# Euler-Bernoulli equation for a cantilever strained by a force

I'm trying to model an experiment where a cantilever, fixed at one end, is oscillating under an applied force at the free end. Specifically, I'm focusing a laser on a rectangular cantilever and measuring its natural frequency. As I increase the laser power, I have calculated that there should be an appreciable radiation pressure on the cantilever.

I assume that this should change the natural frequency of the cantilever, and I measure a change in the cantilever's frequency. However, every time I solve Euler-Bernoulli beam theory, it seems that the force does not influence the frequency. This seems totally non-intuitive to me: a strained cantilever should oppose additional displacement against the applied force and the cantilever should oppose additional displacement in the direction of force since it is already strained.

Is my intuition completely wrong? Am I setting up this problem improperly?

• How have you set the problem up exactly?
– JMac
Commented Sep 13, 2017 at 22:42