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In this paper, the results of an experimental campaign focused on the vibrations of shells are presented. More specifically, the goal is to investigate the effect of thermal gradients across the shell thickness on the nonlinear dynamics. The shell is made of polymeric material and an aluminum mass is clamped on one end of the shell; the other shell end is clamped to an electrodynamic shaker, which provides a base harmonic excitation. Tests are performed in a controlled environment where a thermal gradient on the shell thickness is generated by means of a climatic chamber and an internal cartridge heater. Different temperature gradients and base excitation levels have been considered. The nonlinear dynamic scenario is analyzed through amplitude–frequency diagrams, bifurcation diagrams, waterfall diagrams, time histories, Fourier spectra, phase portraits, and Poincaré maps. Results show a strong effect of the temperature on the dynamic response of the shell: subharmonic, quasi-periodic, and chaotic vibrations take place as well as large amplitude vibrations, high sound levels are detected.

The post-buckling and nonlinear dynamic response of shallow spherical caps subjected to external pressure are analyzed. The Novozhilov's nonlinear thin shell theory is used to express the strain-displacement relations. Following the Rayleigh-Ritz method, the displacement fields are expanded using a mixed series: Legendre polynomials in the meridional direction, harmonic functions in the circumferential direction. Once the linear analysis is completed, the displacement fields are re-expanded, and the nonlinear dynamic model is obtained by using the Lagrange equations. The response of clamped caps, made of isotropic and homogeneous material, is investigated. The bifurcation analyses of equilibrium points and periodic orbits are presented by using continuation techniques. Benchmark results are provided in terms of natural frequencies and critical buckling loads. The dynamic effects due to the interaction between static and dynamic pressure are investigated. Numerical results pointed out that, under particular load conditions, dynamic bifurcation results in non-negligible asymmetric states activation in the response of the structure.