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Stiffness introduces a restoring force proportional to the fourth spatial
derivative:
where
-
(moment constant)
- string radius
- Young's modulus (stress/strain)
(spring constant for solids)
- Stiffness is a linear phenomenon
- Imagine a ``bundle'' or ``cable'' of ideal string fibers
- Stiffness is due to the longitudinal springiness
Limiting cases
- Reverts to ideal flexible string at very low frequencies
(
)
- Becomes ideal bar at very high frequencies
(
)
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