Dynamics 70 M2 Modal

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Modal Analysis

Module 2


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Module 2

Modal Analysis

A. Define modal analysis and its purpose.

B. Discuss associated concepts, terminology, and mode extraction

methods.

C. Learn how to do a modal analysis in ANSYS.

D. Work on one or two modal analysis exercises.


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Modal Analys is

A. Def ini t ion & Purpose

What is modal analysis?

A technique used to determine a structures vibration

characteristics:

Natural frequencies

Mode shapes

Mode participation factors (how much a given mode participates in agiven direction)

Most fundamental of all the dynamic analysis types.


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Modal Analys is

Definition & Purpose

Benefits of modal analysis

Allows the design to avoid resonant vibrations or to vibrate at a

specified frequency(speakers, for example).

Gives engineers an idea of how the design will respond to

different types of dynamic loads.

Helps in calculating solution controls (time steps, etc.) for other

dynamic analyses.

Recommendat ion:Because a structures vibration characteristics

determine how it responds to any type of dynamic load, always perform amodal analysis first beforetrying any other dynamic analysis.


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General equation of motion:

Assume free vibrations and ignore damping:

Assume harmonic motion ( i.e. )

The roots of this equation are i2, the eigenvalues, where i rangesfrom 1 to number of DOF. Corresponding vectors are {u}i, the

eigenvectors.

0uMK 2

0uKuM

tFuKuCuM

Modal Analys is

B. Term inology & Concepts

)tsin(Uu


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Modal Analys is

Terminology & Concepts

The square roots of the eigenvalues are i, the structures naturalcircular frequencies (radians/sec). Natural frequencies fi are then

calculated as fi = i/2p cycles/sec. It is the natural frequencies fithat are input by the user and output by ANSYS.

The eigenvectors {u}i represent the mode shapes - the shapeassumed by the structure when vibrating at frequency fi.


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Modal Analysis

Terminology & Concepts (cont.)

Mode Extract ionis the term used to describe the calculation of

eigenvalues and eigenvectors.

Mode Expansionhas a dual meaning. For the reduced method,

mode expansionmeans calculating the full mode shapes from the

reduced mode shapes. For all other methods, mode expansion

simply means writing mode shapes to the results file.


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Modal Analys is - Terminology & Con cepts

Mode Extract ion Methods

Several mode extraction methods are available in ANSYS: Block Lanczos (default)

Subspace

PowerDynamics

Reduced

Unsymmetric

Damped (full)

QR Damped

Which method you choose depends primarily on the model size

(relative to your computer resources) and the particular

application.


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Mode Extraction Methods - Bloc k Lanczos

The Block Lanczos method is recommended for most

applications.

Efficient extraction of large number of modes (40+) in most models

Typically used in complex models with mixture of

solids/shells/beams etc.

Efficient extraction of modes in a frequency range

Handles rigid-body modes well


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Mode Extraction Methods - Subspace

When extracting a small number of modes (


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Mode Extraction Methods - PowerDynamics

For large (100K+ DOF) models and a small number of modes

(< 20), use the PowerDynamics method. It can be significantly

faster than Block Lanczos or Subspace, but:

Requires large amount of memory.

May not converge with poorly shaped elements or an ill-conditioned

matrix.

May miss modes (No Sturm sequence check) Recommended only as a last resort for large models.


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Mode Extraction Methods - Reduced

For models in which lumping mass does not create a local

oscillation, typically beams and spars, use the Reduced method.

Memory and disk requirements are low.

In general fastest eigen solver

Employs matr ix reduc t ion, a technique to reduce the size of [K] and

[M] by selecting a subset of DOF called masterDOF.

Reduction of [K] is exact but [M] loses some accuracy

Accuracy of [M] depends on number and location of master DOF.

