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1、Free Vibration AnalysisChapter FiveANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisChapter OverviewIn this chapter, performing free vibration analyses in Simulation will be covered. In Simulation, performing a free vibration analysis is similar to a linear s
2、tatic analysis.It is assumed that the user has already covered Chapter 4 Linear Static Structural Analysis prior to this section.The following will be covered:Free Vibration Analysis ProcedureFree Vibration with Pre-Stress Analysis ProcedureThe capabilities described in this section are generally ap
3、plicable to ANSYS DesignSpace Entra licenses and 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.April 22, 2004Inventory #0020715
4、-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisBasics of Free Vibration AnalysisA free vibration analysis (a.k.a. modal or normal modes analysis) is performed to obtain the natural frequencies and mode shapes of a structureFree Vibration analysis does not
5、consider the response of the structure under dynamic loads but just solves for the natural frequencies. A free vibration analysis is usually the first step before solving more complicated dynamic problems.A free vibration analysis is a subset of the general equation of motion:April 22, 2004Inventory
6、 #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisBasics of Free Vibration AnalysisIn free vibration 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
7、 natural circular frequency for mode i. By substituting this value in the earlier equation, the following is obtained:Noting that the solution f fi =0 is trivial, w wi is solved for:April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Ana
8、lysisBasics of Free Vibration AnalysisFor a free vibration analysis, the natural circular frequencies w wi and mode shapes f fi are calculated from:This results in certain assumptions related to the analysis:K and M are constant:Linear elastic material behavior is assumedSmall deflection theory is u
9、sed, and no nonlinearities includedC is not present, so damping is not includedF is not present, so no excitation of the structure is assumedThe structure can be unconstrained (rigid-body modes present) or partially/fully constrained, depending on the physical structureMode shapes f f are relative v
10、alues, not absoluteIt is important to remember these assumptions related to performing free vibration analyses in Simulation.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisA. Free Vibration Analysis ProcedureThe free vibrati
11、on 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 free vibration analyses.Attach GeometryAssign Material PropertiesDefine Contact Regions (if applicable)Define Mesh Controls (optional)
12、Include Supports (if applicable)Request Frequency Finder ResultsSet Frequency Finder OptionsSolve the ModelReview ResultsApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Geometry and Point MassSimilar to linear static analyse
13、s, any type of geometry supported by Simulation may be used:Solid bodiesSurface bodies (with appropriate thickness defined)Line bodies (with appropriate cross-sections defined)For line bodies, only mode shapes and displacement results are available.The Point Mass feature can be used:Input for the Po
14、int Mass was described earlier in Chapter 4.The Point Mass adds mass only in a free vibration analysis. It is connected to selected surfaces as if no stiffness is present, so the effect is to add only mass (not stiffness) to a structure.Useful for including the effect of distributed weight on select
15、ed surfaces. Because of this, the Point Mass will decrease the natural frequency in free vibration analyses.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Material PropertiesFor material properties, Youngs Modulus, Poissons
16、 Ratio, and Mass Density are requiredSince no loading is assumed, no other material properties will be used, if definedApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Contact RegionsContact regions are available in free vibr
17、ation analyses. However, since this is a purely linear analysis, contact behavior will differ for the nonlinear contact types:There are two important things to remember when using contact in a free vibration analysis:The two nonlinear contact behaviors rough and frictionless will behave in a linear
18、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 will depend on the pinball region size.The pinball region is automatically determined by
19、defaultApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Contact RegionsFor ANSYS Professional licenses and above, additional contact options can be used in free vibration analyses:For rough and frictionless contact, the “Inte
20、rface 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 touching if this option is set.)The size of the “Pinball Region” may be changed as
21、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 Structural licenses and above, frictional contact will behave similar to bonded contact i
22、f surfaces are touching but act as free (no contact) if contact is open.It is not recommended to use frictional contact in a free vibration analysis since it is nonlinear. April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Load
23、s and SupportsStructural and thermal loads not used in free vibrationSee Section B later in this chapter for a discussion on free vibration with pre-stress analysis. In this situation, loads are considered but only for their pre-stress effects.Supports can be used in free vibration analyses:If no or
24、 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, free vibration analyses do not require that rigid-body motion be prevented.The boundary conditions are important, as they affect the mode shapes an
25、d 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 support.April 22, 2004Inventory #0020715-ANSY
26、S Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Requesting ResultsMost of the options for free vibration analyses are similar to that of static analysis. However, Simulation knows to perform a free vibration analysis when the Frequency Finder tool is selected u
27、nder 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 increase the solution time.T
28、he 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 specified if “Limit Search to Ra
29、nge” 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.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Requesting R
30、esultsUnder 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 directional displacements
31、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 relative stress or strain results are needed, be sure to add results u
32、nder the Frequency Finder branch, not the Solution branch.Recall that mode shapes are relative values since no excitation is present. Hence, stresses and strains are also relative.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analy
33、sis Requesting ResultsThe corresponding ANSYS commands for the Frequency Finder branch are as follows:If Frequency 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 t
