Vibration frequency of a square diaphragm

SQDFRQ,wdh,thc,den,ymod,pois,sel
Vibration frequency of a square diaphragm

wdh      side length of the diaphragm in µm
thc       thickness of the diaphragm in µm
den       density of the material in kg/m³
ymod    Young's modulus of the material of the diaphragm in GPa
pois       Poisson's ratio
sel        number denoting the selected result.
              Use 2 for vibration frequency

Notes

Diaphragms or membranes as it is sometimes called, form the basic structural element of MEMS pressure sensors. They are easy to fabricate, offer good dynamic response and can be used over a wide range of pressures.

This design interface can be used to determine the natural vibration frequency of a square diaphragm. The vibration frequency for the lowest vibration mode can be estimated.

The plot shows the two lowest modal frequencies for the given diaphragm. Those are the frequencies at which there is a sharp rise in amplitude. Using the cross hair tool, those frequencies can be read out from the graph.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa and Poisson's ratio of 0.3.
-The diaphragm has uniform thickness.
-The diaphragm is assumed to be held rigidly at the outer edges. In reality it may be slightly flexible.
-The property of the material remain constant across the diaphragm.
-The diaphragm is not subjected to any pre-stress, and damping is not considered.