Learning Forum

[JAY]

A cantilever beam is kept in refrigerator and other is kept in normal atmosphere. How the natural frequency will vary in both cases?
Will the temperature affect frequency or not? Whose natural frequency will be more?

[peteroznewman]

Natural Frequency depends on mass, material stiffness (Young's modulus) and geometry.

How does the Young's modulus change as a function of temperature? Most materials get softer as the temperature rises and stiffer as the temperature drops. So a colder material would be stiffer and therefore have a higher natural frequency.  Depending on the material, this effect could be easily measured.

How does geometry change as a function of temperature?  Materials have a coefficient of thermal expansion, so a colder cantilever will be shorter and a shorter cantilever will have a higher natural frequency.  While the length may get slightly shorter in the fridge, the thickness is also getting very slightly thinner, and a thinner cantilever would have a lower natural frequency.  But since the length is much, much longer than the thickness, I think the net effect of the shrinking geometry will be to raise the natural frequency.  However I expect the magnitude of these changes to frequency will be too small to measure.

We could rule out a mass change unless the material can absorb moisture and the high humidity of the normal atmosphere and the low humidity of the refrigerator causes the cantilever in the fridge to lose some mass due to the dry air pulling moisture out of the cantilever material. Less mass due to moisture loss in the fridge would be a higher natural frequency, but this will be a ridiculously small effect; just ignore it.

[JAY]

Thanks