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1、Modal AnalysisChapter FiveANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal AnalysisChapter OverviewIn this chapter, performing modal analyses in Design Simulation will be covered. In Design Simulation, performing a modal analysis is similar to a linear analysis.It is assu
2、med that the user has already covered Chapter 4 Linear Static Structural Analysis prior to this section.The following will be covered:Modal Analysis ProcedurePrestressed Modal Analysis ProcedureThe capabilities described in this section are generally applicable to ANSYS DesignSpace Entra licenses an
3、d above.Some options discussed in this chapter may require more advanced licenses, but these are noted accordingly.Harmonic and nonlinear static structural analyses are not discussed here but in their respective chapters.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench
4、- SimulationTraining ManualModal AnalysisBasics of Modal AnalysisA modal analysis, or a free vibration analysis, is performed to obtain the natural frequencies and mode shapes of a structureModal analysis does not consider the response of the structure under dynamic loads but rather the natural freq
5、uencies. A modal analysis is usually the first step before solving more complicated dynamic problems.A modal analysis is a subset of the general equation of motion:February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal AnalysisBasics of Modal
6、AnalysisIn modal analysis, the structure is assumed to be linear, so the response is assumed to be harmonic:where f fi is the mode shape (eigenvector) and w wi is the natural circular frequency for mode i. By substituting this value in the earlier equation, the following is obtained:Noting that the
7、solution f fi =0 is trivial, w wi is solved for:February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal AnalysisBasics of Modal AnalysisFor a modal analysis, the natural circular frequencies w wi and mode shapes f fi are obtained from the matri
8、x equation:This results in certain assumptions related to the analysis:K and M are constant:Linear elastic material behavior is assumedSmall deflection theory is used, and no nonlinearities includedC is not present, so damping is not includedF is not present, so no excitation of the structure is ass
9、umedThe structure can be unconstrained (rigid-body modes present) or partially/fully constrained, depending on the physical structureIt is important to remember these assumptions related to performing modal analyses in Design Simulation.February 2, 2004Inventory #0020105-ANSYS Workbench - Simulation
10、ANSYS Workbench - SimulationTraining ManualModal AnalysisA. Modal Analysis ProcedureThe modal analysis procedure is very similar to performing a linear static analysis, so not all steps will be covered in detail. The steps in yellow italics are specific to modal analyses.Attach GeometryAssign Materi
11、al PropertiesDefine Contact Regions (if applicable)Define Mesh Controls (optional)Include Supports (if applicable)Request Frequency Finder ResultsSet Frequency Finder optionsSolve the ModelReview ResultsFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraini
12、ng ManualModal Analysis Geometry and Material PropertiesSimilar to linear static analyses, any type of geometry supported by Design Simulation may be used:Solid bodiesSurface bodies (with appropriate thickness defined)Line bodies (with appropriate cross-sections defined)For line bodies, only mode sh
13、apes and displacement results are available.For material properties, Youngs Modulus, Poissons Ratio, and Mass Density are requiredSince no loading is assumed, no other material properties will be used, if definedFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - Simulat
14、ionTraining ManualModal Analysis Contact RegionsContact regions are available in modal analysis. However, since this is a purely linear analysis, contact behavior will differ for the nonlinear contact types, as shown below:There are two important things to remember when using contact in a modal anal
15、ysis:The two nonlinear contact behaviors rough and frictionless will behave in a linear fashion, so they will internally behave as bonded or no separation instead.If a gap is present, the nonlinear contact behaviors will be free (i.e., as if no contact is present). Bonded and no separation contact w
16、ill depend on the pinball region size.The pinball region is automatically determined by defaultFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Contact RegionsFor ANSYS Professional licenses and above, additional contact options
17、 are present for use in modal analyses:For rough and frictionless contact, the “Interface Treatment” can be changed to “Adjusted to Touch,” which will make the contact surfaces behave as bonded and no separation, respectively. (Even if a gap is present, the parts will behave as if they are initially
18、 touching if this option is set.)The size of the “Pinball Region” may be changed as well as viewed to ensure that bonded and no separation contact is established, even if a gap is present.Please refer to Chapters 3 and 4 for discussions on the pinball region and how to define its sizeFor ANSYS Struc