Generally not recommended due to

Expertise required in picking master DOF

Efficient alternatives such as Block Lanczos

reduced cost of hardware


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Mode Extraction Methods - Unsymmetr ic

The unsymmetric method is used for acoustics (with structural

coupling) and other such applications with unsymmetric [K] and [M].

Calculates complex eigenvalues and eigenvectors:

Real part is the natural frequency.

Imaginary part indicates stability - negative means stable, positive

means unstable.


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Mode Extraction Methods - Damped

Damping is normally ignored in a modal analysis, but if its effects

are significant, the Damped method is used.

Typical application is rotor dynamics, where gyroscopic damping

effects are important.

Two ANSYS elements, BEAM4 and PIPE16, allow gyroscopic effects to

be specified in the form of real constant SPIN (rotational speed,

radians/time).

Calculates complex eigenvalues and eigenvectors:

Imaginary part is the natural frequency.

Real part indicates stability - negative means stable, positive

means unstable.


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Modal Analysis - Termino logy & Concepts

Mode Extraction Methods - Q-R damped

A second mode extraction method that considers damping effects

is the Q-R Damped method.

Faster and more stable than the existing Damped Solver

Works with poorly conditioned models

All forms of damping allowed including damper elements

Combines the best features of the real eigensolution method (Block

Lanczos) and the Complex Hessenberg method (QR Algorithm) Outputs complex eigenvalues ( frequency and stability) and damping

ratio of each mode


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MODOPT,QRDAMP,NMODE


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FEA Model Characteristics:

111,129 active dofs

10 damped modes

Alpha, Beta and Element damping

0

20000

40000

60000

80000

100000

120000

140000

160000

QRDAMP DAMP

CPU (sec)

ELAPSE (sec)



Comparison Demonstrating the Superior Solution Performanceof the QR Damped Mode Extraction Method


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Extraction

method

Linear Solver

UsedRemarks

Block Lanczos Sparse Matrix Recommended for most applications; Most stable;

Subspace Frontal Solver

Stable but slow; Requires large disk space; Has

difficulty with constraint equations / rigid body

modes

Powerdynamics PCG solver

Same as subspace but with PCG solver; Can

handle very large models; Lumped mass only; May

miss modes; Modes cannot be used in

subsequent spectrum and PSD analyses

Reduced Frontal Solver

In general fastest; Accuracy depends on Master

DOF selection; Limitations similar to Subspace;

Not recommended due to expertise required inselecting Master DOF.


Summary for s ymmetr ic , undamped solvers


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Modal Analys is

C. Procedure

Four main steps in a modal analysis:

Build the model

Choose analysis type and options

Apply boundary conditions and solve

Review results


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Modal Analys is Procedure

Bu i ld the Model

Remember density!

Linear elements and materials only. Nonlinearities are ignored.

See also Model ing Considerat ionsin Module 1.


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Choose Analys is Type & Opt ions

Build the model

Choose analysis type and

options

Enter Solution and choose

modal analysis.

Mode extraction options*

Mode expansion options*

Other options*

*Discussed next


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Choose Analysis Type & Options

Mode extraction options

Method: Block Lanczos

recommended for most applications.

Number of modes: Must be specified

(except Reduced method).

Frequency range: Defaults to entire

range, but can be limited to a desired

range (FREQB to FREQE).

Normal izat ion:Discussed next.

defaults to 1e8


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Normalization of mode shapes:

Needed because the DOF solution does not have real meaning. It

only shows the mode shape - how the nodes move relative to each

other.

Modes are normalized either to the mass matrix or to a unit matrix

(unity).

Normalization to mass matrix is the default, and is required for a

spectrum analysis or if a subsequent mode superposition analysis is

planned.

Choose normalization to unity when you want to easily compare

relative values of displacements throughout the structure.

Modes normalized to unity cannot be used in subsequent mode

superposition analyses (transient, harmonic, spectrum or random

vibration)


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Mode expansion:

You need to expand mode shapes if you want to do any of the

following:

Review mode shapes during postprocessing.

