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Zhigang Suo's picture

A file on elastic waves is attached.

Return to the outline of the course

PDF icon Waves 2013 11 05.pdf4.27 MB


Teng zhang's picture

Dear Prof. Suo

Prof. Zhong wanxie and Dr. Gao qiang have developed a systematic method for wave in laminates in the framwork of Hamilton system. I have ever posted a blog to introduce that theory and here is the link

Here I summary the advantage and the disadvantage of that method as follows:


1. precise and avoid the missing root for the surface wave frequency equation

2. the same simple formula and uniform steps for anisotropic layered media and the isotropic


1. only for the linear elastic now, most time the traditional methods are efficient enough in these areas

2. people are not very used to these, so they maybe not want to change their familiar method to these new ones

I also add a paper in the above link to illustrate this idea. Since we do not have a solid background of the application and modeling of the wave in laminates, we could not go further in one certain area. Gao qiang is applying this method to waves in piezoelectric crystals now. I want to hear some suggestions from you that are there some areas that are suitable for frying this new methods?

I am not sure whether I make myself clearly. Thanks a lot in advance!

Zhang teng

Zhigang Suo's picture

Dear Teng:  Thank you very much for letting me know your progress.  I know little about the applications of elastic waves, and would like to learn when I have an opportunity. 

Teng zhang's picture

Dear Prof. Suo

Thanks a lot for your reply.

Most work of the Dr. Gao's PH.D thesis is focused on the earthquake wave propagation. The random and viscoelastic effects are also involved in his thesis. Could you give some examples of the current applications of waves in which you are interested now? We could try to extend the present numerical methods to these areas.

I will appreciate your kind help

Best regards

Zhang teng

Zhigang Suo's picture

I have never really worked on waves, but have always found the phenomena of waves fascinating.  I have had a lot of fun preparing these notes on waves for the course, which I have just updated this year.  I'll learn more when I teach the subject next time, probably two years from now.

Some time ago I coauthored papers on dynamic cracks:

I wish that I knew something about device applications, such as those described in Surface Acoustic Wave Devices for Mobile and Wireless Communications by Colin K. Campbell.

Like you, I wish to hear from experts of waves on recent applications.

Teng zhang's picture

Dear prof. suo

Thank you very much for your information.

Fracture mechanics is always the challenging and exciting area, I will try to understand the papers you posted. I also try to find the book you suggested to find the applications of waves.

By the way, we have tried to do some work about phononic / photonic crystals. Journal Club December 2007 : Elastodynamic band gaps and metamaterials, posted by Biswajit Banerjee , is just the related issues, whose link is .

We are interested in the defect state of phononic/photonic crystals, but unfortunately, we failed to obtain the right Wannier function which is one methods to solve the defect problem in periodical phononic/photonic crystals. What's worse, we do not have a solid background about this area and the above numerical methods combining PIM and extend W-W algorithm have no advantage to this problem with large freedoms , so we give up finally.

Best regards

Zhang teng

Zhigang Suo's picture

Dear Teng:  Similar to the analysis of waves is that of deformation localization.  The subject is classic.  I try to teach it in my graduate class; see notes on finite deformation.  The technique is used actively in research by many people.  Here is a paper from my group:

T. Li, Z.Y. Huang, Z.C. Xi, S.P. Lacour, S. Wagner, Z. Suo. "

Delocalizing strain in a thin metal film on a polymer substrate
Mechanics of Materials.


Teng zhang's picture

Dear Prof. Suo,

Thank you for your help. I have learned a lot from your notes and imechanica. Your paper and recent work also show me the linking between theoritical and computational mechanics. I have had a misunderstanding that theory is more fundamental so that it is superior to computation. Now I realize that each of them has different concerned issues and different views of research which we can not simply compare with each other and their combination is more and more important as the problem we face become more and more complex.

Thank you again!

Best regards

Zhang teng 

Ji Wang's picture

It is great that Zhigang has been undertaking a challeging task to summerize the fundamentals of wave propgation to students in solid mechanics context.  There are many upper level textbooks on waves, but to give in such a concise and easy-to-understand way is worth to try.  Particularly because such knowledge are scattered around in Physics, Acoustics, and even Mathematics, we need to make them available to students in Mechanics for simple reasons: we are responsible to explain some complicated wave propagation phenonmena in many ways.  As professional scientists, many challenges like storms, earthquakes, and EM waves, need to be studied.  Or, as a learned person, some essential concepts should be familar to understand daily news at least.

Wave propagation has another important applications: acoustic wave sensors.  Research work on this subject is centered in electrical engineering, but there are strong presence of Mechanicians also.  Challenges are in the selection of materials and geometry of piezoelectric solid for the enhancement of interactions between sensing element and samples in the form of frequency change.  This kind research has been poineered by famous Mechanicians like Mindlin and a few others.

Important references are




JS Yang

Conferences on this subject is organized by the IEEE UFFC Society.  You can check out the latest information at

Hope to see more involvment from the Mechanicians in the iMechanica.

 One thing that would be interesting is to look into wave propagation in porous media. A lot of work in this area comes from geophysics folks, but there are things like nanoporous gold, titanium foams, thermal barrier coatings etc where numerical methods could be useful in evaluating experimental data). 

 Sridhar Krishnaswamy

Northwestern University

Henry Tan's picture

Dear Sridhar,
Can you give an introduction of the analytical work on wave propagation in porous media?
Thanks a lot.

Biot's theory would be a good starting point.  And here is a recent reference to some biomedical applications:  J Acoust Soc Am. 2008 Apr;123(4):2415-23


Northwestern University

2008eml's picture

Dear Teng Zhang,

I'm so interested to elastic wave propagation in solid medias. I have a question about. I'll be so pleased if you could answer. is it important the propagation of high frequency elastic waves in dynamic design of structures in impact's loading? for example if we have a kind of loading like hammer impact, is it important the elastic waves with frequencies about KHz or MHz? thank you for your consideration.

Hi every body,I'm a senior student in mechanics and really I need an example of wave propagation in a thin plate to conduct my project. At now,main problem for me is how to apply load to get answers with obvious wave propagtion contour plot without any thing more in just one refelection.

Thanks in advance,



shahin Eskandari's picture


What is the scattered fields? and Scattering cross section?


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