IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS

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1 IOP Confrnc Sris: Marials Scinc an Enginring PAPER OPEN ACCESS Gomrically nonlinar ransin vibraions of acivly amp anisymmric angl ply lamina composi shallow shll using aciv fibr composi (AFC) acuaors o ci his aricl: M H Asho al 018 IOP Conf. Sr.: Mar. Sci. Eng Viw h aricl onlin for upas an nhancmns. his conn was ownloa from IP arss on 06/01/019 a 3:45

2 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 Gomrically nonlinar ransin vibraions of acivly amp ani-symmric angl ply lamina composi shallow shll using aciv fibr composi (AFC) acuaors Asho M H 1, Shivaumar J, Sanosh Nanurar 3, Vishwanah Khaabhavi 1, Sanjay Pujari 4 1 Faculy, Mch Engg. Dp., AIM, Blagavi , Karnaaa, Inia Principal, Chhaisgarh Enginring Collg, Durg , Chhaisgarh, Inia 3 Faculy, Mch Engg Dp., KLE Dr MSSCE, Blagavi , Karnaaa, Inia 4 Principal, AIM, Blagavi , Karnaaa, Inia sanoshnn.1988@gmail.com Absrac. In prsn wor, h hin lamina composi shallow shll as smar srucur wih AFC marial s ACLD ramn is analyz for gomrically nonlinar ransin vibraions. h AFC marial is us o ma h consraining layr of h ACLD ramn. Golla- Hughs-Mcavish (GHM) is us o mol h consrain viscolasic layr of h ACLD ramn in im omain. Along wih a simpl firs-orr shar formaion hory h Von Kármán yp non-linar srain isplacmn rlaions ar us for riving his lcromchanical coupl problm. A 3-imnsional fini lmn mol of smar composi panls ingra wih h ACLD ra pachs has bn moll o rval h prformanc of ACLD ra pachs on improving h amping propris of slnr ani-symmric angl-ply lamina shallow shll, in conrolling h ransin vibraions which ar gomrically nonlinar. h mahmaical rsuls xplain ha h ACLD ra pachs consirably nhanc h amping propris of ani-symmric angl-ply panls unrgoing gomrically nonlinar ransin vibraions. 1. Inroucion In h avancmn of sign of lighwigh flxibl srucurs ncssia h us of lamina composi srucurs in h form of bams, plas an panls. hs ligh wigh srucurs ar vulnrabl o ousiz vibraions wih xnsiv cay im bcaus of small inrnal amping. o circumvn hs problms appropria aciv conrol sysm which compriss of acuaors an/or snsors is ingra on h hos srucur maing hm as smar srucur [1]. h us of isribu acuaors an/or snsors ma of pizolcric marial is prominan an nic h anion of svral rsarchrs from pas svral yars [-6]. hs lighwigh flxibl srucurs whn coupl wih h layr/pachs of pizolcric marials acing as isribu snsors an/or acuaors ar cusomarily nown as smar srucurs. I has bn obsrv ha PZ pizocramics us as snsor/acuaor in rsarch wors rla o smar srucurs has rawn anion owars incrasing h prformanc of srucural conrol. h PZ pizocramics has isavanags such as brilnss, low conrol auhoriy u o hir low srss/srain consans, non-conformabiliy o curv surfac an rlaivly highr nsiy compar o convnional composi srucural marials, c. In an amp o Conn from his wor may b us unr h rms of h Craiv Commons Aribuion 3.0 licnc. Any furhr isribuion of his wor mus mainain aribuion o h auhor(s) an h il of h wor, journal ciaion an DOI. Publish unr licnc by L 1

3 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 g h br prformanc from h xising monolihic pizolcric marials, Hau an Fung [7] focus on h ffc of aciv consrain layr amping (ACLD) ramn on analysis of a flxibl bam. h unwan vibraions of h subsra srucur can b minimiz by aing ACLD ramn o i. Sinc, ACLD ramn givs h characrisics of boh aciv an passiv amping [8] occurring simulanously an has bn xpansivly us for silful an consisn aciv amping of flxibl srucurs. An analysis of ACLD of gomrically nonlinar ransin vibraions of hin composi plas using horizonally rinforc pizo-fibr composi marial is carri ou by R. Sursh Kumar an M C Ray [9]. Ray an co-worrs [10] conuc h aciv amping of nonlinar vibraions of funcionally gra plas an vrically rinforc 1-3 PZC as h consraining layr ACLD ramn marial for aciv conrol of gomrically nonlinar vibraions of composi srucurs [11]. Much of h wor is no rpor in opn liraur o arss h ACLD ramn of gomrically nonlinar vibraions of lamina composi shallow shlls using AFC marial so ha in-plan acuaion coul b us for aciv conrol.. Fini lmn molling Figur 1 rprsns h shallow shll composi panl consis of N orhoropic layrs. h lrs h, s, ϕ, a, an R ar us o no hicnss, circumfrnial wih, shallownss angl, lngh an avrag raius of h panl rspcivly. h AFC pachs ar appli on h op surfac of h panl hrough ACLD chniqu as shown in Figur 1. ACLD ra viscolasic consrain layr is having a hicnss of h v an h lcro spacing in inr-igia lcro parn for acuaing AFC pach marial is h p. h ovrall formaion inmaics of h nir panl consiss of lamina panl an ACLD ra AFC pachs is sui using firs orr shar formaion hory (FSD). Lrs u, v, an w ar us o rprsn h gnraliz isplacmns along x, y, an z ircions a any poin in any coa of h nir panl rspcivly an can b wrin as: { { [ Z]{ r (1) whr{ [ u v w], { [ uo vo w], { [ ] r x y x y x y, Figur 1. Lamina shallow shll wih pachs of ACLD ramn.

