Updated frequency domain analysis in LS-DYNA

Transcription

1 Updated frequecy doma aalyss LS-DYNA Yu Huag, Zhe Cu Lvermore Software Techology Corporato 1 Overvew A seres of frequecy doma features have bee mplemeted to LS-DYNA sce verso 971 R6. These features ca be used to perform vbrato, acoustc ad fatgue aalyss for users from varous dustres [1]. These features clude FRF (frequecy respose fuctos) Keyword: *FREQUENCY_DOMAIN_FRF SSD (steady state dyamcs) Keyword: *FREQUENCY_DOMAIN_SSD Radom vbrato (fatgue) Keyword: *FREQUENCY_DOMAIN_RANDOM_VIBRATION_{FATIGUE} Respose spectrum aalyss Keyword: *FREQUENCY_DOMAIN_RESPONSE_SPECTRUM BEM acoustcs Keyword: *FREQUENCY_DOMAIN_ACOUSTIC_BEM FEM acoustcs Keyword: *FREQUENCY_DOMAIN_ACOUSTIC_FEM These features ca fd applcato NVH of automotves ad ar plaes Acoustc desg ad aalyss of buldgs ad products Defese dustry Fatgue of maches ad eges Safety evaluato of cvl ad hydraulc structures Earthquake egeerg Offshore dustres May others Regardg post-processg of the frequecy doma aalyss, a seres of ASCII ad BINARY databases have bee mplemeted. The ASCII databases clude FRF_AMPLITUDE (for FRF aalyss) FRF_ANGLE (for FRF aalyss) Press_Pa (for acoustc aalyss) Press_dB (for acoustc aalyss) NODOUT_PSD (for radom vbrato) NODOUT_SSD (for steady state dyamcs) NODOUT_SPCM (for respose spectrum aalyss) ELOUT_PSD (for radom vbrato) ELOUT_SSD (for steady state dyamcs) ELOUT_SPCM (for respose spectrum aalyss) Partcularly the NODOUT (_PSD, _SSD, _SPCM) ad ELOUT (_PSD, _SSD, _SPCM) databases are dumped to bary fle BINOUT ad oe ca use LS-PrePost or l2a.exe to extract them from BINOUT. The Nodes whose odal results are output to NODOUT_ databases are specfed by card *DATABASE_HISTORY_NODE. The sold, beam, shell ad thck shell elemets whose elemetal results are output to ELOUT_ databases are specfed by the followg cards:

2 *DATABASE_HISTORY_SOLID_{OPTION} *DATABASE_HISTORY_BEAM_{OPTION} *DATABASE_HISTORY_SHELL_{OPTION} *DATABASE_HISTORY_TSHELL_{OPTION} For BINARY plot databases, they are actvated by keyword *DATABASE_FREQUENCY_BINARY_{OPTION}, where the {OPTION} ca be ay oe of the followg databases: Database Lspcode Used for D3SSD 21 Steady state dyamcs D3SPCM 22 Respose spectrum aalyss D3PSD 23 Radom vbrato PSD D3RMS 24 Radom vbrato RMS D3FTG 25 Radom vbrato fatgue D3ACS 26 FEM acoustcs D3ATV 27 BEM acoustc trasfer vector Table 1: New bary databases for frequecy doma aalyss. These databases are output the same format as D3PLOT, ad are accessble to LS-PrePost. Partcularly the parameter lspcode (saved the header fle of the database) s a flag to tell LS- PrePost or other post-processg softwares that what kd of database t s. As ca be see from Table 1, the cotet of these databases s dfferet from those D3PLOT. Thus some updates or revso from LS-PrePost or other post-processg softwares are eeded to get them workg approprately wth these ew databases. The updates or revso clude markg the x-axs of amato as frequecy stead of tme, ad correctg the ame of the varables Some of such updates or revsos have bee accomplshed LS-PrePost. Some updates have bee made to these frequecy doma aalyss features sce the last forum. These updates were made to exted the capabltes of frequecy doma aalyss of LS-DYNA, or to mprove the computatoal performace. A bref troducto of the updates, accompaed by several examples, s provded the followg sectos of the paper. 2 ATV ad MATV techques for BEM Acoustc solvers A buch of BEM Acoustc solvers (collocato BEM, varatoal drect BEM, dual BEM wth Burto- Mller formulato, Raylegh method ad Krchhoff method) have bee mplemeted to LS-DYNA [2]. They are used to predct the radated ose from a vbratg structure. To facltate the acoustc aalyss for structures whch are subjected to multple loadg cases, two ew techques ATV (Acoustc Trasfer Vector) ad MATV (Modal Acoustc Trasfer Vector) have bee mplemeted to the BEM acoustc solvers. 2.1 ATV ATV s defed as the trasfer fucto betwee the ormal odal (or elemetal) velocty ad the acoustc pressure at feld pots. For example, the acoustc pressure at feld pot due to ut ormal velocty at ode j o the structure surface ca be expressed as, j. Ths provdes Acoustc Trasfer Vector from structural ode j to feld pot acoustc volume. Oe should ote that ATV s a fucto of frequecy. It oly depeds o the propertes of acoustc medum (desty, soud speed), geometry of structures, ad locato of feld pots. It s ot depedet o the real loadg codto.

