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It is easy to imagine how tension changes the natural frequency of a wire. Intuitively it happens with a guitar string when you bend the neck.

However, does putting a beam under stress (internal or external) change its natural frequency?

Imagine a beam of modulus E and moment of inertia I with length l. It has a natural, unconstrained (Free-free) frequency of f.

Now imagine the same material, but when it was cast it had internal stresses, putting the material under a state of internal stress. If the stress is far below the yield point (stress-strain is still linear), isn't the frequency still f? If one were to relieve the stress through annealing, the shape would change, but would the frequency?

Imagine now a beam bolted to a table with a fulcrum in the middle of the beam. One can imagine constraining the beam on both ends such that the beam is bent. When it is bent, is the frequency no matter how much it is bent (as long as it does not reach the point where stress-strain is non-linear)?

Bonus question: Can I simulate this in Nastran? It seems not because the linear normal modes solver does not allow for loads, only constraints.

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