This section describes the following analyses performed for this problem:
- 13.6.1. Modal Cyclic Symmetry Analysis
- 13.6.2. Linear Prestressed Modal Cyclic Symmetry Analysis with Linear Perturbation
- 13.6.3. Nonlinear Prestressed Modal Cyclic Symmetry Analysis with Linear Perturbation
- 13.6.4. Full-Harmonic Cyclic Symmetry Analysis
- 13.6.5. Nonlinear Prestressed Full-Harmonic Cyclic Symmetry Analysis with Linear Perturbation
- 13.6.6. Nonlinear Prestressed Mode-Superposition Harmonic Cyclic Symmetry Analysis with Linear Perturbation
For information about linear perturbation, see Linear Perturbation Analysis in the Structural Analysis Guide.
To begin a cyclic symmetry analysis, issue the CYCLIC command within /PREP7, the model-creation preprocessor.
The CYCLIC command automatically detects cyclic symmetry model information such as edge components, the number of sectors, the sector angles, and the corresponding cyclic coordinate system.
You can display the fully expanded model in the preprocessor (/CYCEXPAND,1,ON).
The Block Lanczos eigensolver is used to extract 10 modes. By default, all harmonic indices (0 to 6 in this case) are calculated (based on (N - 1) / 2, where N is the number of sectors). You can ignore some harmonic indices if desired (CYCOPT,HINDX).
The following input fragment shows the steps in this analysis:
/prep7
allsel, all, all
cyclic ! Default cyclic command detects the number of sectors, the
! sector angle, and the coordinate system
allsel, all, all
finish
/solu
antype, modal ! Perform modal solve.
modopt, lanb, 10 ! Use Block Lanczos solver to extract 10 modes.
mxpand, 10 ! Expand 10 modes, do not evaluate element results.
solve
finish
/post1
set, list,,,,,,,order ! Sorts the harmonic index results in ascending order
! of eigen frequencies
finish
The procedure to perform a linear prestressed modal cyclic symmetry analysis is essentially the same as a standard modal analysis, except that you must first prestress the structure by performing a static cyclic symmetry analysis.
To prestress the structure via static cyclic symmetry analysis:
Obtain a linear static solution. Enable file writing for performing a subsequent linear perturbation analysis (RESCONTROL,LINEAR).
Perform a linear perturbed modal analysis where the linear prestress effects are included automatically.
Expand the modes and then postprocess the results from jobname.rstp.
The following input fragment shows the steps in this analysis:
/solu
antype, static ! Perform Static analysis.
rescontrol,linear,all,1 ! Enable file writing for a subsequent linear
! perturbation analysis
nsub, 10, 10, 10
time, 1.0
omega, 0, 3000, 0 ! Centrifugal load
solve
save, ,db
finish
/solu
antype,static,restart,,,perturb ! Perform a static restart with perturbation
! from the last load step and substep of
! the previous static solve
perturb,modal,,,allkeep ! Set the analysis options for perturbed modal
! analysis
solve,elform ! Reform element matrices
outres,all,all
modopt,lanb,10 ! Use Block Lanczos mode extraction procedure
mxpand,10 ! Expand the modes
solve
finish
/post1
file, ,rstp ! Specify the data file where results are to be found
/out,
set, list,,,,,,,order ! Sort the harmonic index results in ascending order
! of eigen frequencies
finish
Following is the general process for performing a nonlinear prestressed modal cyclic symmetry analysis with linear perturbation:
Obtain a nonlinear (NLGEOM,ON) static solution.
Enable the file writing option for multiframe restart from a static analysis (RESCONTROL).
Perform a linear perturbed modal analysis with nonlinear prestress effects.
Expand the modes and then postprocess the results from jobname.rstp.
To better demonstrate the nonlinear effects in the prestressed model, the rotational velocity is doubled (OMEGA,0,6000,0) from the linear prestressed analysis, and thermal loading is added.
