Page 2 - Mechanical design of microresonators _ modeling and applications

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Source: Mechanical Design of Microresonators

Chapter
1

Design at Resonance of

Mechanical Microsystems

1.1 Introduction
This chapter is an introduction to the main aspects encountered in
modeling and designing mechanical microresonators.
Aside from the technological reasons for realizing systems that int-
egrate the mechanical structure and the associated silicon/semiconduc-
tor electronic circuitry, the drive toward smaller-scale, nano-domain
mechanical resonators is motivated by the need for pushing the limits
to the resonant frequencies in the gigahertz domain. It is known that
the stiffness of a mechanical resonator varies with the inverse of the
length (because the basic definition of stiffness is force divided by
length):

1
k 싀 (1.1)
l
and that the resonant frequency is proportional to the square root of
the stiffness:

Ȧ 싀 k (1.2)
r
As a consequence, increasing the resonant frequency of a mechanical
device implies miniaturization, and therefore very high frequencies
are achieved by very small resonator dimensions. In addition, as this
chapter discusses, higher resonant frequencies (which are achieved

1
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