How to Calculate the Natural Vibration Frequency of a Steel Tube

The natural vibration frequency of a steel member is controlled by these factors:

Stiffness/the second moment of inertia (I) in 4 stiffer = higher freq
Mass per length (lbmass/in) heavier = lower freq
Length of beam (L, in) longer = lower freq
Young’s modulus, elastic strength (lbf/in2) stronger = higher freq
Method that beam is supported simply supported is fairly “loose” and therefore lower freq

Notice that length is by far the most influential in this equation:  Length (L) is squared (exponent = 2), while all other variables are square rooted (exponent = 1/2).  Since 2 is 4 times 1/2, the Length is 4 times more influential than any other of the above factors. As an experiment, we simply supported a 10x10x0.375 steel tube 90ft long (1080 inches).  Count the cycles in the video–about 11 cycles in 10 seconds or 1.1 cycle/sec.  Almost exactly as predicted!

Vibration Frequency Calculation
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