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!
