During the operation of structures based on thin-walled cylindrical shells, limit loads sometimes occur, bringing the structural material close to or into the plastic region of the stressstrain state. In these cases, the elastic modulus of the material changes. This change in the elastic modulus affects the natural vibrations of the thin-walled cylindrical shell, a factor often not considered during design. This oversight can lead to a shift in the natural frequency of the shell and potentially cause its failure due to resonance. This work presents a modal-analytical approach for estimating the natural frequencies of a thin-walled cylindrical shell within the Donnell–Mushtari– Vlasov (DMV) formulation, accounting for the material’s transition into the plastic zone via a secant modulus Esec(ε) defined by an experimental σ–ε tensile diagram. While preserving the linear structure of the equations of motion, the method introduces physical nonlinearity through spectrum scaling and amplitude-frequency dependence. Modal equations for axisymmetric and non-axisymmetric forms are derived, yielding analytical expressions for the natural frequencies in terms of modal parameters. An iterative algorithm for selecting Esec based on the equivalent strain level is proposed. The influence of vibration amplitude on the equivalent strain and the effective stiffness of the shell is demonstrated, and recommendations are provided for the applicability of this approach for rapid engineering assessments in the pre-critical regime.

Oleg E. Sysoev — Doctor of Technical Sciences, Professor; e-mail: fks@knastu.ru; ORCID: https://orcid.org/0000-0002-6193-8584.AuthorID: 446982

Alexander N. Namokonov — Postgraduate Student; e-mail: namokonovsasha@mail.ru; ORCID: 0009-0003-9269-7713.AuthorID: 1162898

Evgeny O. Sysoev — Candidate of Economic Sciences, Associate Professor,; e-mail: fks@knastu.ru; ORCID: 0000-0002-6193-8585.AuthorID: 530062