where expertise comes together - since 1996 -

# The Largest Open Access Portal of Nondestructive Testing (NDT)

Conference Proceedings, Articles, News, Exhibition, Forum, Network and more

where expertise comes together
- since 1996 -

 1148 views
Technical Discussions
Protopappas Vasilis
Protopappas Vasilis
06:42 Dec-02-2003
Lamb wave dispersion equations

Hello,

Could anyone suggest a way to solve the Lamb wave dispersion equations? I want to plot the dispersion curves for a number of symmetric and antisymmetric modes, the equations, however, need a numerical evaluation.

Vasilis Protopappas

Michael Conry
Student
University College Dublin, Ireland, Joined May 2002, 3

Michael Conry

Student
University College Dublin,
Ireland,
Joined May 2002
3
07:43 Dec-02-2003
Re: Lamb wave dispersion equations
----------- Start Original Message -----------
: Hello,
: Could anyone suggest a way to solve the Lamb wave dispersion equations? I
: want to plot the dispersion curves for a number of symmetric and
: antisymmetric modes, the equations, however, need a numerical evaluation.
: Vasilis Protopappas
------------ End Original Message ------------

Plotting the curves can be tricky. The easiest way is as follows:

Divide the frequency/phase-velocity (f/c) space up into small increments.

At each point within this space calculate the value of the
characteristic equation F(f,c)

Then do a contour plot of the resulting numbers, including just a
single contour (at F(f,c)=0)

This is easy to do with Matlab, and I have also done it with Gnuplot and
Python.

This is not an efficient way to plot the curves (it requires a lot of
calculations) but even for a multilayered plate I found it took a pretty
short length of time to prepare a nice dispersion plot.

Doing the job in a more rigorous way requires either that you use curve
following algorithms to plot the curves (e.g. find the solutions for a
particular value of phase velocity, then incrementally reduce the phase
velocity and find solutions at each subsequent point). A difficulty in
this case can be correct handling of the crossovers of the curves.

Best regards,
Michael

khash
khash
00:29 Nov-25-2006
Re: Lamb wave dispersion equations
Hello
I would really be appreciate if somebody ask me why in the lamb wave dispersion curves, just A0 mode close to zero as frequency be zero?
best regards
khash
khash1979@yahoo.com

Product Spotlight

#### PAUT Probes

Typical Phased Array probes have frequencies between 1MHz and 20MHz and the number of wafers is 10
...
to 128. M2 Electronics offers customers conventionally ultrasound probes and the ability to provide high-precision Phased Array Ultrasound Probes of up to 256 wafers. We can also customize the probe for our customers to meet the specific application requirements of the user.
>

#### FAAST-PA! OEM Patented phased Array for high speed UT inspection

Multiangle, Multifocus, Multifrequency, Multibeam. Instead of stacking UT electronics and having m
...
any PA probes, FAAST-PA is able to transmit all delay laws within ONE single shot in Real time.
>

#### Robotic laser shearography enables 100% inspection of complex, flight-critical composite structures

An article in “Composites World Magazine” showcases Non Destructive Testing of aero-structures
...
with Laser Shearography. Over the years Dantec Dynamics has supplied many solutions for the aerospace industry. Referring to specific customer projects several of these cases are examined to outline the advantages of using Laser Shearography for automated defect detection.
>

#### High-performance Linear Phased Array Probes

Available to order from stock in a range of 5MHz – 7.5MHz and from 16 to 64 elements. Designed w
...
ith piezo-composite elements, Phoenix phased array probes provide high-resolution imaging to maximise sensitivity; accurate ultrasonic detection and sizing of defects in welds; and effective corrosion mapping. Housed in a rugged stainless steel case for on-site industrial NDT applications.
>

Share...
We use technical and analytics cookies to ensure that we will give you the best experience of our website - More Info
Accept
top
this is debug window