Published on: 2026-09-29
Source: Saint Petersburg State University of Architecture and Civil Engineering –
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Professor of the Department of Information and Mathematical Modeling Technologies at SPbGASU, Alexey Semenov, studies nonlinear vibrations of thin-walled structural elements – beams, plates, and shells. The goal of the work is to develop a unified approach to describing their dynamic behavior taking into account various models of energy loss.
Accounting for these processes allows for a more accurate assessment of the dynamic response of structures and the selection of their parameters under variable loads. At the same time, shell systems remain less studied compared to beam and plate structures.
The research methodology combines methods of structural mechanics and computational mathematics. The work employs the variational method of L. V. Kantorovich, the Galerkin method, methods for solving stiff systems of ordinary differential equations, as well as software development tools.
The proposed mathematical models enable performing modal analysis of thin-walled elements, determining their natural frequencies and vibration modes, and on this basis forming the damping matrix according to the chosen hypothesis.
To verify the results, the calculation examples were compared with well-known studies on natural frequency values. In the next stage, the oscillatory process under the action of periodic loading was investigated.
Calculations showed that including damping leads to a reduction in oscillation amplitudes and a smoothing of their character.
The obtained results can serve as a basis for further study of dynamic processes in thin-walled shell structures.
The research is being conducted with the support of a grant for scientific research work by the academic staff of Saint Petersburg State University of Architecture and Civil Engineering in 2026.
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