Page 5 - Mechanical design of microresonators _ modeling and applications
P. 5
0-07-145538-8_CH01_4_08/30/05
Design at Resonance of Mechanical Microsystems
4 Chapter One
paddle cantilever
anchor
translatory motion
Figure 1.4 Microcantilever as a single-degree-of-freedom system.
m
x
k
Figure 1.5 Single-degree-of-freedom mass-spring system.
The solution to Eq. (1.3) is
.
x
x(t) = 0 sin(Ȧ t) + x cos (Ȧ t) (1.4)
Ȧ r r 0 r
where the natural (or resonant) frequency is
k
Ȧ = (1.5)
r m
and the initial displacement and velocity conditions are
dx .
x(0) = x | = x (1.6)
0 dt t =0 0
Similarly, the equation of motion of a single-DOF system formed of a
mass and a dashpot (mass-damper combination with viscous damping),
such as the one in Fig. 1.6, is
.. .
mx + cx + kx =0 (1.7)
and the solution to this homogeneous equation can be expressed as
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