19、tural licenses and above, frictional contact will behave similar to bonded contact if surfaces are touching but act as free (no contact) if contact is open.It is not recommended to use frictional contact in a modal analysis since it is nonlinear. February 2, 2004Inventory #0020105-ANSYS Workbench -
20、SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Loads and SupportsStructural and thermal loads not used in a modal analysisSee Section B later in this chapter for a discussion on prestressed modal analysis. In this situation, loads are considered but only for their prestress effe
21、cts.Supports can be used in modal analyses:If no or partial supports are present, rigid-body modes can be detected and evaluated. These modes will be at 0 or near 0 Hz. Unlike static structural analyses, modal analyses do not require that rigid-body motion be prevented.The boundary conditions are im
22、portant, as they affect the mode shapes and frequencies of the part. Carefully consider how the model is constrained.The compression only support is a nonlinear support and should not be used in the analysis.If present, the compression only support will generally behave similar to a frictionless sup
23、port.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Requesting ResultsMost of the options for modal analyses are similar to that of static analysis. However, Design Simulation knows to perform a modal analysis when the Frequen
24、cy Finder tool is selected under the Solutions BranchThe Frequency Finder tool adds another branch to the Solutions branchThe Details View of the Frequency Finder allows the user to specify the “Max Modes to Find.” The default is 6 modes (max is 200). Increasing the number of modes to retrieve will
25、increase the solution time.The search may be limited to a specific frequency range of interest by selecting “Yes” on “Limit Search to Range.By default, frequencies beginning from 0 Hz (rigid-body modes) will be calculated if a search range is not set.The minimum and maximum range (in Hz) can be spec
26、ified if “Limit Search to Range” is enabled. Note that this works in conjunction with “Max Modes to Find.” If not enough modes are requested, not all modes in the frequency range may be found.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualMo
27、dal Analysis Requesting ResultsUnder the Frequency Finder branch are the requests requestedWhen toggling “Max Modes to Find” under the Frequency Finder branch, more mode shapes will automatically be added. The user does not need to request mode shapes from the Context toolbar.If stress, strain, or d
28、irectional displacements are to be requested, this can be done by adding the result from the Context toolbar.For each stress, strain, or displacement result added, the user can specify which mode this corresponds to from the Details view, under “Mode.”If stress or strain results are needed, be sure
29、to add results under the Frequency Finder branch, not the Solution branch.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Requesting ResultsThe corresponding ANSYS commands for the Frequency Finder branch is as follows:If Frequ
30、ency Finder branch is present, ANTYPE,MODAL is setThe number of modes is set with the nmodes argument, and the beginning and ending search frequencies are specified with freqb and freqe of the MODOPT,nmodes,freqb,freqe commandAll modes are expanded via the MXPAND command. To save disk space and calc
31、ulation times, the element solution option of MXPAND is not turned on unless stress or strain results are requested.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Solution OptionsThe solution branch provides details on the typ
32、e of analysis being performedFor a modal analysis, none of the options in the Details view of the Solution branch usually need to be changed.In the majority of cases, “Solver Type” should be left on the default option of “Program Controlled”.If the model is a very large one of solid elements, and on
33、ly a few modes are to be requested, the “Solver Type,” when changed to “Iterative,” may be more efficient.The “Analysis Type” will display “Free Vibration” for the case of a modal analysis.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal
34、 Analysis Solution OptionsFor a regular modal analysis, none of the solution options except for “Solver Type” have much effect“Large Deflection” and “Weak Springs” are meant for static analysis cases and should not be changed.“Solver Type” can be set to “Direct” or “Iterative”“Program Controlled” or
35、 “Direct” result in the Block Lanczos eigenvalue extraction method with the sparse direct equation solver (MODOPT,LANB and EQSLV,SPARSE). This is the most robust eigensolver, as it handles small & large models and beam, shell, or solid meshes, so it is the default option.“Iterative” results in the P
36、owerDynamics solution method, which is a combination of the subspace eigenvalue extraction method with the PCG equation solver (MODOPT,SUBSP and EQSLV,PCG). The PowerDynamics eigensolver can be efficient for large models of solid elements, when requesting only a few modes.February 2, 2004Inventory #
37、0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Solving the ModelAfter setting up the model, one can solve the modal analysis just like any other analysis by selecting the Solve button.A modal analysis is generally more computationally expensive than a s
