ANSYS Modal Analysis

Training Manual

Module 2

Modal Analysis

Module 2

Modal Analysis

Training Manual

July 22, 2004Inventory July 22, 2004Inventory

Module 2

Modal Analysis

Training Manual


Modal Analysis

A. Definition & Purpose –

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Training Manual

Natural frequencies Mode shapes Mode participation factors (how much a given mode participates in a given direction)


Modal Analysis

… Definition & Purpose

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Recommendation: Because a structure’s vibration characteristics determine how it responds to any type of dynamic load, always perform a modal analysis first before trying any other dynamic analysis.

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Modal Analysis

B. Terminology & Concepts •

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Training Manual

[ M]{ u} + [ C]{ u } + [ K ]{ u} = { F( t ) }

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[ M]{u } + [ K ]{ u} = {0} u = U sin(ωt )

([ K ]

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−ω

[ M ] ){ u} = { 0}


Modal Analysis

… Terminology & Concepts

Training Manual


Modal Analysis

… Terminology & Concepts (cont.)

Training Manual


Modal Analysis - Terminology & Concepts

Mode Extraction Methods –

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Block Lanczos (default) Subspace PowerDynamics Reduced Unsymmetric Damped (full) QR Damped



… Mode Extraction Methods - Block Lanczos –

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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



… Mode Extraction Methods - Subspace

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Requires relatively less memory but large diskspace May have convergence problems when rigid body modes are present. Not recommended when constraint equations are present. Generally superseded by Block Lanczos



… Mode Extraction Methods - PowerDynamics

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Requires large amount of memory. May not converge with poorly shaped elements or an illconditioned 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

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Memory and disk requirements are low. In general fastest eigen solver Employs matrix reduction, a technique to reduce the size of [K] and [M] by selecting a subset of DOF called master DOF. 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

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Efficient alternatives such as Block Lanczos

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reduced cost of hardware



… Mode Extraction Methods - Unsymmetric

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Calculates complex eigenvalues and eigenvectors: •

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Real part is the natural frequency. Imaginary part indicates stability - negative means stable, positive means unstable.



… Mode Extraction Methods - Damped

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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: •

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Imaginary part is the natural frequency. Real part indicates stability - negative means stable, positive means unstable.



… Mode Extraction Methods - Q-R damped –

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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 Supports the use of a material dependent damping ratio [MP,DMPR] in a subsequent mode superposition harmonic analysis



… Mode Extraction Methods - Q-R damped

Training Manual

MODOPT,QRDAMP,NMODE

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… Mode Extraction Methods - Q-R damped

Training Manual

Comparison Demonstrating the Superior Solution Performance of the QR Damped Mode Extraction Method FEA Model Characteristics: 111,129 active dofs 10 dampe d modes Alpha, Beta and Element damping 160000 140000 120000 100000

CPU (sec)

80000

ELAPSE (sec)

60000 40000 20000 0 QRDAMP

DAMP



Summary for symmetric, undamped solvers Extraction method

Linear Solver Used

Block Lanczos

Sparse Matrix

Subspace

Frontal Solver

Powerdynamics

PCG solver

Reduced

Frontal Solver

Training Manual

Remarks

Recommended for most applications; Most stable; Stable but slow; Requires large disk space; Has difficulty with constraint equations / rigid body modes 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 In general fastest; Accuracy depends on Master DOF selection; Limitations similar to Subspace; Not recommended due to expertise required in selecting Master DOF.


Modal Analysis

C. Procedure

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Modal Analysis Procedure

Build the Model

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Choose Analysis Type & Options ü

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Build the model

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*Discussed next

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… Choose Analysis Type & Options

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Mode extraction options

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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). Specification of a frequency range requires additional factorizations and it is typically faster to simply request a number of modes which will overlap the desired range. Normalization: Discussed next.

defaults to 1e8 July 22, 2004Inventory July 22, 2004Inventory



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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)



… Choose Analysis Type & Options –

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Have element stresses calculated. Do a subsequent spectrum or mode superposition analysis.




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Mainly used for slender beams and thin shells, or for wave propagation problems. Automatically chosen for PowerDynamics method.

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For Pre-stressed modal analysis (discussed later).

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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.

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All types of damping are allowed.

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Apply BC’s and Solve ü

Build the model

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Choose analysis type and options

Training Manual



… Apply BC’s and Solve

Training Manual



... Apply BC’s and Solve

Full Model

Training Manual

Symmetry BC

Anti-Symmetry BC



… Apply BC’s and Solve 

Training Manual

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.



… Apply BC’s and Solve

Training Manual



Review Results ü

Build the model

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Choose analysis type and options

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Apply boundary conditions and solve

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… Review Results

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… Review Results

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… Review Results

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… Review Results

Training Manual



… Review Results

Training Manual

Modal stresses:

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Available if element stress calculation is activated when choosing analysis options. Stress values have no real meaning, however these can be used to highlight hot spots If mode shapes are normalized to unity, you can compare stresses at different points for a given mode shape



… Review Results

Training Manual

Mode shapes normalized to unity


Modal Analysis

Procedure

Training Manual


ANSYS Modal Analysis

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