To use the residual vector method, you must first calculate residual vectors in the modal analysis. You can use any of these modal analysis mode-extraction methods:

Mechanical APDL stores the calculated residual vectors in the Jobname.mode file and uses them in the subsequent mode-based analysis (for example, mode-superposition harmonic, mode-superposition transient, spectrum, or random vibration (PSD) analysis).

The following process determines the residual vectors:

Specifying Pseudo-Constraints

If rigid body motion exists, specify only the minimum number of displacement constraints necessary to prevent rigid body motion: three constraints (or fewer, depending on the element type) for 2D models and six (or fewer) for 3D models.

To use the residual response method, you must first calculate residual responses in the modal analysis. You can use any of these modal analysis mode-extraction methods:

The program stores the calculated residual responses in the Jobname.rst file as load step 2 for postprocessing. They are also written to the Jobname.resf file and used in the expansion pass of the mode-superposition harmonic or mode-superposition transient analysis.

The notes from the residual vector method also apply to the residual response method.

Use the following procedure to calculate residual responses:

The residual response procedure does not support:

When using the residual response, all significant modes must be extracted. Unlike the residual vector, the residual response reduces to a static contribution.

To run a spectrum analysis, first perform a modal analysis to generate the MODE file. For multiple spectrum analyses, a unique MODE file can be used when the mode-reuse key (modeReuseKey on SPOPT) is enabled. The mode-reuse key prepares the database and the necessary files for a new spectrum analysis that reuses an existing Jobname.mode.

To use new load vectors, residual vector, and/or enforced motion in modal transient or modal harmonic analyses with existing modal analysis results, refer to Restarting a Modal Analysis

In QRDAMP eigensolver the solution occurs in two steps. First, an eigensolver is used to extract the symmetric matrix eigenmodes. These eigenmodes are then used in the second pass to build the modal subspace matrix of the non-symmetric eigensystem and calculate the complex eigenmodes.

When an existing Jobname.modesym containing the eigenmodes of the symmetric eigensolution of the model is available, it can be reused in the second pass by enabling the reuse flag (ReuseKey on QRDOPT).

To use the multiple loads method, you must first generate load vectors in the modal analysis. You can use any of these modal analysis mode-extraction methods:

Mechanical APDL stores the generated load vectors in the Jobname.mode file so that they can be used in the subsequent mode-superposition analysis.

The procedure for generating multiple load vectors is as follows:

The load vectors calculation can be performed during a modal analysis restart. For more information, see Modal Analysis Restart in the Basic Analysis Guide.

The load vectors can then be used in a mode-superposition analysis as follows:

In a modal analysis, Mechanical APDL calculates pseudo-static modes and writes them to the Jobname.mode file. They can then be used in a subsequent mode-superposition analysis with base excitation.

The procedure for calculating pseudo-static modes in a modal analysis is as follows:

To use the pseudo-static modes in the mode-superposition transient/harmonic analysis, issue DVAL.

!  Build the Model
/FILNAM,...	     ! Jobname
/TITLE,…              ! Title
/PREP7                    
---
---			! Generate model
---
NSEL,...
CM, BASE1,NODE	! Define component BASE1 with selected support nodes undergoing the first enforced motion
NSEL,ALL
NSEL,...
CM, BASE2,NODE	! Define component BASE2 with selected support nodes undergoing the second enforced motion
FINISH


!  Generate the pseudo-static modes in Modal Analysis
/SOLU                      
ANTYPE, MODAL               
MODOPT, LANB,10             
MODCONT,, ON	! Activate enforced motion
              
---		! Define constraints
	
CMSEL,S,BASE1,NODE	! Select nodes of component BASE1
D, ALL, UX, 1		! Define enforced motion 1 to be applied on all nodes along UX
CMSEL,S,BASE2,NODE	! Select nodes of component BASE2
D, ALL, UY, 2		! Define enforced motion 2 to be applied on all nodes along UY
SOLVE
FINISH

!  Mode-Superposition Transient Analysis
/SOLU
ANTYPE, TRANSIENT
TRNOPT, MSUP
OUTRES, ALL,ALL
KBC,1
DELTIM,...
DVAL, 1, ACC, 100.0        ! Define constant acceleration for enforced motion 1
DVAL, 2, ACC, %ACCTAB%	! Define tabular acceleration for enforced motion 2
SOLVE

TIME,...
SOLVE

FINISH

The mode selection is performed during a modal analysis or a modal analysis restart. It is applicable to real and complex eigensolvers.