38、tatic analysis on the same model because the equations solved for are different.The Worksheet tab of the Solutionbranch provides detailed solutionoutput, including the amount ofmemory being used and how manymodes have been extracted already.If stress or strain results or morefrequencies/modes are re
39、questedafter a solution is performed, a newsolution is required.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Reviewing ResultsAfter solution, mode shapes can be reviewedBecause there is no excitation applied to the structure
40、, the mode shapes are relative values associated with free vibrationMode shapes (displacements), stresses, and strains represent relative, not absolute quantitiesThe frequency is listed in the Details view of any result being viewed.The animation button on the Results Context toolbar can be used to
41、help visualize the mode shapes better.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Reviewing ResultsThe Worksheet tab of the Frequency Finder branch summarizes all frequencies in tabular formBy reviewing the frequencies and
42、mode shapes, one can geta better understanding of the possible dynamic response ofthe structure under different excitation directionsFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal AnalysisB. Prestressed Modal AnalysisIn some cases, one
43、 may want to consider prestress effects when performing a modal analysis.The stress state of a structure under constant (static) loads may affect its natural frequencies. This can be important, especially for structures thin in one or two dimensions.Consider a guitar string being tuned as the axial
44、load is increased (from tightening), the lateral frequencies increase. This is an example of the stress stiffening effect.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal AnalysisThe way in which prestressed mo
45、dal analyses are solved for is that, internally, two iterations are automatically performed:A linear static analysis is initially performed:Based on the stress state from the static analysis, a stress stiffness matrix S is calculated:The prestressed modal analysis is then solved for, including the S
46、 termFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal ProcedureTo perform a prestressed modal analysis (also known as a free vibration with prestress analysis), it is the same as running a regular free vibratio
47、n analysis with the following exceptions:A load (structural and/or thermal) must be applied to determine what the initial stress state of the structure is.Results for the linear static structural analysis may also be requested under the Solution branch, not the Frequency Finder branchA stress or str
48、ain result requested under the Frequency Finder branch will be relative stress/strain values for a particular modeA stress or strain (or displacement) result requested under the Solution branch will be absolute stress/strain/displacement values for the statically applied loadFebruary 2, 2004Inventor
49、y #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal ExampleConsider a simple comparison of a thin plate fixed at one endTwo analyses will be run free vibration and free vibration with prestress effects to compare the differences between
50、the two.Free VibrationFree Vibration with PrestressFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal ExampleNotice that the only difference of running a modal analysis with or without prestress is the existence
51、of a loadIf a Frequency Finder tool is present and a load is present, Design Simulation knows that a “Free Vibration with Pre-Stress” analysis will be performed.If results such as displacement, stress, or strains are requested directly underneath the Solution branch, the results from the linear stat
52、ic analysis can be reported.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal ExampleIn this example, with the applied force, a tensile stress state is produced, thus increasing the natural frequencies, as illus
53、trated belowFree Vibration1st mode frequency: 141 HzFree Vibration with Prestress1st mode frequency: 184 HzFebruary 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal Analysis Prestressed Modal AnalysisFor prestressed modal analysis, Design Simulat
54、ion performs the two necessary iterations internally:A linear static analysis with PSTRES,ON is runA modal analysis is then run right afterwards with PSTRES,ON to consider prestress effectsOther items useful for ANSYS users to keep in mind:No large-deflection prestress effects are currently supporte
55、d in Design Simulation, so enabling the “Large Deflection: On” in the Solution branch is not permitted.The equation solver for the static analysis and the eigensolver for the modal analysis currently cannot be independently set. Both will be affected by the “Solver Type” setting in the Solution bran
56、ch.February 2, 2004Inventory #0020105-ANSYS Workbench - SimulationANSYS Workbench - SimulationTraining ManualModal AnalysisWorkshop 5 Modal AnalysisGoal:Investigate the vibration characteristics of two motor cover designs manufactured from 18 gage steel. C. Workshop 5February 2, 2004Inventory #0020105-
