Nonlinear Dynamics of Resonant
Microelectromechanical System
(MEMS): A Review
G. Chakraborty and Nikul Jani
1 Introduction
Miniaturized sensors, known as microsensors, are often actuated such that one or
more component structures are driven to resonance. In macromechanical systems,
resonance is generally avoided for safety of equipment. However, micromachined
resonant sensors are used for high accuracy, long-term stability and quasidigital
output. They are widely used in detection of chemical and biological substances [1],
measurements of rheological properties of fluid [2], energy harvesting [3], measuring
pressure [4] and in many other diverse fields [5]. In order to increase the sensitivity of
the instrument, the dissipation is kept to a very small value. The accuracy of a welldesigned resonator is good enough to use them as gyroscopes, timing references,
frequency filters in cell phones and computers. In the field of metrology, resonators
capable of detecting mass of 1 picogram have been fabricated.
One drawback associated with the resonant devices is that during large amplitude
oscillation, when the system is excited to resonance, the effects of nonlinearities
become pronounced. First, the resonant frequency of the flexible microstructure
depends on the amplitude of excitation (amplitude-frequency effect or A-f effect).
Second, nonlinearities make the interpretation of sensor data difficult. Finally, the
noise characteristics of the device deteriorate as the participation of nonlinear term
increases. Nevertheless, paradoxical though it seems, nonlinearities can sometimes
be helpful. One example is that, the pull-in phenomenon resulted by the presence
of nonlinear terms can be advantageously used in electrostatically driven MEMS
switches [6]. Further, nonlinearities sometimes improve the noise behaviour of the
device.
The study of nonlinear dynamics of resonant microsystems has emerged as an
active field of research because of two reasons: (a) Since the nonlinear terms invariG. Chakraborty (B) · N. Jani
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur,
Kharagpur, India
e-mail: goutam@mech.iitkgp.ac.in
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_3
57
Microelectromechanical System
(MEMS): A Review
G. Chakraborty and Nikul Jani
1 Introduction
Miniaturized sensors, known as microsensors, are often actuated such that one or
more component structures are driven to resonance. In macromechanical systems,
resonance is generally avoided for safety of equipment. However, micromachined
resonant sensors are used for high accuracy, long-term stability and quasidigital
output. They are widely used in detection of chemical and biological substances [1],
measurements of rheological properties of fluid [2], energy harvesting [3], measuring
pressure [4] and in many other diverse fields [5]. In order to increase the sensitivity of
the instrument, the dissipation is kept to a very small value. The accuracy of a welldesigned resonator is good enough to use them as gyroscopes, timing references,
frequency filters in cell phones and computers. In the field of metrology, resonators
capable of detecting mass of 1 picogram have been fabricated.
One drawback associated with the resonant devices is that during large amplitude
oscillation, when the system is excited to resonance, the effects of nonlinearities
become pronounced. First, the resonant frequency of the flexible microstructure
depends on the amplitude of excitation (amplitude-frequency effect or A-f effect).
Second, nonlinearities make the interpretation of sensor data difficult. Finally, the
noise characteristics of the device deteriorate as the participation of nonlinear term
increases. Nevertheless, paradoxical though it seems, nonlinearities can sometimes
be helpful. One example is that, the pull-in phenomenon resulted by the presence
of nonlinear terms can be advantageously used in electrostatically driven MEMS
switches [6]. Further, nonlinearities sometimes improve the noise behaviour of the
device.
The study of nonlinear dynamics of resonant microsystems has emerged as an
active field of research because of two reasons: (a) Since the nonlinear terms invariG. Chakraborty (B) · N. Jani
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur,
Kharagpur, India
e-mail: goutam@mech.iitkgp.ac.in
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_3
57