[thedoc (OP)]

sharad asked the Naked Scientists:
   WHEN THE EXCITATION FREQUENCY CHANGES AT THE FIXED END OF A CANTILEVER BEAM, WILL THE NATURAL FREQUENCY OF THE CANTILEVER BEAM CHANGE?
What do you think?

[evan_au]

If you are looking for resonance in a cantilever beam, the excitation is usually applied at the "free" end, not the "fixed" end (or else the "fixed" end is not really fixed).

This can happen in the accelerometer of a smartphone or fitness tracker, where the "fixed" end is actually attached to your moving body, while the inertia of the "free" end actually moves very slightly less, due to its inertia.

If the cantilever is placed under stress, taking it outside it's "linear" range, its small-amplitude resonance frequency will change slightly. Some early chip-level MEMs devices used a DC voltage to restore the cantilever to the center of its linear range, despite changes in external acceleration.

See: http://clifton.mech.northwestern.edu/~me224/Documents_me_20224_20lab_206_mems.PDF

But I think we need some more information about the scenario being considered (preferably with a diagram...) before we can provide a good answer.

[Colin2B]

In addition to what Evan said, you need to be clear what you mean by natural frequency. This would be the frequency (or frequencies) that would occur with say a single strike or blow, this will not change, however the structure can be forced to vibrate at a different frequency by the excitation frequency. How easily this forced vibration can be made to occur - its amplitude -  will depend on the excitation frequency's relationship to the natural frequency, its amplitude, and physical characteristics of the structure e.g.stiffness and the degree of damping. Evan has pointed out that this forced excitation will be more effective at the free end of the structure.

As Evan says, needs more info.