3 Fg. 1: Structural surface odes ad feld pots for acoustc computato. For the structure show Fgure 1, f there are odes o the surface ad m feld pots acoustc volume, the ATV matrx ca be expressed as [ ATV ] m = m 1,1 2,1,1,1 1,2 2,2,2 m,2 1, j 2, j, j m, j Oce the ATV matrx s obtaed, for gve vbrato codto o structure surface, the acoustc pressure at the m feld pots ca be computed by smple matrx-vector multplcato, as follows = ATV v (2) { P } m [ ] m { } Where { P } m s the acoustc pressure vector at the m feld pots; { } the surface odes (or elemets); 1, 2,, m, (1) v s the ormal velocty vector at The ATV ca be plotted o the structural surface for vsualzato. A ew database D3ATV has bee mplemeted LS-DYNA. The database plots the real part, the magary part ad the SPL (Soud Pressure Level, ut of db) of ATV, for each feld pot ad each frequecy. Fgure 2 shows real part of ATV for a smplfed ege model for the feld pot ad the frequecy 100 Hz. Fg. 2: D3ATV for a smplfed ege model. 2.2 MATV If the dyamc respose of structures ca be obtaed usg the modal superposto method (for example, usg keyword *FREQUENCY_DOMAIN_SSD LS-DYNA), the ormal velocty vector { v }

4 (2) ca be obtaed as a product of roud frequecy ω, modal shape matrx ad modal coordates vector. Accordgly the equato (2) ca be revsed as { P} m = [ ATV ] m { v} = [ ATV ] m ω{ u} T = [ ATV ] m ω[ φ] l { q} l = [ MATV ] m l { q} l Where s the magary ut ( = 1 modal shape matrx, provded by mplct modal aalyss. { } l ) ad { u } s the dsplacemet vector. The matrx [ φ] l (3) s the q s the modal coordates (assumg l modes are used); [ MATV ] m l s the MATV matrx, whch s costat for each gve frequecy. For each exctato frequecy f, LS-DYNA wll geerate the psedo-velocty boudary codto { φ} ( ω = 2π f ), j = 1, l j, ω ad ru BEM acoustc computato for the m feld pots to get the MATV matrx. For each load case, oly the modal coordates vector { } l q eed to be updated. Oce t s ready, a smple matrx-vector multplcato ca provde soluto for acoustc pressure at the m feld pots. For a real problem, the umber of ege modes volved modal superposto s usually much less tha the umber of odes (or elemets) the boudary elemets ( l << ). So the MATV approach represeted by equato (3) s more effcet tha the ATV approach represeted by equato (2), f the vbrato smulato ca be accomplshed by modal superposto. Ths s due to the fact that the effort to get MATV matrx s much less tha the effort to get ATV matrx. There are 2 steps volved usg the MATV techque BEM Acoustcs: Step 1: geeratg MATV matrces. The keywords *CONTROL_IMPLICIT_GENERAL, *CONTROL_IMPLICIT_EIGENVALUE are used to. The the keyword perform mplct modal aalyss, to get ege modes { } j *FREQUENCY_DOMAIN_ACOUSTIC_BEM_MATV s used wthout specfyg ay boudary codto, to ru acoustc computato for each psedo-velocty boudary codto for each φ ω { φ} j exctato frequecy. The MATV matrces are saved bary scratch fle b_bepressure. Step 2: acoustc computato for each load case. The keywords *FREQUENCY_DOMAIN_SSD, *FREQUENCY_DOMAIN_ACOUSTIC_BEM_MATV are used, both wth a restart opto. For SSD, t restarts wth exstg d3egv from step 1 (restmd=1); for MATV BEM, t restarts wth exstg MATV matrces, saved b_bepressure, gve by step 1 (restrt=1). Moreover, oe ca defe multple load cases oe put deck, by takg advatage of the coveet CASE scheme. For example, the frst load case (defed by *FREQUENCY_DOMAIN_SSD wth correspodg load codto) ca be put the secto betwee *CASE_BEGIN_1 ad *CASE_END_1. For the other load cases, they ca be smlarly put the CASE secto oe by oe. See Fgure 3 for a example.

