Beam Vibration Check

This spreadsheet calculates the natural frequency of a beam based on the deflection and compares it to a forced frequency (like what it would experience because of a heavy piece of equipment).  It tells you if the forced frequency of vibration in the given system falls within an acceptable range.  (If it does not fall within the acceptable range, the vibration is too close to the natural frequency of the system and the system will resonate.)

 Sources:

 Practical Vibration Design of Structural Framing; L. R. Burkhardt

The above was an article written by the author who was a structural engineer for Meissner Engineers, Inc. in Chicago, Illinois that was written in 1961. 

My results were verified by several other (very old) articles and one book that I only have a photocopy of the chapter on vibration which I can't verify.  The articles are: VIbration Analysis of Members used for Supporting Vibrating Screens, V.D.;  Vibrations in Flexure for Steel Beams, author unknown - from Kaiser Engineers and Constructors, Inc.;  Vibrating Machinery, author unknown but produced by Allis-Chalmers; and then the book, either the title of the book or the title of the chapter is 'Vibrations.'  This book referenced the following: "Mechanical Vibrations," by J.P. Den Hartog, McGraw-Hill Book Co., Inc., New york, 1956.  "Mechanical Engineers Handbook," by Lionel S. Marks, McGraw-Hill Book Co., INc., New York, 1958.   And "Vibration Problems in Engineering," by Stephen Timoshenko, D. Van Nostrand Co., Inc., New York, 1955.

Calculation Reference
Beam Vibration

Structural Dynamics

Beam Analysis