有限元模态分析--ANSYS

July 22, 2004 Inventory #002110 2-5
Modal Analysis
… Terminology & Concepts
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Training Manual
DYNAMICS 8.1
The square roots of the eigenvalues are i , the structure’s natural circular frequencies (radians/sec). Natural frequencies fi are then calculated as fi = i /2p cycles/sec. It is the natural frequencies fi that are input by the user and output by ANSYS.
July 22, 2004 Inventory #002110 2-7
Modal Analysis - Terminology & Concepts
Mode Extraction Methods
• Several mode extraction methods are available in ANSYS:
• Assume free vibrations and ignore damping:
M Ku 0 u
• Assume harmonic motion ( i.e.
u U sin( t ) )
K Mu 0
2
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The roots of this equation are i2, the eigenvalues, where i ranges from 1 to number of DOF. Corresponding vectors are {u}i, the eigenvectors.
Module 2
Modal Analysis
Module 2ຫໍສະໝຸດ Modal Analysis
A. Define modal analysis and its purpose.
Training Manual
DYNAMICS 8.1
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.
Modal Analysis
… Terminology & Concepts (cont.)
•
Training Manual
DYNAMICS 8.1
Mode Extraction is the term used to describe the calculation of eigenvalues and eigenvectors.
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Mode Expansion has a dual meaning. For the reduced method, mode expansion means 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.
Training Manual
DYNAMICS 8.1
– Natural frequencies – Mode shapes – Mode participation factors (how much a given mode participates in a given direction)
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July 22, 2004 Inventory #002110 2-9
Modal Analysis - Terminology & Concepts
… Mode Extraction Methods - Subspace
• When extracting a small number of modes (<40) in similar size models, the subspace method can be more suitable.
– 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 • Efficient alternatives such as Block Lanczos • reduced cost of hardware
Training Manual
DYNAMICS 8.1
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.
July 22, 2004 Inventory #002110 2-10
Modal Analysis - Terminology & Concepts
… 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:
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Helps in calculating solution controls (time steps, etc.) for other dynamic analyses.
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.
– – – –
Training Manual
DYNAMICS 8.1
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
Training Manual
DYNAMICS 8.1
– 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
July 22, 2004 Inventory #002110 2-4
Modal Analysis
B. Terminology & Concepts
• General equation of motion:
Training Manual
DYNAMICS 8.1
M Cu Ku Ft u
– – – – – – – Block Lanczos (default) Subspace PowerDynamics Reduced Unsymmetric Damped (full) QR Damped
Training Manual
DYNAMICS 8.1
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Which method you choose depends primarily on the model size (relative to your computer resources) and the particular application.
July 22, 2004 Inventory #002110 2-8
Modal Analysis - Terminology & Concepts