ANSYS Workbench Simulation_Modal

Free Vibration Analysis

Chapter Five

April 22, 2004Inventory

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Chapter Overview

• In this chapter, performing free vibration analyses in Simulation will be covered. In Simulation, performing a free vibration analysis is similar to a linear static 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 Procedure

– Free Vibration with Pre-Stress Analysis Procedure

• The capabilities described in this section are generally applicable 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.


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Basics of Free Vibration Analysis

• A free vibration analysis (a.k.a. modal or normal modes analysis) is performed to obtain the natural frequencies and mode shapes of a structure– Free Vibration analysis does not 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:

tFxKxCxM

0 xKxM


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• In free vibration analysis, the structure is assumed to be linear, so the response is assumed to be harmonic:

where i is the mode shape (eigenvector) and i is the natural circular frequency for mode i.

• By substituting this value in the earlier equation, the following is obtained:

Noting that the solution i =0 is trivial, i is solved for:

tx ii cos

0cos

0coscos2

2

tKM

tKtM

iii

iiiii

02 ii MK


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• For a free vibration analysis, the natural circular frequencies i and mode shapes i are calculated from:

This results in certain assumptions related to the analysis:– [K] and [M] are constant:

• Linear elastic material behavior is assumed

• Small deflection theory is used, and no nonlinearities included

• [C] is not present, so damping is not included

• {F} is not present, so no excitation of the structure is assumed

• The structure can be unconstrained (rigid-body modes present) or partially/fully constrained, depending on the physical structure

– Mode shapes {} are relative values, not absolute

• It is important to remember these assumptions related to performing free vibration analyses in Simulation.

02 ii MK


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A. Free Vibration Analysis Procedure

• The free vibration 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 Geometry

– Assign Material Properties

– Define Contact Regions (if applicable)

– Define Mesh Controls (optional)

– Include Supports (if applicable)

– Request Frequency Finder Results

– Set Frequency Finder Options

– Solve the Model

– Review Results


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… Geometry and Point Mass

• Similar to linear static analyses, any type of geometry supported by Simulation may be used:– Solid bodies

– Surface 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 Point 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 selected surfaces. Because of this, the Point Mass will decrease the natural frequency in free vibration analyses.

ANSYS License AvailabilityDesignSpace Entra xDesignSpace xProfessional xStructural xMechanical/Multiphysics x


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… Material Properties

• For material properties, Young’s Modulus, Poisson’s Ratio, and Mass Density are required– Since no loading is assumed, no other material properties will

be used, if defined



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… Contact Regions

• Contact regions are available in free vibration 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 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 default

Initially Touching Inside Pinball Region Outside Pinball RegionBonded Bonded Bonded Bonded FreeNo Separation No Separation No Separation No Separation FreeRough Rough Bonded Free FreeFrictionless Frictionless No Separation Free Free

Contact Type Static AnalysisModal Analysis

ANSYS License AvailabilityDesignSpace EntraDesignSpace xProfessional xStructural xMechanical/Multiphysics x


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… Contact Regions

• For ANSYS Professional licenses and above, additional contact options can be used in free vibration 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 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 size

• For ANSYS Structural 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 free vibration analysis since it is nonlinear.

ANSYS License AvailabilityDesignSpace EntraDesignSpaceProfessional /Structural xMechanical/Multiphysics x


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… Loads and Supports

• Structural and thermal loads not used in free vibration– See 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 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 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 support.



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… Requesting Results

• Most 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 under the Solutions Branch– The Frequency Finder tool adds another branch to

the Solutions branch

– The 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.

– 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 specified 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.


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• Under the Frequency Finder branch are the requests requested– When 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 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 under 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.



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• The corresponding ANSYS commands for the Frequency Finder branch are as follows:– If Frequency Finder branch is present, ANTYPE,MODAL is set

– The 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 command

– All 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.

Advanced ANSYS Details


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… Solution Options

• The solution branch provides details on the type of analysis being performed– For 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 Type” 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.”



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… Solution Options

• For 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 “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 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 large models of solid elements, when requesting only a few modes.



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… Solving the Model

• After setting up the model, one can solve the free vibration analysis just like any other analysis 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 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.



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… Reviewing Results

• After solution, mode shapes can be reviewed– Because there is no excitation applied to the structure, the

mode shapes are relative values associated with free vibration• Mode shapes (displacements), stresses, and strains represent

relative, not absolute quantities

– The 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.



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… Reviewing Results

• The Worksheet tab of the Frequency Finder branch summarizes all frequencies in tabular form– By reviewing the frequencies and mode shapes, one can get

a better understanding of the possible dynamic response ofthe structure under different excitation directions



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B. Free Vibration with Pre-Stress

• In 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 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.



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… Free Vibration with Pre-Stress

– In free vibration with pre-stress analyses, 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 free vibration with pre-stress analysis is then solved, including the [S] term

0 ii MSK

FxK o

So


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… Procedure w/ Pre-Stress Effects

• To 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.

– Results for the linear static structural analysis may also be requested under the Solution branch, not the Frequency Finder branch

• A stress or strain result requested under the Frequency Finder branch will be relative stress/strain values for a particular mode

• A stress or strain (or displacement) result requested under the Solution branch will be absolute stress/strain/displacement values for the statically applied load



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… Example w/ Pre-Stress Effects

• Consider a simple comparison of a thin plate fixed at one end– Two analyses will be run – free vibration and free vibration

with pre-stress effects – to compare the differences between the two.

Free Vibration Free Vibration with Pre-Stress



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• Notice that the only difference of running a free vibration analysis with or without pre-stress is the existence of a load– If a Frequency Finder tool is present and a

load is present, 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 static analysis can be reported.



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• In this example, with the applied force, a tensile stress state is produced, thus increasing the natural frequencies, as illustrated below

Free Vibration

1st mode frequency: 141 Hz

Free Vibration with Pre-Stress

1st mode frequency: 184 Hz



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… Prestressed Modal Analysis

• For prestressed modal analysis, Simulation performs the two necessary iterations internally:– A linear static analysis with PSTRES,ON is run

– A modal analysis is then run right afterwards with PSTRES,ON to consider prestress effects



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… Prestressed Modal Analysis

• Other items useful for ANSYS users to keep in mind:– No large-deflection prestress effects are 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 Solution 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 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.



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• Workshop 5 – Free Vibration Analysis

• Goal:– Investigate the vibration characteristics of two motor cover

designs manufactured from 18 gage steel.

C. Workshop 5

ANSYS Workbench Simulation_Modal

Documents

Transcript of ANSYS Workbench Simulation_Modal