# Discussion Forum

## Thermal Expansion in Prestressed Eigenfrequency vs Eigenfrequency Study

Hello,

I am trying to model the natural frequency of a MEMS resonator affected by thermal stresses. I've been having difficulty getting accurate results, so I've stripped down the problem as much as possible and something seems to be fundamentally wrong with my methodology.

I now have a square plate with a thermal expansion node and want to evaluate the natural frequency at various temperatures. I've added a fixed point constraint in the middle of my plate to give a reference point in order to perform a prestressed eigenfrequency study as well as an eigenfrequency study (unstressed). I've made sure to place the BC at a node in the eigenmode to not distort it in either study.

The BC that I've applied should not be appying any stress onto my plate (the solution store backs this up) yet both studies give conflicting results. The eigenfrequency study shows increasing frequency with decrease temperature (which seems physical as the dimensions of my plate are shrinking) while the prestressed study shows a decrease in frequency with a decreasing temperature.

Is it possible to capture the effects of thermal expansion (purely from a dimensional perspective) in the presstressed eigenfrequency study? Am I making a wrong assumptions somewhere?

Thanks,

2 Replies Last Post Oct 3, 2022, 10:32 a.m. EDT

Posted: 2 months ago
Updated: 2 months ago

Prestressed Eigenfrequency is the correct approach. You need the static solution to get the correct deformed shape at the linearization point for the eigenfrequency analysis.

The frequency for the plate should be proportional to sqrt(1+alpha*dT), or with a very good approximation, 1+0.5*alpha*dT.

You need to take into account that when the plate shrinks, not only its dimensions are smaller, but also its density is higher. That’s why the natural frequency decreases with lower temperature.

-------------------
Henrik Sönnerlind
COMSOL