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## Homework Statement

resonant freq. in air for arbitrary length steel pipe with radius in the 3-8 cm range and wall thickness in the o.5 to 1 cm range

## Homework Equations

unable to find a relevant equation

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- Thread starter john.riley2
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resonant freq. in air for arbitrary length steel pipe with radius in the 3-8 cm range and wall thickness in the o.5 to 1 cm range

unable to find a relevant equation

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AlephZero

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1 The frequencies depend on how the pipe is restrained. That is the probably single most important thing which determines the frequences.

2 There are many different modes of vibration of the pipe, each with its own (infinite) set of vibration frequencies and each governed by different equations. For example if the pipe was not restrained at all, it could vibrate by bending (like a beam), axially (changing length), torsionally, and radially (not just panting in and out, but also the cross section changing from a circle to an ellipse, or a "wavy" shape with any number of waves round the pipe).

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I should further qualify this. Pipe would be unrestrained, and length would hopefully be large compared to diameter and wall thickness. I would be primarily interested in the longitudinal pressure wave resonance, but it would be nice to calculate the predominant radial frequencies for the two strongest modes. Thanks

John

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AlephZero

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If you assume the air and pipe resonances are not coupled (that's a very reasonable assumption for a "stiff" thick walled pipe) the longtitudinal resonances are just the standard "open and closed organ pipe" formulas, and are independent of the diameter of the pipe.

Re the radial frequencies, the solutions to the wave equation are Bessel functions. If the wavenumber k = omega/c and the radius is r, the lowest frequencies are when kr = 3.832, 7.015, 10.174, ... See http://www.du.edu/~jcalvert/math/cylcoord.htm

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John

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AlephZero

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OK, now I understand the question.

Finding any formulas for thick shells will be hard. This might give you some leads for thin shells (usually defined as radius/thickness > 10, so your largest radius and smallest thickness are in that range).

"... this thesis presents exact solutions for vibration of closed and open cylindrical shells..." http://library.uws.edu.au/adt-NUWS/public/adt-NUWS20061016.103821/index.html [Broken]

I haven't read all of it (!!!) - and apologies if it tells you a lot more about the subject than you really want to know.

Finding any formulas for thick shells will be hard. This might give you some leads for thin shells (usually defined as radius/thickness > 10, so your largest radius and smallest thickness are in that range).

"... this thesis presents exact solutions for vibration of closed and open cylindrical shells..." http://library.uws.edu.au/adt-NUWS/public/adt-NUWS20061016.103821/index.html [Broken]

I haven't read all of it (!!!) - and apologies if it tells you a lot more about the subject than you really want to know.

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