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I'm trying to make a simulation for Chladni plates

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the diagram above shows the patterns on rectangular plates, and relates them to 2 values (n, m) many of the explanations suggest that (n) is the number of lines parallel to the diagonals, and (m) is the number of perpendicular lines, which does not seem to be true in many cases, like the third pattern of the third line, no lines parallel to the diagonals although (n = 2) I can't relate those explanations to this Diagram, my question is what are (n) and (m) exactly? do they represent any property of the patterns?

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/90021/2451 , physics.stackexchange.com/q/78351/2451 and links therein. $\endgroup$
    – Qmechanic
    Feb 2 '17 at 19:09
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    $\begingroup$ Yes, this is a duplicate of Theory behind patterns formed on Chladni plates?. The answer in this thread contains a complete discussion of those lines, which are the nodal lines of the eigenfunctions of the corresponding differential equation $\endgroup$
    – Pirx
    Feb 2 '17 at 21:26
  • $\begingroup$ well thank you! but let's take a look at the first pattern of the first line of the diagram, why is n = 2 and m = 0 ? is it correct that n is the number of lines parallel to one of the diagonals, and m is the number of perpendicular lines ? if it's so, take a look at the second pattern of the second line, how is n = 2??, I can see 3 diagonal lines!!, and no perpendicular ones, although m = 1 thank you for the articles but I've already made a mathematical describe of the patterns. what I really need is a correct definition of m and n values and relating that definition to that diagram $\endgroup$
    – Ali HS
    Feb 4 '17 at 16:35
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The lines in the pictures show the nodes of the various modes, that is, the location of the points that do not move, while the rest of the points move up and down at the frequency $f_{nm}$ of the related mode. In a rectangular plate, those frequencies take the form $\alpha\left(\frac{n^2}{a^2} + \frac{m^2}{b^2}\right)$ see this article, hence the labels.

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  • $\begingroup$ yeah I do know that, but let's take a look at the first pattern of the first line of the diagram, why is n = 2 and m = 0 ? is it correct that n is the number of lines parallel to one of the diagonals, and m is the number of perpendicular lines ? if it's so, take a look at the second pattern of the second line, how is n = 2??, I can see 3 diagonal lines!!, and no perpendicular ones, although m = 1 thank you for the articles but I've already made a mathematical describe of the patterns. what I really need is a correct definition of m and n values and relating that definition to that diagram $\endgroup$
    – Ali HS
    Feb 4 '17 at 12:47
  • $\begingroup$ @Ali HS Sorry, I don't know what you know, only what is written in your question. Your rule of thumb gives the general picture, but for something more precise one needs to know the exact boundary conditions (or any other condition such as being fixed in the center). The nodal lines can be parallel to the edges (plate with simply supported edges), but also oblique (free edges), etc. $\endgroup$
    – user130529
    Feb 4 '17 at 14:23
  • $\begingroup$ it's okay thank you so much, in fact I'm working on the simulation of both cases, where the boundaries are fixed and not fixed, and the center is the driving point. $\endgroup$
    – Ali HS
    Feb 4 '17 at 16:33

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