5 Fg. 3: Defg multple load cases wth CASE for rug MATV BEM. The wth a sgle LS-DYNA ru (wth flag CASE the commad le), oe ca get the soluto of acoustc pressure ad SPL for all the load cases (e.g. case1.press_pa, case1.press_db, case2.press_pa, case2.press_db,...) Fg. 4: usg MATV for a door model. For a smplfed door model show Fgure 4, bechmark testgs are performed to check the accuracy ad effcecy of the MATV method, comparg wth the tradtoal BEM. Fgure 5 shows the SPL (db) value of the ose at a feld pot, for the case wth a harmoc odal force exctato appled o the door. The exctato s gve the frequecy rage of Hz, wth 101 equally spaced frequeces. For rug mplct modal aalyss, ormal modes up to 600 Hz s

6 used, whch s 20% hgher tha the maxmum exctato frequecy. The soluto of the problem s based o the combato of SSD ad BEM acoustcs. Two sets of results are gve Fgure 5: Oe s obtaed wth MATV BEM, ad the other s obtaed wth tradtoal BEM. The two sets of results are actually detcal, as llustrated by the Fgure. Fg. 5: SPL at feld pot. To study the effcecy of the MATV BEM, we cosder 1 load case ad 10 load cases, by three approaches. The computato s performed o Itel Xero CPU GHz (CPU MHz: cache sze 4096 KB). The three approaches are: 1) SSD + tradtoal BEM, whch meas that LS-DYNA goes through the whole procedure (modal aalyss, SSD ad tradtoal BEM) for each load case; 2) Restart SSD + tradtoal BEM, whch meas that startg from the 2d load case, the modal aalyss s skpped (sce the D3EIGV bary database has bee geerated durg the soluto for the frst load case) ad LS-DYNA rus a restart SSD ad the tradtoal BEM; 3) Restart SSD + MATV BEM, whch meas that LS-DYNA skps the modal aalyss part startg from the 2d load case, ad rus a restart SSD ad the uses the MATV based BEM to get the acoustc pressure for all the load cases. As show Table 2, the approach 3) Restart SSD + MATV BEM shows sgfcat savg CPU cost comparg wth the other two approaches, whe 10 load cases are cosdered. Whe there s oly 1 load case, the MATV BEM s slower tha the other two approaches, sce the computato ad the savg of MATV matrces take some extra CPU tme. However, oce the MATV matrces are ready the soluto for the addtoal load cases takes oly a ty CPU tme. Cases 1) SSD + tradtoal BEM 2) Restart SSD + tradtoal BEM 3) Restart SSD + MATV BEM 1 load case 2 h 39 m 50 s 2 h 39 m 50 s 4 h 40 m 56 s 10 load cases 26 h 38 m 18 s 25 h 53 m 13 s 4 h 41 m 10 s Table 2: CPU tme for acoustc computato of door model. 3 Icdet acoustc wave A ew keyword *FREQUENCY_DOMAIN_ACOUSTIC_INCIDENT_WAVE has bee troduced to cosder cdet acoustc waves. The cdet wave s useful modelg soar system a submare ad explosve waves. The keyword format s Card Varable TYPE MAG XC YC ZC Type I F F F F Default 1 oe oe oe oe

7 For plae wave (TYPE=1), the cdet wave s defed by p k ( α x + βy + γz ) = (4) Ae For sphercal wave (TYPE=2), the cdet wave s defed by p e A R kr = (5) I equatos (4) ad (5), A s magtude or stregth of cdet wave (parameter MAG the keyword); k s wave umber (= ω / c, where ω s roud frequecy ad c s wave speed); α, β ad γ are drectoal coses for plae wave (see equato (4)), ad are defed by (XC, YC, ZC) from the keyword. R s dstace betwee sphercal source ad feld pot for sphercal cdet wave; (XC, YC, ZC) defe the ceter of the sphercal wave or the source pot. Oe ca defe multple cdet waves oe model, by repeatg the keyword *FREQUENCY_DOMAIN_ACOUSTIC_INCIDENT_WAVE, or smply repeatg the Card 1 the keyword. A bechmark example of soud scatterg o rgd sphere s adopted to valdate the mplemetato. See Fgure 6 below. Fg. 6: Soud scatterg o rgd sphere. The sphercal source s located at 4r from the ceter of the rgd sphere (r s the radus of the rgd sphere). Two feld pots are located at 5r from the ceter of the rgd sphere. Oe s o the same sde of the source (Feld pot A), ad the other s located o the opposte sde (Feld pot B). We compare the real part ad magary part of the pressure, gve by LS-DYNA ad by aalytcal soluto (gve as fte seres expaso, trucated computato) [3]. LS-DYNA results match very well wth the aalytcal soluto, as show Fgure 7. Fg. 7: Acoustc pressure at the two feld pots. 4 Frequecy depedet complex soud speed To take to accout dampg the acoustc system, a ew keyword *FREQUENCY_DOMAIN_ACOUSTIC_SOUND_SPEED s troduced to LS-DYNA, to allow defg the frequecy depedet complex soud speed by two load curves.

