Explicit Determination of Pinned-Pinned Beams with a Finite Number of Given Buckling Loads

We present an analytical procedure for the exact, explicit construction of Euler-Bernoulli beams with given values of the first N buckling loads. The result is valid for pinned-pinned (P-P) end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm-Liouville operators with prescribed natural frequencies.