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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.

Thank you in advance,

Vasilis Protopappas


    
 
 Reply 
 
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.
: Thank you in advance,
: 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



    
 
 Reply 
 
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


    
 
 Reply 
 

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