Cantilever oscillating under an applied 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?

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

1 Answer 1


Your intuition is wrong. The frequency of the cantilever depends on the spring constant (which doesn't change for small displacements) and the mass (which is constant).

You would not expect a cantilevered beam in the emptiness of space to have a different natural frequency than the same beam on earth, where gravity pulls on it. The constant force just gives it a constant deflection away from the "unforced" equilibrium position, but the curvature of the potential well in which the beam moves is unchanged. As long as the displacement is in the linear regime.


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