The following example input shows the steps in this analysis:
/solu
csys,0
antype,static ! Perform Static analysis
nlgeom,on ! Include large deformation effects
rescontrol,define,all,1 ! Enable the file writing in multiframe restart
nsub,10,10,10 ! Number of substeps = 10
allsel,all,all
nsle
bf,all,temp,50 ! Define temperature = 50
time,1.0
omega, 0, 6000, 0, ! Centrifugal load
kbc,0
solve
finish
/solu
antype,static,restart,,,perturb ! Perform a static restart with perturb
! from the last load step and substep of the previous
! static solution
perturb,modal,,,allkeep ! Set the analysis options for perturbed modal analysis
solve,elform ! Reform element matrices
outres,all,all
modopt,lanb,10 ! Use Block Lanczos mode extraction procedure
mxpand,10 ! Expand the modes
solve
finish
/post1
file, ,rstp ! Specify the data file where results are to be found
/out,
set,list,,,,,,,order ! Sort the harmonic index results in ascending order
finish
A full-harmonic analysis of the cyclic-sector model is performed in the frequency range of 1200-5500 Hz with 20 substeps. The frequency range of excitation is chosen based on the modal frequency values. With this frequency range, the first few modes of the impeller blade assembly are excited.
The following input fragment shows the steps involved in this analysis:
/solu antype, harm ! Perform harmonic analysis harfrq,1200, 5500 ! Frequency range of excitation 1200 - 5500 Hz hropt, full ! Perform full-harmonic analysis kbc, 1 ! Use Stepped loading nsub, 20 ! Use substep 20 solve finish
To perform a nonlinear prestressed full-harmonic cyclic symmetry analysis with linear perturbation, you must first prestress the structure with nonlinear effects in a static solution. Then, the perturbed procedure is used to perform a full-harmonic analysis from the prestressed stiffness matrix in a manner similar to the standard full-harmonic analysis.
Note: A nonlinear prestressed perturbed full-harmonic cyclic symmetric analysis is supported for the following methods (HROPT): FULL or VT
The following example input shows the steps in this analysis:
/solu
csys,0
antype,static ! Perform Static analysis
nlgeom,on ! Include large deformation effects
rescontrol,define,all,1 ! Enable the file writing in multiframe restart
nsub,10,10,10 ! Number of substeps = 10
allsel,all,all
nsle
bf,all,temp,50 ! Define temperature = 50
time,1.0
omega, 0, 6000, 0, ! Centrifugal load
kbc,0
solve
finish
/solu
antype,static,restart,,,perturb ! Perform a static restart with perturb
! from the last load step and substep of the previous
! static solution
perturb,harm,,,allkeep ! Set the analysis options for perturbed harmonic analysis
solve,elform
thexpand,off ! Thermal loading is not included in the load vector
omega, 0, 0, 0
harfrq,1200,5500 ! Frequency range of excitation
hropt,full ! Use full-harmonic analysis option
kbc,1
nsub,20,20,20
solve
finish
To perform a nonlinear prestressed mode-superposition harmonic cyclic symmetry analysis with linear perturbation, you must first prestress the structure with nonlinear effects in a static solution. The perturbed procedure is used to perform a modal analysis from the prestressed state, followed by a mode-superposition harmonic analysis.
The following example input shows the steps in this analysis:
/solu
csys,0
antype,static ! Perform Static analysis
nlgeom,on ! Include large deformation effects
rescontrol,define,all,1 ! Enable the file writing in multiframe restart
nsub,10,10,10 ! Number of substeps = 10
allsel,all,all
nsle
bf,all,temp,50 ! Define temperature = 50
time,1.0
omega, 0, 6000, 0, ! Centrifugal load
kbc,0
solve
finish
/solu
antype,static,restart,,,perturb ! Perform a static restart with perturb
! from the last load step and substep of the previous
! static solution
perturb,modal,,,allkeep ! Set the analysis options for perturbed modal analysis
solve,elform
outres,all,all
modopt,lanb,2
mxpand,2,,,yes
thexpand,off ! Thermal loading is not included in the load vector
omega, 0, 0, 0
solve
finish
/solu
csys,0
antype,harm
hropt,MSUP ! Choose MSUP harmonic analysis option
harfrq,1200,5500 ! Frequency range of excitation
nsub,20,20,20
cycfreq,eo,0 ! Engine order = 0
kbc,1
dmprat,1.0e-002 ! Define damping ratio of 1.0%
outres,all,all
solve
finish