Critical re-examination and numerical verification of Sorokin and Arkhipov's approach to free transversal vibrations of beams using plane elasticity theory

Cazzani, A.

;Elishakoff, I.;Eremeyev, V.;Spagnuolo, M.;Ulukhanian, A.

2026-01-01

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Abstract

The paper written by Sorokin and Arkhipov, which appeared in 1966 in a commemorative volume, and is still largely unknown to the non-Russian speaking scientific community, is here thoroughly analyzed and commented. For the convenience of potential readers, a complete, unabridged translation into English is also provided. The transverse free vibrations of a beam are analyzed in this work: the problem is formulated within the framework of plane elasticity theory, following the original approach, where the beam is considered as a two-dimensional elastic body, in plane stress conditions. The equations describing its dynamic behavior are deduced, along with the relevant boundary conditions, from the general theory by a truncated power series method. All details of the original formulation have been re-examined and verified, and a critical check of the numerical results, which are relevant to the free vibration of a simply supported beam, confirmed their correctness. New results, which extend the cases analyzed in the original paper, are presented and discussed. In particular, a promising field of investigation stems from the obtained results, which outline the need to validate such higher-order beam models both analytically and through experimental tests. Scholars interested in the dynamics of beams treated as a 2-D problem of elasticity will find a useful reference and interesting insights for their current and future work.