In this step, you define the analysis type and options, apply loads, specify load step options, and begin the finite element solution for the natural frequencies, as follows:
Enter the solution processor (/SOLU).
After you have entered the solution processor, you define the analysis type and analysis options. Mechanical APDL offers the options listed in Table 3.1: Analysis Types and Options for a modal analysis. Each of the options is explained in detail below.
Table 3.1: Analysis Types and Options
Option | Command | GUI Path |
---|---|---|
New Analysis | ANTYPE | |
Analysis Type: Modal (see Note below) | ANTYPE | |
Mode-extraction Method | MODOPT | |
Number of Modes to Extract | MODOPT | |
Number of Modes to Expand (see Note below) | MXPAND | |
Mass Matrix Formulation | LUMPM | |
Prestress Effects Calculation | PSTRES | |
Control Output to the Results File | OUTRES | |
Residual Vector Calculation | RESVEC |
When you specify a modal analysis, a Using Abridged Solution Menus in the Basic Analysis Guide.
menu that is appropriate for modal analyses appears. The menu is either "abridged" or "unabridged," depending on the actions you took prior to this step in the current session. The abridged menu contains only those solution options that are valid and/or recommended for modal analyses. If you are on the abridged menu and you want to access other solution options (that is, solution options that are valid for you to use, but their use may not be encouraged for this type of analysis), select the option. For details, see3.4.2.1. Option: New Analysis (ANTYPE)
Select New Analysis. If you wish to compute additional load vectors, residual vectors, or enforced motion terms subsequent to a prior modal analysis, select Restart.
3.4.2.2. Option: Analysis Type: Modal (ANTYPE)
Use this option to specify a modal analysis.
3.4.2.3. Option: Mode-Extraction Method (MODOPT)
Select one of the following mode-extraction methods:
Mode-Extraction Method | Comments |
---|---|
Block Lanczos | Used for large symmetric eigenvalue problems. This method uses the sparse matrix solver, overriding any solver specified via EQSLV. |
PCG Lanczos | Used for very large symmetric eigenvalue problems (500,000+ degrees of freedom), and is especially useful to obtain a solution for the lowest modes to learn how the model will behave. This method uses the PCG iterative solver and therefore has the same limitations (that is, it does not support superelements, Lagrange multiplier option on contact elements, mixed u-P formulation elements, etc.). This method works with the various
By default, this method does not perform a Sturm sequence check; however, internal heuristics have been developed to guard against missing modes. If a Sturm sequence check is absolutely necessary, it can be activated via PCGOPT. |
Supernode | Used to solve for many modes (up to 10,000) in one solution. Typically, the reason for seeking many modes is to perform a subsequent mode-superposition or PSD analysis to solve for the response in a higher frequency range. This method typically offers faster solution times than Block Lanczos if the number of modes requested is more than 200. The accuracy of the solution can be controlled via SNOPTION . |
Subspace | Used for large symmetric eigenvalue problems. This method uses the sparse matrix solver. The advantage of the Subspace method over the Block Lanczos method is that both [K] and [S] / [M] matrices can be indefinite at the same time. Some options can be controlled via SUBOPT. |
Unsymmetric | Used for problems with unsymmetric matrices, such as fluid-structure interaction problems or brake-squeal problems. Structural damping is the only damping supported. |
Damped | Used for problems where viscous (or a mix of viscous and structural) damping cannot be ignored, such as a structure with dampers or material dependent damping. System matrices can be unsymmetric. Full system is resolved. |
QR damped | Used for problems where viscous damping cannot be ignored, such as rotordynamics problems. System matrices can be unsymmetric. It uses the reduced modal damped matrix to calculate complex damped frequencies in modal coordinates. Faster than Damped when applicable. See QR Damped Method for applicability. |
For more detailed information, see Comparing Mode-Extraction Methods.
For most applications, you will use the Block Lanczos, PCG Lanczos, Subspace, or Supernode method. The unsymmetric, damped, and QR damped methods are applicable in special applications. (The damped, unsymmetric, and QR damped methods may not be available, depending upon the Ansys, Inc. product license in use at your site.)
