FRSHIFT,len,wid,thc,frc,den,ymod,sel
Resonant frequency of a clamped beam with axial force

len         length of the beam in µm
wid        width of the beam in µm
thc         thickness of beam in µm
frc         axial force in µN
den       density of the material of the beam in kg/m3
ymod    Young's modulus in GPa
sel         number denoting the selected result.
              Use 1 for first modal frequency, 2 for resonant frequency with axial force and 3 for frequency shift

Notes

When a beam is subjected to an axial load, the resonant frequency of the beam will undergo a shift in frequency. This is utilized in resonant sensors to detect the axial force for instance, which in turn will be related to the measurand.

Using this design interface, the fundamental frequency, resonant frequency with axial load and the resulting frequency shift can be estimated. The solution is done by assuming an approximate mode shape function. The error involved in this solution is very small if the axial load is small or the frequency shift is 15% or less.

The plot shows the frequency shift for the given beam due to the axial load. The frequency shift is equal to the difference in frequency of the two amplitude peaks. It can be observed that when the axial force is increased, the separation between the amplitude peaks increases.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa.
-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.
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Mechanics > Vibration > Free vibration > Clamped beam > With axial force


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