign, 5(3), (4). [6] D. Gura-Dgorgs, P. Thvnt, S. Maison, Damag tolranc of sanwich structurs, in: Procings of Euromch 36 Colloquium, Kluwr Acamic Publishrs, Saint Etinn, 9 36 (1977). [7] S. Abrat, Localiz impact on sanwich structurs with laminat facings, Appli Mchanics Rviw, 5(), 6 8 (1997). [8] J.E. Shafizah, J.C. Sfris, E.F. Chsmar, R. Gyr, Evaluation of th in-srvic prformanc bhaviour of honycomb composit sanwich structurs, Journal of Matrials Enginring an Prformanc, 8(6), (1999). [9] B. O. Baba, S. Thoppul, Exprimntal valuation of th vibration bhavior of flat an curv sanwich composit bams with fac/cor bon, Composit Structurs, 91(1), (9). [1] K. Suzuki, I. Kimpara, K. Kagyama, Non linar vibration an amping charactrizations of laminat composit laminats by using multilayr finit lmnts, 4th Intrnational Congrss of th Aronautical Scincs ICAS