Page 139 - Mechanics of Microelectromechanical Systems
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126 Chapter 2
Problems
Problem 2.1
For a constant rectangular cross-section microcantilever, the tip force
that corresponds to the tip deflection and slope can be expressed as shown in
Eq. (2.21) with the stiffnesses being:
However, one can approximate the individual compliances
as being the algebraic inverses of the corresponding stiffnesses as:
Determine the maximum relative
errors between the force calculated according to the first set of stiffnesses
and the same force calculated by the second set of stiffnesses, when
and and
Answer:
Maximum relative error = 50%
Problem 2.2
Design a solid rectangular microcantilever such that its linear bending
stiffness about the bending-sensitive axis, is 16 times smaller than the
other linear bending stiffness and 100 times smaller than the axial
stiffness
Answer:
The thickness can be chosen arbitrarily.
Problem 2.3
Determine the mass that adheres to a constant rectangular
microcantilever with and E = 150 GPa
assuming the deposition produces no torsion of the microcantilever. Known
are also the tip displacements and
Answer:
Problem 2.4
A circularly-filleted microcantilever is used in a magnetic writing
application. Find the maximum values of the tip force components and
considering that is negligible. The parameters defining the
microcantilever are: E = 200 GPa, and
