Vibration frequency of a clamped beam with a central mass
length of beam in µm
wid width of beam in µm
thc thickness of beam
length of the mass in µm
mwid width of the mass in µm
mthc thickness of the mass in µm
den density of the material in
ymod Young's modulus of the material in
sel number denoting the
Use 1 for normal vibration frequency, 2 for lateral vibration frequency and 3
for angular vibration frequency
An inertial mass suspended from two clamped beams is a structure often
used in MEMS accelerometers and other motion sensitive devices. A typical
structure is as shown above. It could be considered as a typical spring mass
system. Three different vibration modes are discussed here. Vibration
perpendicular to the plane of the mass, lateral vibration of the mass and a
torsional or angular vibration of the mass about the beam axis are discussed.
Use this form to estimate the vibration frequencies of normal, lateral and
angular modes. The influence of the beam and mass dimensions on these modal
frequencies could be understood.
The plot shows the amplitude frequency relationship for the given beam-mass.
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.
-The default material is Silicon with a Poisson's ratio of 0.27.
-The beam has uniform cross section.
-The weight of the beam and mass is uniformly
-There is no other load acting on the beam other than the weight
of the mass and its own weight.
-The bending of the mass is negligible
is not involved.
Mechanics > Vibration > Free vibration > Clamped beam > Central mass