模態(tài)分析實(shí)例 1平板中央開(kāi)孔模型的模態(tài)分析

1、 這些實(shí)例包括兩個(gè)問(wèn)題： 1. 平板中央開(kāi)孔模型的模態(tài)分析 ： 一步一步地描述了如何進(jìn)行模態(tài)分析； 既可以由學(xué)員自己來(lái)練習(xí)這個(gè)問(wèn)題，也可以由老師把這個(gè)問(wèn)題作為范例來(lái)講。 2. 對(duì)模型飛機(jī)機(jī)翼進(jìn)行模態(tài)分析： 這個(gè)問(wèn)題留給學(xué)員做練習(xí)。 細(xì)節(jié)部分請(qǐng)參考動(dòng)力學(xué)實(shí)例分析補(bǔ)充材料。 為了方便大家學(xué)習(xí)，這里給出具體操作過(guò)程，供大家參考。 1. 平板中央開(kāi)孔模型的模態(tài)分析 ： 說(shuō)明： 確定一個(gè)有孔方板的前 10 階頻率。假設(shè)約束板在孔邊緣的徑向位移。板的材料為鋁，屬性如下： 彈性模量 E = 10 x 106 psi 密度 = 2.4 x 10-4 lbf-sec2/in4 泊松比 = 0.27 操作過(guò)程：

2、1. 清除數(shù)據(jù)庫(kù)并讀入文件 plate.inp 以創(chuàng)建幾何模型和網(wǎng)格。 2. 定義材料屬性 Preprocessor > Material Props > Material Models ? 依次雙擊： Structural Linear Elastic Isotropic ? EX = 10e6 (彈性模量，單位 psi) ? PRXY = 0.27 (泊松比) ? OK Structural Density ? DENS = 2.4e-4 (密度，單位： lbf-sec2/in4) ? OK 退出材料對(duì)話框。 3. 進(jìn)入 /Solution，選擇模態(tài)分析： Solution &

3、gt; New Analysis 選擇 Modal，然后 OK。 4. 設(shè)置分析選項(xiàng)： Solution > Analysis Options 使用 Block Lanczos 方法 (默認(rèn)) 抽取 10 個(gè)模態(tài)；擴(kuò)展 10 個(gè)模態(tài) 可計(jì)算單元結(jié)果 按 OK 在下一個(gè)對(duì)話框中接受默認(rèn)設(shè)置 5. 約束孔的徑向位移： Utility Menu: Plot > Lines Solution > Loads- Apply > Displacement > Symmetry BC > On Lines > 選取孔邊緣線，按下 OK。 注意：(1) 這里在孔邊緣處

4、施加對(duì)稱(chēng)約束，可以起到約束徑向位移的作用，請(qǐng)想一想，為什么？ (2) 這里沒(méi)有對(duì) z 向位移的約束，后面會(huì)出現(xiàn)零頻率，即存在剛體運(yùn)動(dòng)。 6. 開(kāi)始求解： Solution > -> Solve -> Current LS 在 /STAT 窗口中檢查求解信息，然后按下 OK。 7. 查看結(jié)果，首先列出頻率結(jié)果： General Postproc > Results Summary 可以看到，存在一個(gè)零頻率，說(shuō)明約束不足。 8. 繪制第一個(gè)模態(tài)形狀： General Postproc > Read Results > First Set 再 Plot Resul

5、ts > Deformed Shape 選擇 “Def and undef edge” 并按 OK 可以看到，這是一個(gè) Z 向的剛體運(yùn)動(dòng)模態(tài)。 9. 顯示下一個(gè)模態(tài)： Read Results > Next Set Utility Menu: Plot > Replot 這是一個(gè)面內(nèi)轉(zhuǎn)動(dòng)模態(tài) 云圖顯示下一個(gè)模態(tài)：在 General Postproc 中 Read Results > Next Set Plot Results > Contour Plot > Nodal Solu > Disp 10. 云圖顯示后續(xù)模態(tài)： Read Results &g

