有限元模态分析

Training Manual
Benefits of modal analysis
• Allows the design to avoid resonant vibrations or to vibrate at a specified frequency (speakers, for example).
MuKu 0
• Assume harmonic motion ( i.e. u U sin( t) )
K 2Mu 0
• 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.
• 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.
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DYNAMICS 8.1
Modal Analysis
… Terminology & Concepts
Training Manual
• 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.
DYNAMICS 8.1
Modal Analysis
… Terminology & Concepts (cont.)
Training Manual
• Mode Extraction is the term used to describe the calculation of eigenvalues and eigenvectors.
given direction)
• Most fundamental of all the dynamic analysis types.
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DYNAMICS 8.1
Modal Analysis
… Definition & Purpose
Module 2
Modal Analysis
DYNAMICS 8.1
Module 2
Modal Analysis
Training Manual
A. Define modal analysis and its purpose.
B. Discuss associated concepts, terminology, and mode extraction methods.
• The eigenvectors {u}i represent the mode shapes - the shape assumed by the structure when vibrating at frequency fi.
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• 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.
A. Definition & Purpose
Training Manual
• What is modal analysis?
• A technique used to determine a structure’s vibration characteristics:
– Natural frequencies – Mode shapes – Mode participation factors (how much a given mode participates in a
C. Learn how to do a modal analysis in ANSYS.
D. Work on one or two modal analysis exercises.
July 22, 2004 Inv源自文库ntory #002110
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DYNAMICS 8.1
Modal Analysis
July 22, 2004 Inventory #002110
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DYNAMICS 8.1
Modal Analysis
B. Terminology & Concepts
Training Manual
• General equation of motion:
MuCuKu Ft
• Assume free vibrations and ignore damping:
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.