模态分析实例 1平板中央开孔模型的模态分析

1、 这些实例包括两个问题： 1. 平板中央开孔模型的模态分析 ： 一步一步地描述了如何进行模态分析； 既可以由学员自己来练习这个问题，也可以由老师把这个问题作为范例来讲。 2. 对模型飞机机翼进行模态分析： 这个问题留给学员做练习。 细节部分请参考动力学实例分析补充材料。 为了方便大家学习，这里给出具体操作过程，供大家参考。 1. 平板中央开孔模型的模态分析 ： 说明： 确定一个有孔方板的前 10 阶频率。假设约束板在孔边缘的径向位移。板的材料为铝，属性如下： 弹性模量 E = 10 x 106 psi 密度 = 2.4 x 10-4 lbf-sec2/in4 泊松比 = 0.27 操作过程：

2、1. 清除数据库并读入文件 plate.inp 以创建几何模型和网格。 2. 定义材料属性 Preprocessor > Material Props > Material Models ? 依次双击： Structural Linear Elastic Isotropic ? EX = 10e6 (弹性模量，单位 psi) ? PRXY = 0.27 (泊松比) ? OK Structural Density ? DENS = 2.4e-4 (密度，单位： lbf-sec2/in4) ? OK 退出材料对话框。 3. 进入 /Solution，选择模态分析： Solution &

3、gt; New Analysis 选择 Modal，然后 OK。 4. 设置分析选项： Solution > Analysis Options 使用 Block Lanczos 方法 (默认) 抽取 10 个模态；扩展 10 个模态 可计算单元结果 按 OK 在下一个对话框中接受默认设置 5. 约束孔的径向位移： Utility Menu: Plot > Lines Solution > Loads- Apply > Displacement > Symmetry BC > On Lines > 选取孔边缘线，按下 OK。 注意：(1) 这里在孔边缘处

4、施加对称约束，可以起到约束径向位移的作用，请想一想，为什么？ (2) 这里没有对 z 向位移的约束，后面会出现零频率，即存在刚体运动。 6. 开始求解： Solution > -> Solve -> Current LS 在 /STAT 窗口中检查求解信息，然后按下 OK。 7. 查看结果，首先列出频率结果： General Postproc > Results Summary 可以看到，存在一个零频率，说明约束不足。 8. 绘制第一个模态形状： General Postproc > Read Results > First Set 再 Plot Resul

5、ts > Deformed Shape 选择 “Def and undef edge” 并按 OK 可以看到，这是一个 Z 向的刚体运动模态。 9. 显示下一个模态： Read Results > Next Set Utility Menu: Plot > Replot 这是一个面内转动模态 云图显示下一个模态：在 General Postproc 中 Read Results > Next Set Plot Results > Contour Plot > Nodal Solu > Disp 10. 云图显示后续模态： Read Results &g

6、t; Next Set Plot Results > Contour Plot > Nodal Solu > Disp11. 动画显示模态 Utility Menu: PlotCtrls > Animate > Mode Shape 10 frames Time delay = 0.05 (其余用默认值) 为消除刚体模态，可以增加对 Uz 和 ROTz 的约束。 自己试试看？ 附录： plate.inp 文件内容 ! 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 ! 如果将此句改为 complete = 1，将会执行完整的分析，否则只是生成模型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