58
G. Chakraborty and N. Jani
ably show themselves up in the system’s response characteristics, an analysis based
only on linear term does not predict correct results. (b) Nonlinear terms can be advantageously exploited to improve system’s performance and also to design new kinds
of devices. Thus, whether good or bad, nonlinearities cannot be ignored altogether.
The effects of nonlinearities on the dynamics of resonant microdevices have been
reviewed by many authors. Notable among them are the ones by Lifshitz and Cross
[7], Rhoads et al. [8], Tiwari and Candler [9]. These reviews have emphasized on
different aspects of nonlinearity. For example, Rhoads et al. [8] have studied effects
of different types of excitation on the nonlinear dynamics of MEMS resonators,
while Tiwari and Candler [9] have studied both types of devices where nonlinearity
is undesirable and where it is to be exploited to the advantage.
The present review aims to provide a comprehensive overview of nonlinear effects
on the response of resonant MEMS devices. Along with the usual sources of nonlinearity in a resonant MEMS, discussion has been made also on different ways by
which nonlinearities are tailored to improve the system’s performance. The beneficial and undesirable effects of nonlinearity have been pointed out by means of simple
models, which are valuable tools for getting insight into the design of such systems.
The review is divided into several sections. The basic operating principal of resonant
MEMS has been explained in Sect. 2 restricting to the linear theory. The effects of
nonlinearity on differently excited resonators are discussed in Sect. 3. Only one kind
of nonlinearity, namely, duffing-type nonlinearity has been treated in this section in
order to highlight various roles that the nonlinearities can play in the dynamics of
such systems. The real nature and origin of nonlinearities that appear in resonant
MEMS devices are explained in the next section (Sect. 4). In Sect. 5, we compare the
effects of nonlinearity and discuss the desirable and undesirable effects. In the final
section (Sect. 6), various methods of modifying the nonlinearities of the device have
been outlined.
2 Working Principle of Resonant MEMS Sensor
The working principal of a resonant device can be explained with the help of a
forced single-degree-of-freedom (SDOF) oscillator, whose equation of motion can
be written as
m ¨
x + c ˙
x + kx = f (t)
(1)
where the symbols have usual significance. In a resonant microsystem, the oscillator
is driven to resonance by means of harmonic excitation f (t) = f 0 cos ωt. The steadystate response amplitude
X =
F 0
k
1 −
ω 2
ω 2
n
2 +
2ζ
ω
ω n
2
, where, ω n =
k
m
and ζ =
c
2
√
mk
(2)
G. Chakraborty and N. Jani
ably show themselves up in the system’s response characteristics, an analysis based
only on linear term does not predict correct results. (b) Nonlinear terms can be advantageously exploited to improve system’s performance and also to design new kinds
of devices. Thus, whether good or bad, nonlinearities cannot be ignored altogether.
The effects of nonlinearities on the dynamics of resonant microdevices have been
reviewed by many authors. Notable among them are the ones by Lifshitz and Cross
[7], Rhoads et al. [8], Tiwari and Candler [9]. These reviews have emphasized on
different aspects of nonlinearity. For example, Rhoads et al. [8] have studied effects
of different types of excitation on the nonlinear dynamics of MEMS resonators,
while Tiwari and Candler [9] have studied both types of devices where nonlinearity
is undesirable and where it is to be exploited to the advantage.
The present review aims to provide a comprehensive overview of nonlinear effects
on the response of resonant MEMS devices. Along with the usual sources of nonlinearity in a resonant MEMS, discussion has been made also on different ways by
which nonlinearities are tailored to improve the system’s performance. The beneficial and undesirable effects of nonlinearity have been pointed out by means of simple
models, which are valuable tools for getting insight into the design of such systems.
The review is divided into several sections. The basic operating principal of resonant
MEMS has been explained in Sect. 2 restricting to the linear theory. The effects of
nonlinearity on differently excited resonators are discussed in Sect. 3. Only one kind
of nonlinearity, namely, duffing-type nonlinearity has been treated in this section in
order to highlight various roles that the nonlinearities can play in the dynamics of
such systems. The real nature and origin of nonlinearities that appear in resonant
MEMS devices are explained in the next section (Sect. 4). In Sect. 5, we compare the
effects of nonlinearity and discuss the desirable and undesirable effects. In the final
section (Sect. 6), various methods of modifying the nonlinearities of the device have
been outlined.
2 Working Principle of Resonant MEMS Sensor
The working principal of a resonant device can be explained with the help of a
forced single-degree-of-freedom (SDOF) oscillator, whose equation of motion can
be written as
m ¨
x + c ˙
x + kx = f (t)
(1)
where the symbols have usual significance. In a resonant microsystem, the oscillator
is driven to resonance by means of harmonic excitation f (t) = f 0 cos ωt. The steadystate response amplitude
X =
F 0
k
1 −
ω 2
ω 2
n
2 +
2ζ
ω
ω n
2
, where, ω n =
k
m
and ζ =
c
2
√
mk
(2)