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I looked on Ohiolink for journal articles and through Timoshenko's

*Vibration Problems in Engineering*but can't come up with anything. If anyone has an article, or a link somewhere I would appreciate it. Thansk,

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- Thread starter minger
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In summary, a set of pressure rakes has natural frequencies that may cross some of their excitation lines. It might be a good idea to plink them before using them, but it is also possible to do a numerical analysis first.

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I looked on Ohiolink for journal articles and through Timoshenko's

Engineering news on Phys.org

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Science Advisor

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- #3

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Either way it might be a good idea to plink them after we receive them, but I'd like to have an idea of their response before.

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- #5

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Yea,

OK, so this directly applies to torsional vibration, but I can assume it applies to lateral as well. If so, then how can I calculateIf the shaft consists of two parts having lengths [tex]l_1 \,\mbox{and}\, l_2[/tex] with diameters [tex]d_1\, \mbox{and}\, d_2[/tex], the separate torsional constants may be calculated from eq. (c).

[tex] k_r = \frac{GJ}{l} = \frac{\pi d^4 G}{32l} [/tex]

The equivalent spring constant can then be obtained from eq. (k)

[tex] k_{eq} = \frac{k_1 k_2}{k_1 + k_2}[/tex]

Would the individual spring constants simply be a long bar, with several hollow cylinders?

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Edit: try finding the following paper if your subscription covers it - the approach and references should give you some help.

Yu, S.D. and Cleghorn, W.L.

Free Vibration of a Spinning Stepped Timoshenko Beam

J. Appl. Mech. -- December 2000 -- Volume 67, Issue 4, 839 (3 pages)

DOI:10.1115/1.1331282

The natural frequency of a stepped shaft is the frequency at which the shaft naturally vibrates when no external forces are applied. It is determined by the material properties, geometry, and boundary conditions of the shaft.

The natural frequency of a stepped shaft can be calculated using the equation f = (1/2π) x √(k/m), where f is the natural frequency, k is the stiffness of the shaft, and m is the mass of the shaft.

The natural frequency of a stepped shaft is influenced by several factors, including the material properties of the shaft, such as density and stiffness, the geometry of the shaft, and the boundary conditions, such as the supports and applied loads.

Knowing the natural frequency of a stepped shaft is important for ensuring the structural integrity and stability of the shaft. It can also help identify potential vibration issues that could lead to failure or malfunction of the shaft.

The natural frequency of a stepped shaft can be controlled by altering the material properties, geometry, or boundary conditions of the shaft. This can be achieved through design modifications or the use of damping materials to reduce vibrations.

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