6、t; Next Set Plot Results > Contour Plot > Nodal Solu > Disp11. 動(dòng)畫(huà)顯示模態(tài) Utility Menu: PlotCtrls > Animate > Mode Shape 10 frames Time delay = 0.05 (其余用默認(rèn)值) 為消除剛體模態(tài)，可以增加對(duì) Uz 和 ROTz 的約束。 自己試試看？ 附錄： plate.inp 文件內(nèi)容 ! 1:! corrected the hrcplx HRCPLX command line to reflect the negative phase

7、 angle! to run harmonic only set! 2:! modified transient option to match PPT slides of dynamics training M4-50 ff! Uwe, Kx Inc., 11/30/00! *finish/clear/udoc,1,date,offmodel=1qtr=0complete=0 ! 如果將此句改為 complete = 1，將會(huì)執(zhí)行完整的分析，否則只是生成模型modal_x=1harm=0tran=0! DYNAMICS WORKSHOP! Square plate with a hole!/

8、filnam,plate/title,PLATE DYNAMIC ANALYSIS! Build the model*if,model,eq,1,then /prep7 et,1,63 ! Shell element type r,1,0.1 ! Shell thickness *if,complete,eq,1,then mp,ex,1,1e7 ! Material properties mp,prxy,1,0.27 mp,dens,1,2.4e-4 *endif ! Start with quarter plate xwidth=6 yheight=6 holerad=0.75 rect,

9、xwidth,yheight pcirc,holerad asba,1,2 *if,complete,eq,1,then !/show,plmodel,grph !/plopts,leg2,off *endif /view,1,1,1 aplot smrt,6 amesh,all eplot save,plate_qtr,db *if,complete,eq,1,then ! Symmetry BC csys,0 ! Select quarter symmetry lines lsel,loc,x,0 lsel,a,loc,y,0 ! dl,all,symm ! Symmetry BC lse

10、l,all dtran /pbc,u,1 eplot save,plate_qtr_sym,db *endif ! Generate full plate arsym,x,all ! Two reflect operations arsym,y,all nummrg,node nummrg,kp aplot eplot /edge,1 eplot /edge finish save,plate_full,db*endif ! if model=1!-! STATIC ANALYSIS - FULL PLATE PRESTRESS!-*if,complete,eq,1,then *if,moda

11、l_x,eq,1,then ! Choose analysis type and options /solu antype,static ! Static analysis pstres,on ! Prestress effects ON ! Apply boundary conditions and solve csys,1 ! Select hole lines lsel,loc,x,holerad dl,all,symm ! Radial constraints at selected lines lsel,all /show,plstatic,grph /pbc,all,1 lplot

12、 aplot dtran eplot csys,0 lsel,loc,y,yheight ! Select top and bottom lines. lsel,a,loc,y,-yheight sfl,all,pres,-20 ! . and apply traction lsel,all sftran /psf,pres,2 eplot pivcheck,off ! Turn off pivot checking solve finish /post1 /title,PLATE PRESTRESS plnsol,s,y finish !- ! MODAL ANALYSIS - FULL P

13、LATE !- ! Choose analysis type and options /solu antype,modal ! Modal analysis modopt,lanb,10 ! Block Lanczos, 10 modes mxpand,10,yes ! Expand all 10 modes pstres,on ! Prestress ON ! Apply boundary conditions and solve solve finish ! Review results /post1 set,list /show,plmodalps,grph *do,i,1,10 set

14、,i pldisp,2 *enddo *if,animate,eq,1,then ! For animation, cut & paste the following in interactive mode /plopts,info,off ! Legend column off /plopts,frame,off ! Frame off /ui,wsiz,0,0,400,325 ! Graphics window location and size (undocumented) /dev,text,1,200 /triad,off /edge,1 set,1 pldisp,2 anm

15、ode,10,.05 *endif ! if animate=1 finish ! Re-do modal analysis with prestress off /solu pstres,off /title,PLATE STRESS-FREE solve finish /post1 set,list /show,plmodal,grph *do,i,1,10 set,i pldisp,2 *enddo finish ! Re-do modal analysis with normalization to unity /solu modopt,lanb,10,on solve finish

