有限元模态分析讲义--ANSYS

July 22, 2004 Inventory #002110
2-4
DYNAMICS 8.1
Modal Analysis
B. Terminology & Concepts
Training Manual
• General equation of motion:
M u C u K u F t
July 22, 2004 Inventory #002110
2-5
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.
• Assume free vibrations and ignore damping:
M u K u 0
• Assume harmonic motion ( i.e. uUsint())
K 2 M u 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.
• The eigenvectors {u}i represent the mode shapes - the shape assumed by the structure when vibrating at frequency fi.
July 22, 2004 Inventory #002110
2-6
given direction)
• Most fundamental of all the dynamic analysis types.
July 22, 2004 Inventory #002110
2-3
DYNAMICS 8.1
Modal Analysis
… Definition & Purpose
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.
DYNAMICS 8ຫໍສະໝຸດ 1Modal Analysis
… Terminology & Concepts (cont.)
Training Manual
• Mode Extraction is the term used to describe the calculation of eigenvalues and eigenvectors.
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
• 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.
Training Manual
Benefits of modal analysis
• Allows the design to avoid resonant vibrations or to vibrate at a specified frequency (speakers, for example).
C. Learn how to do a modal analysis in ANSYS.
D. Work on one or two modal analysis exercises.
July 22, 2004 Inventory #002110
2-2
DYNAMICS 8.1
Modal Analysis
有限元模态分析-ANSYS
精品
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.