I am trying to find a closed form solution for the natural frequency of cantilever Timoshenko beam. In mechanical vibration (Rao, 5th edition) he outlined the details to include the Effects of Rotary Inertia and Shear Deformation (thick beam theory) and applied that for the simply supported case only.

I searched some online resources like this but I didn't find what I am looking for. There are some questions here and there, but didn't answer by question. Is there any reference to find the closed from solution for natural frequency of a cantilevered Timoshenko beam?

Rao's solution for simply supported Timoshenko beam

  • $\begingroup$ Why not check Timoshenko's own publications? $\endgroup$
    – Solar Mike
    Mar 12 at 6:47
  • $\begingroup$ I searched a lot actually, I need someone to help me or suggest specific reference. $\endgroup$
    – AlFagera
    Mar 12 at 9:22


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