Aleksey Semenov, Professor at the SPbGASU Department of Information and Mathematical Modeling Technologies, investigates the nonlinear vibrations of thin-walled structural elements—beams, plates, and shells. The aim of the work is to develop a unified approach to describing their dynamic behavior, accounting for various energy loss models.
Accounting for these processes enables a more accurate assessment of the dynamic response of structures and the selection of their parameters under variable loads. However, shell systems remain less studied compared to beam and plate structures.
The research methodology combines methods from structural mechanics and computational mathematics. The study employs L. V. Kantorovich’s variational method, the Galerkin method, methods for solving stiff systems of ordinary differential equations, and software development tools.
The proposed mathematical models make it possible to perform modal analysis of thin-walled elements, determine their natural frequencies and mode shapes, and, on this basis, construct a damping matrix in accordance with the selected hypothesis.
To verify the results, the calculated examples were compared with known studies on natural frequencies. In the next stage, the oscillatory behavior under periodic loading was investigated.
Calculations showed that the inclusion of damping leads to a reduction in oscillation amplitudes and a smoothing of their nature.
The obtained results can serve as a basis for the further study of dynamic processes in thin-walled shell structures.
The research is supported by a grant for research activities to be conducted by academic staff of Saint Petersburg State University of Architecture and Civil Engineering in 2026.
