natural frequency of a hanging tube with two guided supports
natural frequency of a hanging tube with two guided supports
(OP)
a hanging aluminum 6061 tube (from a long 3/16 aircraft cable). Dimensions: 3.125" OD x .125" wall x 120" long. ~20 lb distributed. guide support at bottom and guide support at 90 inches from bottom (30 inches from top). How to calculate the natural frequency? Any help would be appreciated.
Thank you in advance.
Thank you in advance.





RE: natural frequency of a hanging tube with two guided supports
M
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Dr Michael F Platten
RE: natural frequency of a hanging tube with two guided supports
RE: natural frequency of a hanging tube with two guided supports
f=(1/2pi)*(k/M)^0.5 where k=EA/L for the cable. Second is the pendulum mode (between the guide boundaries)of the concentrated mass about the cable end pivot point f=(1/2pi)*g/L where L is cable length. Third is the beam bending modes of the rod with end and 2/3*l guided or hinged supports where l is tube length. Tables 8-3a to f in Blevins give equations and parametric data for 6 modes of up to 15 equal spans of pinned supports. Table 12-1 in Blevins gives equations for shell modes of the tube in the unrestrained condition, at best an apprtoximation to a guided tube's shell responses. The total range of "natural frequencies" for these four types of vibration probably range from very low (pendular<10 Hz) to rather high (shell modes>1000 Hz)so criticality of calculation accuracies depends on what kind of damage concerns you.
RE: natural frequency of a hanging tube with two guided supports