4 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 bu hin srucurs ar subjc o shar locing ffc an o avoi his, Slciv ingraion rul is mploy by slcing h sa of h srains as ransvrs shar srains{ s an in-plan srains { b rspcivly, whr: { s [ xz yz ] an { [ x y xy] b () In h nir panl, h in-plan an ransvrs shar srsss sa a any poin can b wrin as: { [ x y xy] b an{ s [ xz yz ] (3) h hos panl s consiuiv rlaions for h orhoropic layrs ar givn by { [ C ]{ an { [ C ]{ b b b s s s, 1,,3,... N (4) h AFC layr appli on h panl will unrgo h ffc of appli lcric fil ( Ex) acing along is lngh (i.. in x-ircion). hrfor h smar srucur s coupl consiuiv rlaions can b givn as: { [ C ]{ { { E x,{ [ C ] { b b b b s s s an D [ ] { x E, b b 11 x N (5) I is assum ha marial us for h viscolasic layr is linarly viscolasic an isoropic marial. Hr, o analyz an mol h viscolasic marial of h ACLD ra smar srucur in im omain h Golla-Hughs-Mcavish (GHM) mho is us. Using Siljs ingral [1] form, h viscolasic marial s consiuiv quaion can b xprss as: { { σ = G( - τ) sv sv τ (6) 0 whr Gis () h rlaxaion funcion for viscolasic marial. h wo yps of nrgis of h smar srucur wih ACLD ra pachs ma of AFC marial i.. oal ponial nrgy p an inic nrgy can b xprss as: 1 N ({ { { { ) { p s s Ex Dx { f A b b 1 A (7) 1 N an ( u v w ) (8) 1 whr { f is h xrnally appli surfac racion vcor acing ovr a surfac ara A an Ω is h volum of h concrn omain. ρ is h mass nsiy of h layr. Using igh no iso-paramric quarilaral lmns for iscrizaion of h ovrall panl h oal ponial nrgy of a ypical lmn wih ACLD ramn ma of AFC marial can b quanifi as: 1 [{ [ ]{ { [ ]{ { [ ]{ { [ ]{ { [ ] ( ) { p K Kr r r Kr r Krr r Ksv G 0 { [ ] ( ) { { [ ] K G K G( ) { { [ K rsv r r rsv r rrsv] G( ) { (9) r { [ F ] V { [ F ] V { [ F ] V { E [ N ]{ E V { { F pn p r rp ] Using GHM mho o mol viscolasic layr [8] an o fin h global quaions of quilibrium, h lmnal govrning quaions ar assmbl ino h global spac rprsn as: p 3

5 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 [ M ]{ X [ K ]{ X [ Kr ]{ Xr [ Ksv] G( ) { X [ Krsv] G( ) { Xr (10) { F ({ Fpn { Fp) V 0 0 A simpl vlociy fbac conrol law is us o fin h conrol volag n o apply for acivaing h pachs. h conrol volag of ach pach is givn in h form of rivaivs of h global noal grs of from as shown in quaion 11. V j K j w K j [ U j ]{ X (11) j Whr, K is h conrol gain for h j h pach an uni vcor [ U j ] is a fining h locaion of snsing h vlociy signal which woul b f bac o his pach. Using quaion 11 h moion quaions govrning h clos loop ynamics of h subsra plas aciva by h pachs of ACLD ramns can b obain as follows: [ M]{ X [ C ]{ X [ K]{ X { F (1) m whr an aciv amping marix is givn by [ C ] [ C ] K j { F [ U j ] p j 1 3. Numrical rsuls h numrical rsuls ar obain using h FE mol riv in h arlir scion for valuaing h prformanc of h ACLD pachs on conrolling h gomrically nonlinar vibraions of lamina composi shallow shlls. Ani-symmric angl-ply hin circular shallow shll having h squar plan form a x a an ingra wih wo rcangular pachs of ACLD ramn ar us for valuaing h numrical rsuls. Marial propris of h orhoropic layrs of h subsra panl, AFC layr an viscolasic layr ar an as follows [13]: E L =17.9GPa, EL / E =5, G L =0.5E, G =0.E, L = 0.5, ρ = 1600g/m 3 wih h symbols inicaing h common maning. h PZ5H an poxy ar us o ma h pizolcric fibrs an h marix of h aciv pachs rspcivly. For AFC marial h ffciv lasic wih 40% fibr volum fracion ar an as [11] C 11 = 131.8GPa; C 1 = 71.15GPa; C = 148.9GPa; C 44 = C 55 = 3.35GPa; C 66 = 39.14GPa; ρ = 3640g/m 3, whil h pizolcric cofficins of h AFC marial ar givn by 1 = 13 = 3.34C/m ; 16 = 0 h iffrn hicnsss of h AFC pach, viscolasic pach an h subsra panl ar consir as 50µm, 50.8µm an 3mm, rspcivly. h valus of h axial lngh (a), h shallownss angl (ϕ) of h panl an h pizolcric fibr orinaion angl ( ) in h AFC pachs ar an as 0.5m, 0º an 0, rspcivly unlss ohrwis mnion. Also, h hicnsss of h orhoropic layrs of h subsra panl ar qual. h mchanical loa P acing upwar is suppos o b uniformly isribu. h SS bounary coniions a h gs of h ovrall panls an for valuaing h numrical rsuls ar spcifi by v w a x 0, a an u0 w 0 a y 0, s 0 y y y 0 x x x Now o valia h currn FE mol wih [8] for h ACLD pachs ma of AFC marial an wih inical coniions for SS symmric cross-ply (0 o /90 o /0 o ) subsra panl wih shallownss angl 4

