Session: 07-09-01: Vibrations of Continuous Systems

Paper Number: 113288

113288 - Nonlinear Vibrations of a Shallow Spherical Cap Under Pressure Loading 

Abstract

Shallow spherical caps are of interest for various fields of science and engineering, including mechanics, materials science, and biophysics. These structures are successfully used in several fields thanks to their characteristics, and common spherical cap applications can be found in pressure vessels, pipes, domes, or spacecraft fuselages.

Experimental studies on spherical shells have provided valuable insights into the mechanics and physics of curved structures, showing that when subjected to external loads, these structures could exhibit static and dynamic instabilities [1], which are possible routes to catastrophic failures. Hence the need for accurate geometric and material models, taking into account the role of geometric imperfections or complex rheology. Recently, thanks to a deeper knowledge on nonlinear phenomena like buckling or bistabilty [2], several studies have been devoted to exploit the hidden potentiality of nonlinearities.

Despite several papers have been published on thin shallow spherical caps, most of the available literature is concerned to buckling or dynamic analyses limited to axisymmetric deformations and oscillations [3,4], while studies in which the asymmetric motion has been considered are still a few [5,6].

In this paper, the nonlinear dynamic response of a thin shallow spherical cap subjected to a uniform pressure load is analyzed using Novozhilov’s nonlinear thin shell theory [7]. The possibility of having asymmetric oscillations is considered, geometric nonlinear terms are retained within the stress-strain relations, and the shell is modeled as homogenous and made of isotropic material. The equations of motion, which are derived using the Rayleigh-Ritz method and Lagrange equations, are solved through direct integration and continuation methods, and the presence of nonlinear phenomena is discussed using frequency response curves, bifurcation diagrams, Poincarè maps, time histories, and Fourier spectra.

 

References

[1]          Krenzke, M. A., and Kiernan, T. J., 1963, “Elastic Stability of Near-Perfect Shallow Spherical Shells,” AIAA J., 1(12), pp. 2855–2857.

[2]          Taffetani, M., Jiang, X., Holmes, D. P., and Vella, D., 2018, “Static Bistability of Spherical Caps,” Proc. R. Soc. A Math. Phys. Eng. Sci., 474(2213).

[3]          Huang, N. C., 1964, “Unsymmetrical Buckling of Thin Shallow Spherical Shells,” J. Appl. Mech. Trans. ASME, 31(3), pp. 447–457.

[4]          Gonçalves, P. B., 1993, “Jump Phenomena, Bifurcations, and Chaos in a Pressure Loaded Spherical Cap under Harmonic Excitation,” Appl. Mech. Rev., 46(11), pp. S279–S288.

[5]          Touzé, C., and Thomas, O., 2006, “Non-Linear Behaviour of Free-Edge Shallow Spherical Shells: Effect of the Geometry,” Int. J. Non. Linear. Mech., 41(5), pp. 678–692.

[6]          Iarriccio, G., Zippo, A., and Pellicano, F., 2022, “Asymmetric Vibrations and Chaos in Spherical Caps under Uniform Time-Varying Pressure Fields,” Nonlinear Dyn., 107(1), pp. 313–329.

[7]          Novozhilov, V. V., 1953, Foundations of the Nonlinear Theory of Elasticity, Graylock Press.

Presenting Author: Giovanni Iarriccio University of Modena and Reggio Emilia

Presenting Author Biography: Giovanni Iarriccio is a postdoctoral researcher at the University of Modena and Reggio Emilia in Italy. He holds a MSc in Vehicle Engineering and a PhD in Industrial end Environmental Engineering from the same institution. His research interests are focused on the areas of Nonlinear Dynamics, Structural Vibrations, Fluid-Structure Interaction, and Experimental Testing,

Authors:

Giovanni Iarriccio University of Modena and Reggio Emilia
Antonio Zippo University of Modena and Reggio Emilia
Francesco Pellicano University of Modena and Reggio Emilia