Hi,
I am trying to model Lamb waves propagation in an Aluminum plate using Abaqus. If I choose the frequency of 5-cycle Hanning excitation source is 0.2 MHz (to make sure that only 2 modes S0 and A0 appear in the result), the result showing good (see Fig.1) and the amplitudes of displacements does not decrease along measuring points (which have been proven by analytical approach). When I increase the frequency to 1.5 MHz (still have only 2 modes A0 and S0 depend on the dispersion curves in Fig.2) the results become disorder and instability, and the amplitude decrease along these measuring points.
Mesh size has been chosen to satisfy CFL conditions (= 1/15 x wavelength) and the time incrementation has been chosen to ensure that the fastest wave mode can propagate through element size (= element size / longitudinal wave speed).
So why the results become inaccurate?
Thank you for reading this post.
I don't know much about the formulation of your model.
Assuming you are solving the 2D wave equation using an explicit central finite difference method, you have to fulfil the following stability criterion:
\delta s
Hi Ductho,
I believe that you have already tried an even finer mesh and the results are the same (convergence study). Maybe you should change the element type increasing the order of the shape functions (e.g. 2nd order elements if you use 1st order elements) because of the high frequency and wavenumber.
Hi Ductho Le ,
I am not sure but maybe classic finite elements are not capable of solving this particular problem. Maybe you need higher order elements like spectral finite elements or an extremely fine and dense mesh.
Ductho Le Thank you for your feedback. I am wondering if a numerical error due to the finite precision of the digital number cannot be the root cause of observed problems. Have you tried a nondimensionalization of your problem?
Its not a finite element error. Its a finite element limitation. You are trying to simulate propagation of high frequency and disparsive wave A0. Are you sure the dispersion curves are correct? Whats the thickness of your plate/beam? Is there a case that there are normalized to thickness hence there are more complex and dispersive modes. In any case you need better elements. And by better I mean high order elements such us time domain spectral elements. Unfortunatelly, Abaqus boesnt support high order elements for explicit analysis, therefore you should use a Uel. My suggestion would be to increase even more the mesh. To overcome the high dispersion nature of A0
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