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Evanescent waves at change of cross section

  1. Aug 2, 2017 #1
    Hey guys,

    if I consider a Bernoulli-Beam with a constant jump in cross- section as shown below picture1.png
    Then I get the two differential equations for the bending mentioned above.

    Let us now assume that a travelling wave from the left w_incident = C*cos(k_1*x - ωt) arrives at t = 0 at the jump of cross section. If I know claim the following transition conditions:
    Screen Shot 2017-08-03 at 00.33.39.png
    I get the following results for w_1 and w2:
    Screen Shot 2017-08-03 at 00.34.44.png

    The question is: How do the evanescent waves (exponential decaying waves) propagate? The formula says, that every point x of w_2 already has a displacement so that might be the steady state solution. But how can I get the transient behaviour? Therefore I need to know how the evanescent wave propagates. But I often read that evanescent waves do not propagate...But they cannot just be there all of a sudden, can they?

    Your help is much appreciated,
    Jens
     
  2. jcsd
  3. Aug 7, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Aug 23, 2017 #3

    tech99

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    Gold Member

    I can only look at the beam as an electrical analogy.
    How can you have a travelling wave if the end of the system is free and does not absorb the energy? With your system, all energy is trapped and will appear as standing waves.
     
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