Page 295 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Interacting Subsystems
dξ
dξ
V
θ
S
M M
θ B V

Figure 7.15. The deformation of a differential beam element is generated by a bending
deformation and by a shear deformation. Pure bending deformation is generated by a
bending moment across the differential element, and a pure shear deformation by a shear
force across the element.

The proportionality constants of these two squared displacement terms
reflect the resistance of the beam to deflection:

• E ξ()I ξ() is the Young modulus of the beam material times the sec-
ond moment of area (often called the area moment of inertia) of the
beam cross section about the axis of bending rotation. Hence this
term mixes geometrical shape and material composition, and tells us
that prudent choice of shape can more than compensate for a weak
material. Recall that we often cannot freely choose materials, due to
production constraints, but often can design shapes with considerably
more freedom;
• k ξ() is a correction factor that accounts for the non-uniformity of
T
the actual strain over the beam cross section [7.5].

The stored kinetic coenergy is a sum of linear and angular momentum
stores

292 Semiconductors for Micro and Nanosystem Technology