Published since 1923
DOI: 10.33622/0869-7019
Russian Science Citation Index (RSCI) на платформе Web of Science


  • STRUCTURAL MECHANICS
  • Mathematical Models For Accounting For The Damping Of The Timoshenko Beam In A Geometrically Nonlinear Formulation
  • UDC 624.074.43+534.1
    doi: 10.33622/0869-7019.2026.03.13-21
    Alexey A. SEMENOV, sw.semenov@gmail.com
    Nadezhda V. OSTROVSKAYA, ostrovskaya.nv@yandex.ru
    Olga P. NESTEROVA, neona975@yandex.ru
    Saint Petersburg State University of Architecture and Civil Engineering, 2-ya Krasnoarmeyskaya ul., 4, St. Petersburg 190005, Russian Federation
    Abstract. The complexity of the nature of the resistance forces has led to the emergence of various models for accounting for these forces. The authors of the article attempted to summarize the data on several known damping accounting options, reduce them to a single recording form and apply them to modify the mathematical model of Timoshenko beam deformation. Hypotheses of accounting for resistance forces are considered, such as the Voigcht resistance in the Rayleigh form, the Soroka-Sorokin hypothesis, and the Voigcht-Reznikov-Zeitlin hypothesis. The process of obtaining matrices containing damping coefficients is described. A mathematical model of Timoshenko beam deformation is presented in the form of a functional of the total deformation energy, and equations of motion are derived. The Vlasov-Kantorovich method in the form of the Galerkin method was applied to the considered model to obtain a system of equations. There is a lack of unified approaches to accounting for resistance forces. The proposed mathematical model with different damping accounting options forms the basis for further investigation of oscillatory processes in structural elements and structuring of known techniques.
    Keywords: Timoshenko beam, damping consideration, Voigcht hypothesis, Soroka-Sorokin hypothesis, Voigcht-Reznikov-Zeitlin hypothesis, oscillatory process, resistance forces
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  • For citation: Semenov A. A., Ostrovskaya N. V., Nesterova O. P. Mathematical Models for Accounting for the Damping of the Timoshenko Beam in a Geometrically Nonlinear Formulation. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2026, no. 3, pp. 13-21. (In Russ.). doi: 10.33622/0869-7019.2026.03.13-21

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