24.10.2013 Tobias Kaufmann - COMSOL · 2013. 11. 14. · 2D solid mechanics model «simple» PDE...
Transcript of 24.10.2013 Tobias Kaufmann - COMSOL · 2013. 11. 14. · 2D solid mechanics model «simple» PDE...
Lamb Waves in Fluid-Loaded Plates 24.10.2013 Tobias Kaufmann
Frank Kassubek, Detlef Pape, Miklos Lenner ABB Corporate Research, Baden-Dättwil, Switzerland
Outline
Lamb waves
Generation and properties
Dispersion curve calculation using Comsol
Time-dependent vs. eigenfrequency approach
Equation-based modeling description for fluid
Experimentical validation and conclusions
Lamb waves – elastic waves in solid plates Generation and detection with piezo transducers
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Lamb waves:
plate displacements
parallel and normal to
plate
Lamb waves
Two families of
modes:
- symmetric
- antisymmetric
Velocity dispersion
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Lamb waves: free plate 2D Comsol time-dependent simulation
Force (sinoid pulse)
alu plate
Antisymmetric mode A0
Symmetric mode S0
Lamb waves: plate loaded with fluid 2D Comsol time-dependent simulation
water
Force (sinoid pulse)
Symmetric mode S0
alu plate
Antisymmetric mode A0
Lamb waves: plate loaded with fluid Eigenfrequency calculation, parameterized plate length L
2D solid mechanics model
«simple» PDE for fluid
description
L
Periodic boundary conditions
Fluid described as incompressible and irrotational Laplace equation (as in Landau/Lifshitz)
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Δ ϕ = 0
Equation based modeling
Fluid allowed to be compressible and rotational Helmholtz equation (as in Wu & Zhu 1992)
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Δ ϕ +𝑘2ϕ = 0
Lamb waves: plate loaded with fluid Solution: one eigenmode shown (for Laplace eq.)
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Dispersion curves for free plate and plate - water S0, A0 modes calculated with comsol, Laplace eq.
Month DD, Year
| Slide 11
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frequency
vpha
se
Experimental vericfiaction with alu plate Pulse generation & detection with piezo transducers
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0 50 100 150 200 250 300 350 400 450
0
0.05
0.1
0.15
0.2
time / us
Am
plit
ud
e / V
Excitation: 2 Sinusperiods, 540 kHz, 10Vpp
Piezo 1--> Piezo 2, Distance 0.45m, Piezos on backside, Different water sizes
Receiving: 540 kHz bandpass filter
No Clay
No Water
l= -2cm
l= 3cm
l= 8cm
l=13cm
l=23cm
l=33cm
S0 A0
Vphase – frequency plot Compressible vs. incompressible & irrotational flow
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Δ v ~ 2%
Δ v ~ 10%
Conclusions
Comsol allowed the calculation of dispersion
curves for coupled plate-liquid system
Fluid model critical for correct results
The use of Comsol helped understanding the
complex physics of the system
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