34、he MODOPT,nmodes,freqb,freqe commandAll modes are expanded via the MXPAND command. To save disk space and calculation times, the element solution option of MXPAND is not turned on unless stress or strain results are requested.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench
35、 SimulationTraining ManualFree Vibration Analysis Solution OptionsThe solution branch provides details on the type of analysis being performedFor a free vibration analysis, none of the options in the Details view of the Solution branch usually need to be changed.In the majority of cases, “Solver Typ
36、e” should be left on the default option of “Program Controlled”.If the model is a very large one of solid elements, and only 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.”April 22, 2004Inventor
37、y #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration 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 shou
38、ld not be changed.“Solver Type” can be set to “Direct” or “Iterative”“Program Controlled” or “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 model
39、s and beam, shell, or solid meshes, so it is the default option.“Iterative” results in the PowerDynamics 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
40、large models of solid elements, when requesting only a few modes.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Solving the ModelAfter setting up the model, one can solve the free vibration analysis just like any other anal
41、ysis by selecting the Solve button.A free vibration analysis is generally more computationally expensive than a static analysis on the same model because of the equations solved.If a “Solution Information” branchis requested under the Solutionbranch, detailed solution output, including the amount of
42、 memory used and solution progress, willbe available in the Worksheet tab.If stress or strain results or morefrequencies/modes are requestedafter a solution is performed, a newsolution is required.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFre
43、e Vibration Analysis Reviewing ResultsAfter solution, mode shapes can be reviewedBecause there is no excitation applied to the structure, the mode shapes are relative values associated with free vibrationMode shapes (displacements), stresses, and strains represent relative, not absolute quantitiesTh
44、e frequency is listed in the Details view of any result being viewed.The animation button on the Results Context toolbar can be used to help visualize the mode shapes better.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Re
45、viewing ResultsThe Worksheet tab of the Frequency Finder branch summarizes all frequencies in tabular formBy reviewing the frequencies and mode shapes, one can geta better understanding of the possible dynamic response ofthe structure under different excitation directionsApril 22, 2004Inventory #002
46、0715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisB. Free Vibration with Pre-StressIn some cases, one may want to consider prestress effects when performing a free vibration analysis.The stress state of a structure under constant (static) loads may affect
47、 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 load is increased (from tightening), the lateral frequencies increase. This is an example of the stress stiffening effect.April 22, 2004Inventory
48、 #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Free Vibration with Pre-StressIn free vibration with pre-stress analyses, internally, two iterations are automatically performed:A linear static analysis is initially performed:Based on the stress st
49、ate from the static analysis, a stress stiffness matrix S is calculated:The free vibration with pre-stress analysis is then solved, including the S termApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Procedure w/ Pre-Stress
50、EffectsTo perform a free vibration with pre-stress analysis (a.k.a. prestressed modal analysis), it is the same as running a regular free vibration 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
51、.Results for the linear static structural analysis may also be requested under the Solution branch, not the Frequency Finder branchA stress or strain result requested under the Frequency Finder branch will be relative stress/strain values for a particular modeA stress or strain (or displacement) res
52、ult requested under the Solution branch will be absolute stress/strain/displacement values for the statically applied loadApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Example w/ Pre-Stress EffectsConsider a simple compari
53、son of a thin plate fixed at one endTwo analyses will be run free vibration and free vibration with pre-stress effects to compare the differences between the two.Free VibrationFree Vibration with Pre-StressApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining
54、ManualFree Vibration Analysis Example w/ Pre-Stress EffectsNotice that the only difference of running a free vibration analysis with or without pre-stress is the existence of a loadIf a Frequency Finder tool is present and a load is present, Simulation knows that a “Free Vibration with Pre-Stress” a
55、nalysis will be performed.If results such as displacement, stress, or strains are requested directly underneath the Solution branch, the results from the linear static analysis can be reported.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vi
56、bration Analysis Example w/ Pre-Stress EffectsIn this example, with the applied force, a tensile stress state is produced, thus increasing the natural frequencies, as illustrated belowFree Vibration1st mode frequency: 141 HzFree Vibration with Pre-Stress1st mode frequency: 184 HzApril 22, 2004Invent
57、ory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Prestressed Modal AnalysisFor prestressed modal analysis, Simulation performs the two necessary iterations internally:A linear static analysis with PSTRES,ON is runA modal analysis is then run rig
58、ht afterwards with PSTRES,ON to consider prestress effectsApril 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration Analysis Prestressed Modal AnalysisOther items useful for ANSYS users to keep in mind:No large-deflection prestress effects are
59、 currently supported in 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 S
60、olution branch.If a Point Mass is present, rigid-body modes may be introduced in a prestressed modal analysis. This is due to the fact that the RBE3-type of surface constraint defined with CONTA174 and TARGE170 introduce 6 DOF but the MASS21 element has no rotary inertial terms (3 DOF).The user can
61、usually ignore these rigid-body modes, as they are associated with the MASS21 elements (verify by checking displacement scale of these mode shapes).No such problems exist for a regular modal with Point Masses.April 22, 2004Inventory #0020715-ANSYS Workbench SimulationANSYS Workbench SimulationTraining ManualFree Vibration AnalysisWorkshop 5 Free Vibration AnalysisGoal:Investigate the vibration characteristics of two motor cover designs manufactured from 18 gage steel. C. Workshop 5April 22, 2004Inventory #0020715-