6 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 ϕ = 0 o. h rsuls shown in figurs an 3, inica ha h rsuls obain by h currn orr agr in an xclln mannr wih h xising on [8] in passiv an aciv mo rspcivly. Figur. Comparison of prsn mol wih [11] for rsponss of a SS1 symmric cross-ply (0 o /90 o /0 o ) subsra panl wih ACLD (ϕ = 0 o, Q =750) using AFC unr passiv mo Figur 3. Comparison of prsn mol wih [8] for rsponss of a SS symmric cross-ply (0 o /90 o /0 o ) subsra panl wih ACLD (ϕ = 0 o, Q =750) using AFC unr aciv mo Figur 4 illusras nonlinar ynamic rsponss of a SS ani-symmric angl-ply (-45 0 /45 0 /-45 0 /45 0 ) subsra panl unrgoing ACLD. In his cas h AFC pach significanly amps 5

7 Conrol Volag (Vols) w/h IConAMMA-017 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/01101 ou h vibraion of h shallow shll. h conrol volag n o achiv his conrol rspons shown in figur 4 is illusra in figur 5 in which h valus of h volags ar qui nominal an h corrsponing phas plo is shown in figur Passiv, K =0 Aciv, K = im, (s) Figur 4. Nonlinar ynamic rsponss of a simply suppor ani-symmric angl-ply (-45 0 /45 0 /-45 0 /45 0 ) subsra panl unrgoing ACLD (ϕ = 0 o, Q=750) using AFC 00 Aciv, K = im, (s) Figur 5. Conrol volags n for h ACLD of nonlinar ransin vibraions of an ani-symmric angl-ply (-45 0 /45 0 /-45 0 /45 0 ) subsra panl (ϕ = 0 o, Q=750) using AFC 6

8 Vlociy w/, (m/s) IConAMMA-017 IOP Conf. Sris: Marials Scinc an Enginring (018) oi: / x/310/1/ Aciv, K = Cnral Dflcion, w (m) x 10-3 Figur 6. Phas plo of h simply suppor ani-symmric angl-ply (-45 0 /45 0 /-45 0 /45 0 ) subsra panl ingra wih pachs of ACLD ramn using AFC (ϕ = 0 o, Q=750) 4. Conclusions In his aricl, a 3D FE analysis has bn conuc o xamin h prformanc of h ACLD ra pachs for conrolling gomrically nonlinar ransin vibraions of hin ani-symmric angl ply shallow shll composi panls. AFC marial is consir for h consraining layr of h ACLD pachs. h rsuls isplay h ffciv us of AFC marial pachs us in ACLD ramn in achiving h aciv conrol o supprss h gomrically nonlinar ransin vibraions of ani-symmric angl ply lamina composi shallow shll. 5. Rfrncs [1] Rogrs C A 1994, Sci. Mach. J [] Malli N, Ray M C 005, In J of Mch an Ma in Dsign, [3] Yang S M, L Y J 1994, J. Soun an Vibraion, [4] Maurini C, Porfiri M, Poug J 006, J. Soun an Vibraion, [5] Maxwll N D, Asoanhan S F 004, J. Soun an Vibraion, [6] Kusculuoglu Z K, Fallahi B, Royson J 004, J. Soun an Vibraion [7] Hau L C, Fung E H K 004, J. Soun an Vibraion, [8] Shivaumar J, Asho M H, Ray M C 013, Aca Mchanica, [9] Sursh Kumar R, Ray M C 016, J. Mch of Av Marials an Srucurs, [10] Pana S, Ray M C 008, Smar Marials an Srucurs, [11] Sarangi S, Ray M C 010, Smar Marials an Srucurs, [1] Mcavish D J, Hughs P C 1993, [13] Shivaumar J, Ray M C 008, J. Rinforc Plasics an Composi,