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Eigenvalue for Multispan Beam's Natural Frequency Calc

Eigenvalue for Multispan Beam's Natural Frequency Calc

Eigenvalue for Multispan Beam's Natural Frequency Calc

(OP)
I am trying to calculate the natural frequency of a fuel line for a FBO/windmill condition. In the guideline document supplied by the prime, it references Blevin's Pin-Pin Multispan & pin-clamp. (Table 8-3 d & e) with the formula.

In the formula, it is asking for the eigenvalue... is there a way to hand-calculate this for a multispan tube? I am sure i can run a SOL103 beam model and pick it up, but i'd like to do it by hand... if possible.

References I have access to:
Bruhn, Flabel, Hartog (vibe), Niu(stress), Roarks, Shanley, Peery, Petersons, Timoshenko (vibe)

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