Nonlinear dynamics of heterogeneous shells. Part 2. Chaotic dynamics of variable thickness shells

In the second part of the article, the nonlinear dynamics and stability of nonhomogeneous variable thickness axisymmetric shells are analyzed. The mathematical model is based on the Kirchhoff–Love kinematic hypothesis. The resulting system of partial differential equations is reduced to an algebraic equations system by the Ritz method. The convergence of the applied numerical methods is investigated. The chaotic vibrations’ control of variable thickness shells using dynamic charts of vibration regimes is also developed. •Bifurcations and stability of shells with variable stiffness are studied.•The employed method holds for both parabolic and hyperbolic PDEs.•Ritz method in higher approximations is used.•Feigenbaum’s scenario governs route from periodic to chaotic vibrations.•Fourier spectra, Morlet wavelets and Lyapunov exponents are analyzed.