Page 268 - Mechanical design of microresonators _ modeling and applications

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Resonant Micromechanical Systems

Resonant Micromechanical Systems 267
nanowire
F

I
B

1
Figure 5.42 Nanowire for magnetomotive detection.

F
z
m

k

Figure 5.43 Lumped-parameter model of the nanowire under the action of the Lorentz
force.

The Lorentz force which is generated through the interaction
between the external magnetic field B and the current I is

F = Il × B (5.100)
When the current is an ac input signal of the form:

I = I sin (Ȧt) (5.101)
0
and the external magnetic field is perpendicular to the wire, the sensed
magnetomotive force is

F = I lB sin (Ȧt) (5.102)
0
Example: Determine the excitation frequency that will produce maximum
vibrational amplitudes that are twice the static deflection for the case of a
fixed-fixed constant circular cross-section wire by the interaction between a
constant magnetic field B and an alternating current of amplitude I 0 and
frequency Ȧ passing through the wire.
Figure 5.43 shows the lumped-parameter model of the wire
The resonant frequency of the fixed-fixed wire is

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