Vibration frequency of a cantilever beam with an end
length of the
cantilever in µm
wb width of
the cantilever in µm
thickness of the cantilever in µm
lm length of
the mass in µm
wm width of the
mass in µm
of the mass in µm
den density of the material
ymod Young's modulus of the material of
the beam in GPa
denoting the selected result.
Use 2 for first harmonic frequency
A mass suspended from a cantilever is used in MEMS devices for
sensing inertial signals like in accelerometers. This design
interface can be used to estimate the first harmonic frequency of
the system. The displacement is assumed to be perpendicular to the
plane of the cantilever. For mathematical modeling, the beam-mass
system is considered as a compound cantilever in a fixed-free
configuration. The limitation in this analysis is that the mass is
usually rigid and will not be subjected to bending as experienced
by the beam.
The plot shows the amplitude frequency
relationship for the given beam-mass system. 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 Young's modulus of 180GPa
and Poisson's ratio of 0.3.
-The beam and mass has uniform cross section.
-The weight of the mass and beam are uniformly distributed.
-The property of the material remain constant across the beam-mass
-Damping is not considered.
-Axial loading and cross-axis bending are not considered.
Mechanics > Vibration > Free vibration > Cantilever >
Mass at free end