cantilever tube - fundamental frequency calculation

Hello all,
By training I'm an electrical engineer, but the problem in hand is a
mechanical in nature. I want to calculate fundamental frequency of a
cantilever tube. I ask this group to help me get started with this
problem: literature (web links), formulas, etc. I will ask more
questions as they will come.
Many Thanks,
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Dear Amad,
Amad wrote:
Mechanical engineers get paid for doing this.
I have some fundamental questions about designing a high voltage power supply to power an ozone production cell (extremely capacitive, high current spikes, high voltage, high frequency, yet need a near-unity power factor from 60Hz line power). How much are you willing to answer these questions for free? Plus any others I might come up with?
Google is your friend. You need to identify modes of vibration. You need stiffness of the shape, and you need to know the material properties. You will eventually need to consider whatever devices are connected to this, as they will alter the frequency by both dampening and as point masses.
A Google search phrase might start off with: mode vibration stiffness oscillation analysis
Sorry about the grouse...
David A. Smith
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My reply would be pointing some one in a correct direction instead of rebuffing him...Anyways, thank a lot for you help!
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"Amad" wrote in news:1162592561.611325.137330
I use Blevins, _Formulas for Natural Frequency and Mode Shape_ ISBN0-89464-894-2
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Charly Coughran
formatting link

Fn= Sqrt (K/Meff) / (2*Pi)
K= 3*
E*I E= elastic modulus I= moment of interis
Meff= effective mass (either 1/3 or .236 of beam mass....cannot remember)
cheers Bob
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Amad: Undamped fundamental natural frequency of a cantilever tube of circular cross section is as follows.
f = (0.13990/L^2)[(E/rho)(D^4 - d^4)/(D^2 - d^2)]^0.5,
where f = frequency (Hz), L = cantilever length (m), E = modulus of elasticity (Pa), rho = density (kg/m^3), D = tube outside diameter (m), d = tube inside diameter (m). Typical values are E = 200e9 Pa, rho = 7850 kg/m^3 for steel; or E = 69.0e9 Pa, rho = 2715 kg/m^3 for aluminum. If you instead want circular natural frequency, omega, which is in units of rad/s, corresponding to the above natural frequency, then omega = 2*pi*f.
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