16、/post1 *do,i,3,10 set,i plnsol,s,eqv *enddo finish !- ! MODAL ANALYSIS - QUARTER PLATE !- *if,qtr,eq,1,then resume,plate_qtr,db ! Resume quarter plate model /filnam,plate_qtr /show,plqtr,grph ! Choose analysis type and options /solu antype,modal ! Modal analysis modopt,lanb,5 ! Block Lanczos, 5 mode

17、s mxpand,5,yes ! Expand all modes ! Apply boundary conditions and solve csys,1 ! Select hole lines lsel,loc,x,holerad dl,all,symm ! Radial constraints ! First load step: symmetry BC csys,0 ! Select quarter symmetry lines lsel,loc,x,0 lsel,a,loc,y,0 dl,all,symm ! Symmetry BC lsel,all dtran /pbc,u,1 /

18、title,QUARTER PLATE WITH SYMMETRY BC eplot solve ! Second load step: anti-symmetry BC csys,0 ! Select quarter symmetry lines lsel,loc,x,0 lsel,a,loc,y,0 dldele,all,all dl,all,asymm ! Anti-symmetry BC lsel,all dtran /title,QUARTER PLATE WITH ANTI-SYMMETRY BC eplot solve ! Review results /post1 set,li

19、st *do,i,1,5 set,1,i pldisp,2 set,2,i pldisp,2 *enddo !anmode,10,.05 finish *endif ! if qtr=1 *endif ! if modal_x=1 !- ! HARMONIC ANALYSIS !- *if,harm,eq,1,then finish *if,qtr,eq,1,then resume,plate_qtr_sym,db ! Quarter plate *else resume,plate_full,db ! Whole plate *endif /filnam,plharm /show,plhar

20、m,grph /solu antype,harmic ! Harmonic analysis hropt,full dmprat,0.2 ! Damping ratio ! csys,1 nsel,s,loc,x,.74,.76 cm,n_hole,node dofsel,u,rot ! Unselect ROT dof dsym,symm,x,1 ! Radial constraint around hole dofsel,all ksel,s,loc,x,6.1,9 nslk cm,n_corner,node d,all,uz ! UZ constraint at corner node(

21、s) allsel /title,PLATE HARMONIC ANALYSIS- CONSTRAINTS /pbc,u,1 eplot f,n_hole,fz,10 ! 10-lb FZ forces around hole /title,PLATE HARMONIC ANALYSIS- CONSTRAINTS & FORCES /pbc,f,1 eplot harfrq,0,40 ! Frequency range nsubst,4 kbc,1 solve harfrq,40,60 nsubst,10 solve ! /post26 csys,0 nsol,2,node(0.75,

22、0,0),u,z /title,PLATE HARMONIC ANALYSIS- DISP VS FREQ /plopts,info,on /plopts,leg2,off plvar,2 prcplx,1 prvar,2 finish ! /post1 set,list /title,PLATE HARMONIC ANALYSIS hrcplx,2,4,-85.7 /dsca,1 pldisp,2 plnsol,s,eqv finish *endif ! if harm=1 ! End of harmonic analysis !- ! TRANSIENT ANALYSIS !- *if,t

23、ran,eq,1,then finish *if,qtr,eq,1,then resume,plate_qtr_sym,db ! Quarter plate *else resume,plate_full,db ! Whole plate *endif /filnam,pltran /show,pltran,grph /solu antype,trans ! Transient analysis trnopt,full d_beta=0.0005 betad,d_beta !alphad,3 ! csys,1 nsel,s,loc,x,.74,.76 cm,n_hole,node dofsel,u,rot ! Unselect ROT dof dsym,symm,x,1 ! Radial constraint around hole dofsel,all ksel,s,loc,x,6.1,9 nslk cm,n_corner,node d,all,uz ! UZ constraint at corner node(s) allsel /title,PLATE TRANSIENT ANALYSIS- CONSTRAINTS /pbc,u,1 eplot ! ! Define a force table array *dim,force,table,4,1,time for