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Some questions about wave propagation
Dear Sir，
As we know, periodic signals are best analysed in the frequency domain while stochastic signals are usually more profitably analysed in the time domain. The analysis in the frequency domain usually concern only one signal while in the time domain often involves the comparison of several different signals.
1) what are the general methods for transforming the frequency domain into time domain, and which should be superior?
2) The periodic signal should be decomposed by fourier series expansion. However, how to get the analytic solution for wave with ruptures (such as shock wave)? (please show me some previous journal papers or books)
If it's possible, Please kindly allow me to learn your brilliant comments.
Thanks very much
Comments
The Fourier decompositions for shock waves
Yesterday I opened my blog iMechanica and had become acquainted with your reply Some questions about wave propagation . I answer on your questions.
a) In the
any series of shock waves (two or more) all it have the different amplitudes:
the periodic shock waves not exist.
b) To be decomposed by fourier series
expansion the function must satisfy to the
Lejeune-Dirichlet conditions. The
profile of single shock wave is such function. To use
such decomposition for integration of
the differential equations with shock waves it is
impossible: the parameters of shock
waves are the distributions.
/The monography about distributions I
had shown you in my letter 04.08.09/
1)
I not "closely"
worked with the decompositions of the stochastic signals. Excuse me.
With regard L.G.Ph.
04.09.09.
The Fourier decompositions for shock waves
Dear Leonid,
in the duration of past few monthes, i still tried to learn much from the book you mentioned "Theory of distributions" by P.Antosik, J. Mikusinski and R.Sikorski and the theory of lebesgue integral in the last mail. However , these problems are still around me. what you instructed should be correct.
How about your book L.G.Philippenko, "Strong Shock Waves in the Continuous Bodies" Russian at 1992 year (Kiev, Ukraine)?
Shock wave: Got a doubt to clear
Dear Leonid and LG
I find, the brief exchange, posted in this blog useful, and wanted to clear my doubt here. Can we equate a moving load as a series of shock loads with equal amplitude (because that's how the direct time integration treats the problem, if I am correct). I am just curious. I guess, you will say 'No, because once it started moving, the initial conditions are renewed continuously (I mean the load is now in contact with the structure) and could not be considered a shock load unless either the magnitude of the load changes or loss of contact between load and structure occurs'. This is my guess but your comments could help me get a different perspective.
(Edited post: Apologize I was thinking of shock load, and I just read your other post on shock waves)
Vgn
Graduate Student
University of Oklahoma
the research of shock waves
Dear Mr. LG!
This comment is written in
connection with your note The Fourier decompositions for shock waves from 4.09.09 in
iMechanica.
--- In USSR the theory of integral Lebesgue was stated in
text-book on the Classical analysis. It may be the same was in your country?
The monography by Antosic .... (in English) was published at 1973 by
Elsevier Scientific Publishing Company in Amsterdam. Try address there. I don't know the more suitable manual for the work
with the shock waves.
--- The first issue of "Strong
Shock waves...." (1992y.) was made hastily and was contained mistakes; since that
time it was essentially corrected by author. For to publish it in Ukraine - I have not the possibility and hope.
With regard L.G.Ph.
7.09.09
P.S.
I am the weak user on PC, for to
find necessary record in iMechanica - I often make mistakes and confuse
himself. Therefore I ask you: please if it possibly write your comment as reply
in my blog (the address of which is contained in my Firefox).
L.G.Ph.
P.P.S.
For Mr. Gopinath Venkatesan : about of the idea of a
moving load as a series of shock loads with equal amplitude - see please my
address to Mr. LG from 04.09.09., n0
2a.
With
regard L.G.Ph.
some topics attract me for wave propagation
Dear Leonid and Vgn,
Thanks very much for your thoughtful comments.
At this stage, i am very interested in some topics related to wave propagations (include: optical, electromagnetic, elastic, and acoustic. For the linear conditions, which can be mathematically attributed into the solve of Helmholtz equation. However, we should realize that why we do the research fully aim to solve the practical problems relate to engineering applications ranther than publish ugly papers) :
a. negative refraction for invisible cloak
b. acoustic band gap materials
c. acoustic cavitation bubble
if it's possible, please kindly allow me to study your smart comments.
Cheers