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

© ABB Group

Lamb waves:

plate displacements

parallel and normal to

plate

Lamb waves

Two families of

modes:

- symmetric

- antisymmetric

Velocity dispersion

© ABB Group

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)

© ABB Group

Δ ϕ = 0

Equation based modeling

Fluid allowed to be compressible and rotational Helmholtz equation (as in Wu & Zhu 1992)

© ABB Group

Δ ϕ +𝑘2ϕ = 0

Lamb waves: plate loaded with fluid Solution: one eigenmode shown (for Laplace eq.)

© ABB Group

Dispersion curves for free plate and plate - water S0, A0 modes calculated with comsol, Laplace eq.

Month DD, Year

| Slide 11

© ABB Group

frequency

vpha

se

Experimental vericfiaction with alu plate Pulse generation & detection with piezo transducers

© ABB Group

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

© ABB Group

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

© ABB roup