8 = (6) c( f ) c ( f ) c ( f ) r + For a smple muffler model show Fgure 8, a ut ormal velocty boudary codto s prescrbed at oe ed. A mpedace boudary codto s gve at the other ed. The rest of the muffler surface s assumed to be rgd. The rage of frequecy uder study s Hz. The acoustc pressure at oe feld pot sde the muffler s computed by LS-DYNA. Oe ca see that the peak db values of the acoustc pressure are reduced by usg complex soud speed. Fg. 8: Acoustc pressure due to real ad complex soud speed. 5 Fatgue aalyss based o SSD (Steady state dyamc aalyss) Fatgue s the weakeg of materal due to repeated or cyclc loadg. Fatgue falure uder harmoc or steady state vbrato codto s very commo varous dustres, e.g. a se sweep test. Fg. 9: A sample se sweep test load curve. A fatgue aalyss method s mplemeted based o steady state vbrato codto. The correspodg keyword s *FREQUENCY_DOMAIN_SSD_{FATIGUE}. Ths feature s based o the raflow coutg algorthm ad the materal s S-N fatgue curve. The raflow coutg algorthm s used to get the umber of stress cycles for Vo-Mses stress for each exctato frequecy. Lear superposto s employed to get the total fatgue damage uder dfferet stress levels. The cumulatve damage rato R ca be expressed as = R = R (7) N Where R s the damage rato due to stress level, s the actural umber of cycles for stress level, ad N s the umber of cycles for fatgue falure for stress level (obtaed from materal s S-N curve). R s a real umber larger tha 0. If R s equal to or larger tha 1, t meas that the materal has faled due to fatgue. I hgh-cycle fatgue stuato, the materal s fatgue behavor s usually characterzed by a S-N curve, whch s also kow as a Wöhler curve. To defe the materal s S-N curve, a ew keyword

9 *MAT_ADD_FATIGUE s added to LS-DYNA. Three optos are avalable for defg the S-N fatgue curve. 1) By curve ID (see *DEFINE_CURVE) 2) By equato N S m = a 3) By equato log( S) = a b log( N) Whe the S-N fatgue curve s defed by optos 2) or 3), the parameters a ad m ( opto 2) or a ad b ( opto 3) are costats whch are depedet o materal model. For a model show Fgure 10, the cumulatve damage rato s computed ad plotted D3FTG, whch s accessble to LS-PrePost. The loadg codto s gve as base accelerato spectrum, see Table 3. To get the soluto for SSD, mplct modal aalyss s frst performed for the structure. The frst 300 Normal modes, whch provdes atural frequecy up to 2703Hz (35% hgher tha the maxmum frequecy 2000 Hz for exctato) are used SSD. Table 3: Loadg codto. Frequecy (Hz) Accelerato (g) Durato (mute) The materal s S-N fatgue curve s defed as Table 4: S-N fatgue curve. σ (MPa) N Fg. 10: Cumulatve damage rato for the beam uder SSD. As show Fgure 10, the two eds of the structure, whch are costraed to the shaker table, are characterzed wth hgher cumulatve damage ratos, whch suggests a more severe damage to the materal. But the peak value of the cumulatve damage rato s stll less tha 1. It meas that the structure s stll safe after the whole loadg process.

10 6 Summary A lst of updated frequecy doma features LS-DYNA are revewed the paper. They clude ATV ad MATV techques for BEM Acoustc solvers; cdet waves acoustc aalyss; usg frequecy depedet complex soud speed acoustc aalyss ad fatgue aalyss based o SSD (steady state dyamcs). Several examples are provded to demostrate the effectveess of the updated features. 7 Lterature [1] LS-DYNA Keyword User s Maual, Lvermore Software Techology Corporato, [2] Yu Huag, Mhamed Soul, Rogfeg Lu, BEM Methods for acoustc ad vbroacoustc problems LS-DYNA. Proceedgs of the 11 th Iteratoal LS-DYNA Users Coferece, Smulato (2), , [3] Yuepg Guo, Computato of Soud Propagato by Boudary Elemet Method. NASA Cotract Report, NAS A003, 2005.