The user-defined array is a *DIM array with a dimension equal to the number of extracted modes. The array values are 1 for selected modes and 0 otherwise.

Damped eigensolver solutions (MODOPT,DAMP) are pairs of complex conjugate modes. When filling in the table array, select the pairs (and not individual modes) to ensure that the MODE file remains consistent. (For example, modes #3 and #4 are a pair, so indices 3 and 4 in the array should have the same value, 0 or 1.)

! Build the Model
/filnam,…
/title,…
/prep7
…
finish

! Obtain the Modal Solution
/solu
antype, MODAL
modopt, UNSYM, 10	! Unsymmetric eigensolver, 10 modes are requested
solve
finish
save

/post1
…		! Postprocess the modes to identify the modes of interest
finish

/clear, nostart	! Start a new session
resume,, db

*dim, tab, ARRAY, 10	! Create the array 
tab(1) = 1
tab(2) = 0
tab(3) = 0
tab(4) = 0
tab(5) = 1
tab(6) = 1
tab(7) = 1
tab(8) = 0
tab(9) = 1
tab(10) = 1

! Perform the modal selection and expansion
/solu
antype, MODAL, RESTART
mxpand, %tab%,,, yes	! Mode selection is based on user input array, and element results are 
		! requested
solve
finish

! Postprocess the modal results or perform a mode-superposition analysis

For the selection of complex modes from the QR damped eigensolver (MODOPT,QRDAMP), you must input MXPAND,-1 in the modal solution. Doing so forces the generation of a complex MODE file that enables complex mode selection.

The mode selection is performed during a modal analysis restart and applies to real eigensolvers only.

You can select the modes per direction using either of the following methods:

! Build the Model
/filnam,…
/title,…
/prep7
…
finish

! Obtain the Modal Solution
/solu
antype, MODAL
modopt, LANB, …             ! Block Lanczos
solve
finish

! Perform the modal selection and expansion
/solu
antype, MODAL, RESTART
mxpand,,,, yes,,, EFFM	! Mode selection is based on the modal effective mass, and element
						! results are requested
modseloption, .90, no,no, no,no,no     ! Only direction X is selected, a minimum of 90% of the total 
			! mass is requested in this direction
solve
finish

! Postprocess the modal results or perform a mode-superposition analysis

If the minimum ratio cannot be achieved, you may need to extract more modes and run the procedure again.

If you want to calculate residual vectors, do so during the modal restart analysis. Note that the residual vectors calculation is always based on all the extracted modes and not the selected modes.

If groups of repeated frequencies (Repeated Eigenvalues in the Theory Reference) are present, note the following. The sum of the effective masses of all the eigenmodes in a group is unique. However, the effective mass, and therefore, the modal effective mass ratio of each eigenmode in the group is not. It can lead to different mode selection results depending on the machine and SMP/DMP settings. When minimum ratios are defined (MODSELOPTION), set them in all the directions of the eigenmodes of a group with repeated frequencies so that all the eigenmodes of the group are selected.

The mode selection is performed during a modal analysis restart and applies to real eigensolvers only. This mode-selection method is used when a Single Point Response Spectrum (SPRS) analysis is performed following the modal analysis.

You can select the modes using a significance threshold (SIGNIF on the MXPAND command). The significance level of a mode is equal to the mode coefficient divided by the maximum mode coefficients (of all modes per direction). The threshold is the same for all directions.

