Page 271 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

MECHANICAL SENSORS 251

transverse load shown earlier (Figure 8.2l(b)). In this case, the deflection is not linearly
related to the applied load but a solution can be obtained from the buckling equation of
Euler where
(8.24)
dy 2 E mI m

The solution for a bridge of length / fixed at both ends is a sinusoidal one where

AJC = A sin(y/Fy/E mI my) (8.25)

where A is a constant. The beam will buckle when the load reaches a critical value of

2
= 7i E mI m/l 2 (8.26)
F c
In a similar manner, analytical equations that relate the static deflection of a microstructure
of different geometry to point and distributed loads and indeed rotations caused by an
applied moment or torque can be found.
Therefore, the important mechanical parameters and properties in the design of static
microstructures can be summarised as shown in Table 8.5.

8.4.3 Microshuttles and Dynamics

The dynamics of microstructures are also very important for several reasons. First, the
dynamic response of a cantilever beam, microbridge, or diaphragm determines the band-
width of the microsensor, that is, the time taken for the structure to respond to the applied
static load or follow a dynamic load. Second, the kinetics of the structure can be used in
inertial sensors to measure linear and angular accelerations. Finally, there is a class of
mechanical sensors based on a microstructure or a microshuttle that is forced to resonate
at some characteristic frequency.
In an inertial or resonant sensor, the cantilever beam (or bridge) is redesigned so that
the mass is more localised and the supports more convoluted. Figure 8.22 shows the
basic design of an inertial or so-called microflexural type of structure together with its
equivalent lumped-system model.

Table 8.5 Some important mechanical parameters and material properties
in defining the static deflection of microstructures

Parameters/properties Nature
Point/distributed force, torque, stress, pressure Load applied/measurand
Width, breadth, thickness, length Size of structure
Young's modulus, yield strength, buckling Material properties
strength, Poisson's ratio, density
Spring constant, strain, mass, moment of inertia Calculable parameters
Lateral/vertical deflection, angular deflection Response