Title: Nonlinear Dynamics and Stability of Pressure-Loaded Shallow Spherical Caps

Authors: Iarriccio G. and Pellicano F.

Abstract

Thin shells are very common in many engineering applications. Therefore, in the design of thin-walled structures, it is important to consider the instability region of the static and dynamic responses \[1\], as well as in the presence of fluid-structure interaction \[2,3\] or extreme temperature conditions \[4,5\]. In this work, the nonlinear dynamic response of a shallow spherical cap subjected to a time-dependent pressure load is analyzed. The Novozhilov's nonlinear thin shell theory \[6\] is used to express the strain-displacement relations, geometric imperfections are considered. Using the Rayleigh-Ritz method, the displacement fields are expanded using a mixed series: Legendre polynomials are considered in the azimuthal direction and harmonic functions in the circumferential one. The equations of motion are derived by using Lagrange equations. The response of a homogeneous shell, made of isotropic material, clamped at its ends, and subjected to a harmonic pressure load is investigated: direct numerical time integration is considered for determining the steady and unsteady time response; the bifurcation analysis of periodic response has been performed using the continuation software AUTO \[7\]. the model is validated by means of comparisons with the existing literature for spherical shells having a circular base, in particular with models developed through the Marguerre's theory \[8,9\].

References

1.     NASA. Buckling of Thin-Walled Doubly Curved Shells. *NASA, Space Vehicle Design Criteria (Structures), Report No. NASA SP-8032*, 1969, 1-33.

2.    F. Pellicano, M. Amabili, Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads, *Journal of Sound and Vibration* 293 (1–2) (2006) 227–252.

3.     Tubaldi, E., Amabili, M., & Païdoussis, M. P. (2017). Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation. Theory and numerical results for a single harmonic pulsation. *Journal of Sound and Vibration*, *396*, 217-245.

4.   Zippo, A., Barbieri, M., Iarriccio, G., & Pellicano, F. (2019). Nonlinear vibrations of circular cylindrical shells with thermal effects: an experimental study. *Nonlinear Dynamics*, 1-19.

5.     Iarriccio, G., Zippo, A., Pellicano, F., & Barbieri, M. (2020). Resonances and nonlinear vibrations of circular cylindrical shells, effects of thermal gradients. *Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*, 0954406220907616.

6.     V.V. Novozhilov, Foundations of the Nonlinear Theory of Elasticity, Graylock Press, Rochester, NY, USA, 1953 (now available from Dover, NY, USA).

7.     Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X., 1998. AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). Concordia University, Montreal, Canada.

8.     Huang, N. C. Unsymmetrical buckling of thin shallow spherical shells. *J. Appl. Mech*. Sep 1964, 31(3): 447-457.

9.     GGonçalves, P. B. (1993). Jump phenomena, bifurcations, and chaos in a pressure loaded spherical cap under harmonic excitation. *Appl. Mech. Rev.* 46, S279-S288.


Nonlinear Dynamics and Stability of Pressure-Loaded Shallow Spherical Caps

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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