! Build the Model
/filnam, …
/title, …
/prep7
…
finish

! Obtain the Modal Solution
/solu
antype, MODAL
modopt, LANB, …	! Block Lanczos
solve
finish

! Obtain the SPRS Mode Coefficients
/solu
antype, SPECTRUM
spot, SPRS
svtyp, 2, 386.4	        ! Input spectrum type 
sed, 1, 0, 0		! Input spectrum direction
freq, 1, 2, 5, 15, 30	! Input spectrum frequencies
sv,,   0.1, 0.2, 0.2, 0.05, 0.05	! Input spectrum values
solve
finish

! Perform the modal selection and expansion
/solu
antype, MODAL, RESTART
mxpand,,,, yes, 1e-2,, MODC	! Mode selection is based on the mode coefficients, the significance
								! threshold is 0.01 and element results are requested
solve
finish

! Perform a spectrum analysis (combination step)
/solu
antype, SPECTRUM
spopt, SPRS		! Single Point Response Spectrum analysis
srss                                    ! Square Root of Sum of Square combination
solve
finish 

For multiple input spectra in a SPRS analysis, to obtain the mode coefficients in the spectrum analysis, the spectrum input definitions are requested, each one followed by SOLVE.

This method is not supported for Multiple Point Response Spectrum (MPRS) and Power Spectrum Density (PSD) analyses. However, you can use a dummy SPRS input spectrum to perform the mode selection for the subsequent MPRS and PSD analysis, or else use the mode selection based on the modal effective mass.

The mode selection is performed during a modal analysis restart. It is applicable to real eigensolvers only. The intent of this mode selection method is to perform a Dynamic Design Analysis Method (DDAM) Spectrum and Single Point Response Spectrum (SPRS) analyses following the modal analysis. It is based on the procedure described in NAVSEA [408].

In this procedure, the modes are selected using a significance threshold equal to 0.01. The significance level of a mode is equal to the modal effective weight or mass divided by the total weight or mass. The threshold is the same for all directions.

The sum of the modal effective weights or masses of all calculated modes must be greater than 80% of the total weight or mass, otherwise you may need to extract more modes and run the procedure again.

After the significance calculation, the procedure can select additional modes based on the nodal acceleration check. This check accounts for the localized response of relatively light-weight sub-components of critical areas. To apply the acceleration check, you need to select all the nodes of interest and create a nodal component named “_DDAM_NODCHK” (see Creating Components)

The additional modes included correspond to those for which the nodal acceleration of any of the nodes of interest exceeds by 10 percent the maximum nodal acceleration calculated from the selected modes.

If you want to calculate residual vectors, do so during the modal restart analysis. Note that the residual vectors calculation is always based on all the extracted modes and not the selected modes.

This method is not supported for Multiple Point Response Spectrum (MPRS), Power Spectrum Density (PSD), Mode Superposition Harmonic, or Mode Superposition Transient analyses. However, you can use a dummy SPRS input spectrum to perform the mode selection for the subsequent MPRS and PSD analysis, or use the mode selection based on the modal effective mass.

! Build the Model
/filnam, …
/title, …
/prep7
…
esel,s,,,78,89
esel,a,,,96
esel,a,,,112
nsle				! Select nodes of interest
cm,_DDAM_NODCHK,node			! Create a component  for the
					! nodal acceleration check
allsel,all,all
…

finish

! Obtain the modal solution
/solu
antype, MODAL
modopt, LANB, …			! Block Lanczos

solve
finish

! Obtain the DDAM Mode Coefficients
/solu
antype, SPECTRUM
spopt, DDAM				! DDAM Spectrum analysis
addam,1.0,10.0,37.5,12.0,6.0	! Input spectral acceleration   
vddam,1.0,30.0,12.0,6.0		! Input spectral velocity           
sed,0,1,0				! Input spectrum direction
solve
finish

! Perform the modal selection and expansion
/solu
antype, MODAL, RESTART
mxpand,,,, yes,,, DDAM	! Mode selection is based on DDAM
				! procedure, the default significance 
				! threshold is 0.01 and element results are ! requested
solve
finish

! Perform a DDAM spectrum analysis (Combination Step)
/solu
antype, SPECTRUM
spopt, DDAM			! DDAM Spectrum analysis
nrls,…                     ! NRLSUM mode combination
dmprat,…			! Define damping ratio
solve
finish