When you specify a mode-extraction method, the program automatically chooses the appropriate equation solver.
3.4.2.4. Option: Number of Modes to Extract (MODOPT)
This option is required for all mode-extraction methods.
If groups of repeated frequencies are present, extract all solutions in each group. For more information, see Repeated Eigenvalues in the Theory Reference.
For the unsymmetric and damped methods, requesting a larger number of modes than necessary reduces the possibility of missed modes, but requires more solution time.
3.4.2.5. Option: Number of Modes to Expand (MXPAND)
MXPAND specifies which extracted modes to expand (that is, which extracted modes to write to the results file) and how to calculate element quantities (stress, strains, forces, energies, etc.) for subsequent postprocessing or for downstream mode-superposition analyses (such as spectrum, PSD, transient, or harmonic analyses).
You can specify the following methods of mode expansion via MXPAND:
Input the number of modes to expand (
NMODE
).Select the modes using a table (input using
NMODE
).Select the modes based on their modal mass or mode coefficient (input as
ModeSelMethod
). Refer to Using Mode Selection for more information.Specify a frequency range to extract (
FREQB
,FREQE
).
In a mode-superposition analysis, the degree-of-freedom results can either be
combined in the expansion pass and the element results calculated from the
combined degree-of-freedom solution, or the stresses can be combined directly
during the expansion pass to reduce computation time. This behavior is
controlled by MSUPkey
at the modal analysis
level.
If MSUPkey
= YES
(MXPAND,ALL,,,YES,,YES), the element results are written to
the mode file and then directly combined during the expansion pass. The
expansion using this option reduces the requires solution time. This option is
the default when all of the following conditions
exist:
Elcalc
= YES (Calculate element results, reaction forces, energies, and the nodal degree of freedom solution).The mode shapes are normalized to the mass matrix.
FREQB
andFREQE
are blank or 0.0.No superelement is defined.
The available results are:
Element nodal component stresses
Element nodal component elastic strains
Element summable miscellaneous data
Element nodal forces
Element energies
The following limitations apply for the downstream mode-superposition analyses:
Equivalent strains are evaluated using
EFFNU
=0.0. Use AVPRIN to set to the appropriate Poisson's ratio value.Thermal loads are not supported.
NMISC results are not available.
Superelement expansion is not supported after a transient or harmonic analysis. (See The CMS Use and Expansion Passes in the Substructuring Analysis Guide.)
To include the damping and inertia contributions for reactions in a harmonic or transient analysis, the element nodal loads must be output (OUTRES,NLOAD,ALL); otherwise the reactions reflect only the static contributions.
The damping element forces and reaction forces are not available in a mode-superposition harmonic analysis based on QRDAMP or UNSYM eigensolver if
Cpxmod
was set to ON or CPLX on the MODOPT command.Strains and stresses of PIPE elements are not supported when pressure load is applied.
Inertia forces and kinetic energies are not available when enforced motion is present (DVAL)
Damping forces correspond to the damping settings of the last load step.
If MSUPkey
= NO
(MXPAND,ALL,,,YES,,NO), the element results are not written
to the mode file. For subsequent downstream mode-superposition analysis, the
degree-of-freedom results are combined in the expansion pass and the element
results are calculated from the combined degree-of-freedom results. This option
is used to obtain the NMISC results, or it can be used to calculate thermal
loads in the modal analysis for use in a subsequent mode-superposition harmonic
or transient analysis. This option cannot be used to obtain the damping forces
based on modal damping ratios (MDAMP,
DMPRAT, DMPR on
MP command)
3.4.2.6. Option: Results File Output (OUTRES)
Issue OUTRES to expand only items of interest and in the areas of interest to limit the size of the results file Jobname.rst. For subsequent mode-superposition analyses (spectrum, PSD, transient, or harmonic), issue OUTRES during the modal analysis to control their output as well.
