Chapter 5 Vibration Analysis
Chapter 5 Vibration Analysis
Chapter 5 Vibration Analysis
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<strong>Vibration</strong> <strong>Analysis</strong><br />
C. Free <strong>Vibration</strong> with Pre-Stress<br />
ANSYS, Inc. Proprietary<br />
© 2009 ANSYS, Inc. All rights reserved.<br />
5-12<br />
Training Manual<br />
• In some cases, one may want to consider prestress effects when<br />
performing a free vibration analysis.<br />
– The stress state of a structure under constant (static) loads may affect<br />
its natural frequencies such as a guitar string being tuned.<br />
[ K]{ x } = { F}<br />
o<br />
A linear static<br />
analysis is performed<br />
( [ ] 2<br />
K S −ω<br />
[ ] ){ φ } = 0<br />
+ i M i<br />
The original free vibration equation is<br />
modified to include the [S] term<br />
[ σ ] [ S]<br />
o →<br />
A stress stiffness matrix<br />
is calculated from the<br />
structural analysis<br />
May 5, 2009<br />
Inventory #002593
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