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

Authors

• A. Cazzani, Università degli Studi di Cagliari
• Isaac Elishakoff, Università degli Studi di Cagliari
• V. Eremeyev, Università degli Studi di Cagliari
• M. Spagnuolo, Università degli Studi di Cagliari
• A. Ulukhanian, Università degli Studi dell'Aquila

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Applied Mathematical Modelling

Publication Status

Version of Record

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.

DOI

10.1016/j.apm.2025.116293

Publication Date

1-1-2026

Recommended Citation

Cazzani, A.; Elishakoff, Isaac; Eremeyev, V.; Spagnuolo, M.; and Ulukhanian, A., "Critical re-examination and numerical verification of Sorokin and Arkhipov's approach to free transversal vibrations of beams using plane elasticity theory" (2026). Faculty Scholarship. 143.
https://digitalcommons.fau.edu/faculty_papers/143