Have element stresses calculated.

Do a subsequent spectrum analysis.


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Mode expansion (continued):

Recommendat ion: Always expand as many modes as the number

extracted. The cost of this is minimal.


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Other analysis options:

Lumped mass matrix

Mainly used for slender beams and thin shells, or for wave

propagation problems.

Automatically chosen for PowerDynamics method.

Pre-stress effects

For Pre-stressed modal analysis (discussed later).

Full damping

Used only if Damped mode extraction method is chosen.

Damping ratio, alpha damping, and beta damping are allowed.

BEAM4 and PIPE16 also allow gyroscopic damping.

QR damping

All types of damping are allowed.


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Apply BCs and Solve

Build the model



Displacement con straints: Discussed next.

External loads:Ignored since free vibrations are assumed.

However, ANSYS creates a load vector which you can use in a

subsequent mode superposition analysis.

Solve:Discussed next.


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Apply BCs and Solve

Displacement constraints:

Apply as necessary, to simulate actual fixity.

Rigid body modes will be calculated in directions not constrained.

Non-zero displacements are not allowed.


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... Apply BCs and Solve

Displacement constraints (continued):

Be careful with symmetry

Symmetry BCs will only produce

symmetrically shaped modes, so some

modes can be missed.

Full ModelSymmetry BC Anti-Symmetry BC


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Apply BCs and Solve

Displacement constraints (continued):

For the plate-with-hole model, the lowest non-zero mode for the full and

the quarter-symmetry case is shown below. The 53-Hz mode was missed

by the anti-symmetry case because ROTX is non-zero along the

symmetry boundaries.


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Apply BCs and Solve

Solve:

Typically one load step.

Multiple load steps can be used to study the

effect of different displacement constraints

(symmetry BC in one load step and anti-symmetry

BC in another, for example).


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Review Resu lts

Build the model



Review results using POST1, the general postprocessor

List natural frequencies

View mode shapes

Review participation factors

Review modal stresses


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Review Results

Listing natural frequencies:

Choose Read Results > By Pick in the General Postproc menu.

Notice that each mode is stored in a separate substep.


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Review Results

Viewing mode shapes:

First read in results for the

desired mode using First Set, Next

Set, or By Load Step.

Then plot the deformed shape:General Postproc > Plot Results >

Deformed Shape

Notice that the graphics legend

shows mode number (SUB = ) and

the frequency (FREQ = ).


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Review Results

Viewing mode shapes (continued):

You can also animate the mode shape: Utility Menu > PlotCtrls >

Animate > Mode Shape...


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Review Results

Participation Factors:

Calculated for each mode in global translation and rotation

directions

High value in a direction indicates that the mode will be excited by

forces in that direction

Values are relative based on a unit displacement spectrum

Participation factor values can be retrieved into a parameter using

*GET command

Also printed out (to the output file) is the effective mass. Ideally

the sum of the effective masses in each direction should equal

total mass of structure


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Review Results

Modal stresses:

Available if element stress calculation is activated when choosing analysisoptions.

Stress values have no real meaning, however these can be used tohighlight hot spots

If mode shapes are normalized to unity, you can compare stresses atdifferent points for a given mode shape


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Review Results

Mode shapesnormalized to

unity


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Modal Analys is

Procedure

Build the model



Review results


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D. Workshop - Modal Analysis

This workshop consists of two problems:

1. Modal analysis of a plate with a hole

A step-by-step description of how to do the analysis.

You may choose to run this problem yourself, or your instructor may

show it as a demonstration.

Follow the instructions in yourDynamics Worksho psupplement

(Modal A nalys is Wo rks hop - Plate with a Hole, Page W-17).

2. Modal analysis of a model airplane win g

This is left as an exercise to you.

Follow the instructions in yourDynamics Worksho psupplement

(Modal An alys is Works hop - Model Airp lane Wing, Page W-23).
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Dynamics 70 M2 Modal

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