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.

07:43 Dec-02-2003 Michael Conry Student University College Dublin, Ireland, Joined May 2002 ^{3}

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.

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