Large-amplitude nonlinear forced vibrations of a circular cylindrical panel with a complex base, clamped at the edges are investigated. The Sanders-Koiter and the Donnell nonlinear shell theories are used to calculate the strain energy; in-plane inertia is retained. A mesh-free technique based on classic approximate functions and the R-function theory is used to build the discrete model of the nonlinear vibrations. This allows for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries. The problem is solved in two steps: a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for nonlinear displacements. The system of ordinary differential equations is obtained by using the Lagrange approach on both steps. Numerical responses are obtained in the spectral neighborhood of the lowest natural frequency. The convergence of nonlinear responses is investigated.

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