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 [Formula: see text] 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.