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.
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
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.