Free vibration frequency of a double-clamped beam

CLMPFREQ,len,wid,thc,den,ymod,sel
Free vibration frequency of a double-clamped beam

len      length of the beam in µm
wid       width of the beam in µm
thc         thickness of beam in µm
den       density of the material of the beam in kg/m³
ymod    Young's modulus in GPa
sel        number denoting the selected result.
              Use 2 for first modal frequency

Notes

This design interface can be used to determine the fundamental frequency of vibration of a double-clamped beam. The two ends of the beam are rigidly fixed. For this analytical solution, width of the beam has only minimal influence on the fundamental frequency of vibration.

The plot shows the amplitude frequency relationship for the given beam. It shows the first resonance frequency as a sharp rise in amplitude. Using the cross hair tool, the resonant frequency and the corresponding relative amplitude can be obtained.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa and Poisson's ratio of 0.3.
-The beam has uniform cross section.
-The weight of the beam is uniformly distributed.
-The property of the material remain constant across the beam length.
-Damping is not considered.