Modal Identification of the Elastic Properties in Composite Sandwich Structures

Transcription

1 Modal Identfcaton of the Elastc Propertes n Composte Sandwch Structures M. Matter Th. Gmür J. Cugnon and A. Schorderet School of Engneerng (STI) Ecole poltechnque fédérale f de Lausanne (EPFL) Swterland

2 0. Outlne Introducton to sandwch structures Numercal models applcable to sandwches Epermental setup Identfcaton procedure Test cases and results Conclusons

3 . Introducton Sandwch structures Composte or metal sns Composte or sotropc core hgh stffness wth low weght sns core Issues How to model ths tpe of structures? How to dentf ther propertes?

4 2. Numercal model Sandwch models should tae nto account the dscontnut of the through-the the-thcness thcness dsplacement dervatves at the materal nterfaces the thn nature of the sns Sold FE model accurate subjected to shear locng Shell FE model (FSDT HSDT & PSDT ESL) accurate f gag formulaton added adapted to thn structures

5 2. Numercal model PSDT wth gag dsplacement formulaton PSDT wth gag dsplacement formulaton ( ) ( ) ( ) ( ) ( ) ( ) ZZ p p u u p u u u t u ζ =!... ( ) ( ) ( ) ( ) ( ) ( ) ZZ p p v v p v v v t v ζ =!... ( ) ( ) ( ) ( ) ( ) p p w p w w w t w! = Zgag PSDT

6 2. Numercal model Average dfference between SL and PSDT Shell gag models : 0.5% PSDT Shell gag more stable for coarser meshes Sandwch models wth gag term have appromatel 30% less degrees-of of-freedomfreedom MAC matr: comparson between Shell gag and SL FE (mesh of 66 elements)

7 3. Epermental setup Two means of ectaton Loudspeaer Shaer Measure of ectaton b mcrophone / load cell Measure of response b Laser vbrometer Etracton of modal parameters b MDOF software

8 4. Identfcaton procedure Med numercal-epermental dentfcaton of consttutve parameters Intal guess = 0 FEM egensolutons S num () Epermental modal data S ep Update parameters (mnme the error norm ε) Modal Error Norm ε (S num S ep ) ε > ε mn ε < ε mn Identfed parameters

9 4. Identfcaton procedure Modal error norms based on measured and computed frequences dagonal and off-dagonal terms of the MAC matr for the epermental and numercal mode shapes ε ( ) = μ ; ε ( d j μ ( ) ε ( ) = ( ~ ω ω ) / ω = f [( ϕ ~ [( ϕ ~ T ) ϕ ~ o ) T 2 ϕ j ] ][( ϕ ) = j ) q T j= j ϕ j μ ] j

10 4. Identfcaton procedure Modal error norms based on (con t) sum of the dfferences between the components of two correspondng mode shapes the numercal (2D splne nterpolaton) and epermental (mage correlaton) nodal lnes ε s ε ( ) f ( A) r = ( ϕ ~ ) j ( ϕ ) j j= ma( ϕ ~ ma( ) ϕ l ) l l l 0 f abs( A) δ = abs( A) f abs( A) δ n n n ~ ( ) = [ ( rs ) ( rs 2 f I f I n r= s= < δ )] 2

11 4. Identfcaton procedure Global objectve functon combnaton of the modal error norms weghts determned emprcall senstve to all the parameters ε( ) = { α f ε f d α ε d o α ε o s α ε s n α ε n } T f α =.0 d α = α = s α = 0. n α = 0.25

12 4. Identfcaton procedure Specal case: dentfcaton of sandwches 2 dfferent materals (at least) 2 6 elastc propertes to dentf General case: needs more than measure Assumpton: thn sns wth hgh stffness compared to the core Onl 4 nfluent propertes for the sns: E s E 2s ν 2s G 2s Onl 2 nfluent propertes for the core: G 23c G 3c Then all nfluent propertes are dentfed n measure

13 4. Identfcaton procedure Senstve parameters evaluaton: Carbon 0 /900 /90 wth 5mm foam core Carbon 0 /900 /90 wth 2 mm foam core Carbon 0 /900 /90 5mm honecomb core Sensvt Sensvt: Carbon 0 /90 sns wth 2mm foam core (Are) Es E2s Nu2s G2s G23s G3s Ec E2c Parameter Nu2c G2c G23c G3c Sensvt: Carbon 0 /90 sns wth honecomb core (Nome) Freq Sensvt: Carbon 0 /90 sns wth 5mm foam core (Are) Freq Sensvt MAC MAC2 Nodal Mod Sensvt Es E2s MAC MAC2 Nodal Mod Es E2s Nu2s G2s G23s G3s Ec E2c Parameter Nu2c G2c G23c G3c Nu2s G2s G23s G3s Ec Parameter E2c Nu2c G2c G23c G3c

14 4. Identfcaton procedure Identfcaton wth one measure (one specmen) s applcable for sandwches wth thn sheets wth hgh stffness compared to the core such as carbon or glass sheets wth foam or honecomb core Procedure not applcable to sandwches wth lower propert dfference such as carbon or glass sheets wth wood core Sensvt Sensvt: Carbon 0 /90 sheets wth 5mm foam core (Are) Freq MAC MAC2 Nodal Mod Sensvt Sensvt: Carbon 0 /90 sheets wth wood core (poplar) Freq MAC MAC2 Nodal Mod Es E2s Nu2s G2s G23s G3s Ec E2c Parameter Nu2c G2c G23c G3c Es E2s Nu2s G2s G23s G3s Ec E2c Parameter Nu2c G2c G23c G3c

15 5. Results / eamples Identfcaton of 3 dfferent sandwch plates Carbon 0 /90 sns wth 5mm Are C7075 2mm Are C7075 5mm Nome honecomb

16 5. Results / eamples Identfcaton wth PSDT Shell gag FE model gves results smlar to the SL predctons Less than 2.5% of varaton Shell gag model s 30% faster (wth the same mesh) Sns Core E E 2 ν 2 G 2 G 23 G 3 SWAC5 Average SL 3.55E0 3.47E E E E07 Std devaton % Average ZZ 3.53E0 3.47E E E E07 Std devaton % Varaton SL-ZZ % SWAC2 Average SL 2.98E0 3.02E E E E07 Std devaton % Average ZZ 2.98E0 3.02E E E E07 Std devaton % Varaton SL-ZZ % SWRC5 Average SL 3.78E0 3.65E E E E07 Std devaton % Average ZZ 3.75E0 3.65E E E E07 Std devaton % Varaton SL-ZZ %

17 5. Results / eamples Tpcal convergence for the parameter dentfcaton of sandwch plates Convergence for SWAC E.3.25 E2 n2 G2 0. Relatve value.2.5. G23 G3 e 0.0 Error norm Iteraton 0.000

18 6. Conclusons Elastc parameter dentfcaton of sandwch plates wth one measure s possble Sold FE model s adequate but requres a precse mesh PSDT Shell FE model wth gag term mproves the procedure Faster convergence Hgher accurac for coarser mesh Future nvestgatons Comparson wth other parameter estmaton tests Improved modellng of the nterfaces