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Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds' equation cannot be
Dorel Homentcovschi1, Ronald N Miles
1Department of Mechanical Engineering, State University of New York, Binghamton, New York 13902-6000, USA. homentco@binghamton.edu
The Journal of the Acoustical Society of America
|March 25, 2010
Summary
This study presents a new model for squeeze-film behavior in microstructures, crucial for designing microelectromechanical devices. The model accurately predicts damping and spring forces, essential for device performance at various frequencies.
Area of Science:
- Fluid Dynamics
- Microscale Engineering
- Mechanical Vibrations
Background:
- Squeeze-film dampers are vital in microelectromechanical systems (MEMS).
- Traditional lubrication approximations fail in certain microscale flow regimes.
- Understanding forces in vibrating microstructures is key for device design.
Purpose of the Study:
- To develop an analytical model for squeeze-film behavior in viscous, compressible isothermal flows.
- To derive explicit formulas for damping and spring forces in microstructures.
- To validate the model against numerical and experimental data.
Main Methods:
- Application of Stokes' equations for non-lubrication flow regimes.
- Development of an axisymmetrical unit cell approximation for periodic microstructures.
- Analytical derivation of complex force components (damping and spring).
- Numerical computation of damping force using finite element software.
Main Results:
- An explicit analytical formula for damping and spring forces was derived.
- The model accurately captures the behavior of squeeze films where lubrication approximation is invalid.
- Low frequencies are dominated by damping force, while high frequencies are dominated by spring force.
Conclusions:
- The developed analytical model is validated by numerical and experimental results.
- The model provides a valuable tool for designing microelectromechanical devices.
- Accurate prediction of forces is critical for optimizing MEMS performance.
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