3.4.2.7. Option: Mass Matrix Formulation (LUMPM)
Use this option to specify the default formulation (which is element-dependent) or lumped mass approximation. The default formulation is suitable for most applications; however, for some problems (such as those involving slender beams or very thin shells), the lumped mass approximation often yields better results. Also, the lumped mass approximation can result in a shorter run time and lower memory requirements.
3.4.2.8. Option: Prestress Effects Calculation (PSTRES)
Use this option to calculate the modes of a prestressed structure. By default, no prestress effects are included; that is, the structure is assumed to be stress-free. To include prestress effects, element files from a previous static (or transient) analysis must be available; see Performing a Prestressed Modal Analysis from a Linear Base Analysis. If prestress effects are turned on, the lumped mass setting (LUMPM) in this and subsequent solutions must be the same as it was in the prestress static analysis.
You can use only axisymmetric loads for prestressing harmonic elements such as PLANE25 and SHELL61.
3.4.2.9. Option: Residual Vector Calculation (RESVEC)
Use this option to include the contribution of higher frequency modes in a
subsequent mode-superposition analysis. If rigid body modes are present, define
pseudo-constraints (D) with Value
=
SUPPORT. Only the minimum number of constraints are required. Those constraints
will only be considered for the residual vector calculation.
After you complete the fields on the Modal Analysis Options dialog box, click
OK. A dialog box specific to the selected extraction method appears. You see
some combination of the following fields: FREQB
,
FREQE
, PRMODE
,
Nrmkey
. Refer to MODOPT
description for the meaning of the fields.
In a modal analysis, the only "loads" that typically affect the solution are displacement constraints. If you input a nonzero displacement constraint, the program assigns a zero-value constraint to that degree of freedom instead. For directions in which no constraints are specified, the program calculates rigid-body (zero-frequency) as well as higher (nonzero frequency) free body modes. Table 3.2: Loads Applicable in a Modal Analysis shows the commands to apply displacement constraints. Notice that you can apply them either on the solid model (keypoints, lines, and areas) or on the finite element model (nodes and elements). For a general discussion of solid-model loads versus finite-element loads, see Loading in the Basic Analysis Guide.
Other loads, such as applied nodal forces and element distributed load, do not affect the modal analysis directly. The load stiffness matrix associated with some applied loads, however, may affect a prestressed modal analysis; therefore, any changes to such loads in the modal analysis may lead to a different solution. See the Element Reference or Command Reference for load types that can accommodate load stiffness matrices.
If you intend to perform a downstream harmonic or transient mode-superposition analysis, you can apply other load types as well.
Note: Loads specified using tabular boundary conditions with TIME as the primary variable (*DIM) will have the table value at TIME equal to zero.
Table 3.2: Loads Applicable in a Modal Analysis
Load Type | Category | Cmd Family | GUI Path |
---|---|---|---|
Displacement (UX, UY, UZ, ROTX, ROTY, ROTZ) | Constraints | D |
In an analysis, loads can be applied, removed, operated on, or listed.
Table 3.3: Load Commands for a Modal Analysis lists all the commands you can use to apply loads in a modal analysis.
All loading operations (except List; see Listing Loads) are accessed through a series of cascading menus. From the Solution menu, you select the operation (apply, delete, and so on), then the load type (displacement, force, and so on), and then the object to which you are applying the load (keypoint, line, node, and so on).
For example, to apply a displacement load to a line, follow this GUI path:
- GUI:
The only load step options available for a modal analysis are damping options.
Table 3.4: Load Step Options (Damping)
Option | Command |
---|---|
Global Alpha (mass) Damping | ALPHAD |
Global Beta (stiffness) Damping | BETAD |
Material-Dependent Alpha (mass) Damping | MP,ALPD or TB,SDAMP,,,,ALPD |
Material-Dependent Beta (stiffness) Damping | MP,BETD or TB,SDAMP,,,,BETD |
Element Damping (applied via element real constant or material tables) | R, TB |
Constant Structural Damping Ratio | DMPSTR |
Material-Dependent Constant Structural Damping Ratio | MP,DMPR |
Damped and QR damped mode-extraction methods support all types of damping. UNSYM only supports structural damping.
