VM245
VM245
Squeeze Film Damping: Rectangular Plate
Test Case
A rectangular plate is modeled with length (b) and width (a). Pressure is made zero on all exterior nodes. Velocity loading is applied on the plate and harmonic analysis is performed at an excitation frequency of 100000 Hz.
| Material Properties | Geometric Properties | Loading | |||||||
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Analysis Assumptions and Modeling Notes
The problem is modeling the fluid gap region between two rigid, non-deforming surfaces. The pressure of the fluid entering and exiting the gap creates a damped elastic response which can be modeled by a spring-damper system. The calculations of the stiffness and damping constants are done by summing the pressure distribution over the area, then taking these force calculations and feeding them into the equations
where F(im) and F(re) are the "imaginary" and "real" parts of the force calculated from the harmonic analysis.
According to Blech an analytical solution for the damping and squeeze coefficient for a rigid plate moving with a transverse motion is given by:
where:
| C(Ω) = frequency-dependent damping coefficient |
| KS(Ω) = squeeze stiffness coefficient, |
| po = ambient pressure |
| A = surface area |
| c = ratio of plate length a divided by plate width b |
| d = film thickness |
| Ω = response frequency |
| σ = squeeze number of the system |
The squeeze number is given by:
for rectangular plates where ηeff is the effective viscosity.