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Hello,

I am finding some problems in simulating a Magnetic Force Microscope (MFM). I have a magnetized cantilever which interacts with a non uniform magnetic field; the gradient of the magnetic field acts on the magnetized cantilever with a force, the gradient of the force affects the stiffness of the beam changing its resonance frequency.

The geometry is very simple: a permanent magnet, a magnetized cantilever and air surrounding everything. I am using the Magnetic Field No Currents interface in order to find the field gradient produced by a permanent magnet and in order to evaluate the magnetic force on the magnetized beam. The magnetic force is used as a Body Load of the cantilever in the Solid Mechanic interface. I have also applied a Load to the cantilever to simulate the harmonic forcing term. Basically, the magnetic force gradient seen by the oscillating cantilever changes its stifness; therefore, I need the Body Load (due to the magnetic force) to change with the displacement of the beam.

I have initially set up this study:

STEP 1 - STATIONARY: to evaluate the the field and the force; STEP 2 - FREQUENCY DOMAIN: to calculate the effect of the force on the frequency spectrum of the cantilever oscillations. Since I should observe a shift in the resonance frequency of the cantilever, this step does a sweep on the frequencies.

In the result I plot the RMS displacement of the beam with respect to the frequency sweep.

Clearly this approach was a failure because, as I have understood, STEP 1 evaluates the force without considering the displacement of the beam, then in STEP 2 the applied magnetic force is always the same, i.e. the cantilever does not see any gradient of the force.

My question is: how can I set up the simulation so that I have a Body Load due to the magnetic force which is updated with the displacement of the beam and, in parallel, a Body Load to implement the harmonic forcing term which drives the oscillation of the beam at different frequencies?