Damping is ignored for the other mode-extraction methods.
If you include damping and specify the damped
mode-extraction method, the calculated eigenvalues and eigenvectors are complex. If
you include damping and specify the QR damped
mode-extraction method, the eigenvalues are complex, but the eigenvectors can be
real or complex (Cpxmod
on MODOPT).
The real eigenvectors are used for the mode-superposition analysis. See Comparing Mode-Extraction Methods for details.
For more information about different forms of damping, see Damping.
Damping specified in a non-damped modal analysis — Damping (MP,DMPR) can be specified in a non-damped modal analysis if a spectrum or mode-superposition analysis is to follow the modal analysis. Although the damping does not affect the eigenvalue solution, it is used to calculate an effective damping ratio for each mode, which is then used in the subsequent analysis; see the Mechanical APDL Theory Reference.
Before you solve, save (SAVE) a backup copy of the database to a named file. You can then retrieve your model by reentering the program and issuing RESUME.
Now start the solution calculations (SOLVE).
The output from the solution consists mainly of the natural frequencies, which are printed as part of the printed output (Jobname.out) and also written to the mode shape file (Jobname.mode). The printed output may include mode shapes and the participation factor table, depending on your analysis options and output controls. Element results are written to the results file (Jobname.rst) via MXPAND. If MXPAND is not issued, the element results are not written by default and therefore cannot be postprocessed.
The participation factor table lists participation factors, mode coefficients, and mass distribution percentages for each mode extracted. The participation factors and mode coefficients are calculated based on an assumed unit displacement spectrum in each of the global Cartesian directions and rotation about each of these axes. The mass distribution is also listed.
The total mass used to calculate the ratio of effective mass to total mass is the mass output in the mass summary. Only the precise mass summary (used for 3D models) accurately calculates the total rigid body mass and therefore the directional masses. For more information, see Mass Related Information in the Mechanical APDL Theory Reference.
If you want to include the effect of boundary conditions and CP/CE in the calculation of the total mass, you can use APDL Math. For an example, see Example 4.9: Calculate the Participation Factors and Total Rigid Body Mass in the Ansys Parametric Design Language Guide.
Participation factors may be approximate when you use a force-distributed constraint (deformable constraint surface) defined via MPC contact to apply boundary conditions (see Surface-Based Constraints in the Contact Technology Guide). Some contact nodes on the boundary are considered dependent nodes by the solver, so their contribution is ignored. It is recommended you use a rigid surface constraint instead.
For participation factors calculated in a superelement use pass, refer to The CMS Use and Expansion Passes in the Substructuring Analysis Guide.
Rotational participation factors will be calculated when a real eigensolver mode-extraction method (such as Block Lanczos, PCG Lanczos, Supernode, or Subspace) is used.
For rotational degrees of freedom, the participation factor table output shows the ratios of effective mass to total mass only when the precise mass summary is calculated.
Note: The modal effective mass is equal to the participation factor squared. For a list of exceptions, see Effective Mass and Cumulative Mass Fraction in the Mechanical APDL Theory Reference.
Retrieving a participation factor or mode coefficient — You can retrieve a participation factor or mode coefficient via *GET (with Entity = MODE).
The modal masses, kinetic energies, and translational effective masses are printed out in a summary following the participation factor tables when the modes are expanded (MXPAND).
The modal masses and kinetic energies are always calculated
from modes normalized to unity (independent of Nrmkey
on
MODOPT).
In a superelement use pass, only master degrees-of-freedom are considered. As a consequence, the more master degrees-of-freedom are constrained, the more inaccurate the modal masses and derived kinetic energies become.
The kinetic energy is calculated from the modal mass. Therefore, element results
need not be calculated (independent of Elcalc
on
MXPAND).
You must now exit the solution processor (FINISH).