Nonlinear dynamics of doubly curved shallow microshells

Ghayesh, Mergen and Farokhi, Hamed (2018) Nonlinear dynamics of doubly curved shallow microshells. Nonlinear Dynamics, 92 (3). pp. 803-814. ISSN 0924-090X

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Official URL: http://dx.doi.org/10.1007/s11071-018-4091-7

Abstract

The nonlinear dynamical characteristics of a doubly curved shallow microshell are investigated thoroughly. A consistent nonlinear model for the microshell is developed on the basis of the modified couple stress theory (MCST) in an orthogonal curvilinear coordinate system. In particular, based on Donnell’s nonlinear theory, the expressions for the strain and the symmetric rotation gradient tensors are obtained in the framework of MCST, which are then used to derive the potential energy of the microshell. The analytical geometrically nonlinear equations of motion of the doubly microshell are obtained for in-plane displacements as well as the out-of-plane one. These equations of partial differential type are reduced to a large set of ordinary differential equations making use of a two-dimensional Galerkin scheme. Extensive numerical simulations are conducted to obtain the nonlinear resonant response of the system for various principal radii of curvature and to examine the effect of modal interactions and the length-scale parameter.

Item Type: Article
Uncontrolled Keywords: Nonlinear dynamics, Microshells, Modified couple stress theory, Modal interactions, Nonlinear resonant response
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Becky Skoyles
Date Deposited: 07 Aug 2018 10:54
Last Modified: 07 Aug 2018 10:54
URI: http://nrl.northumbria.ac.uk/id/eprint/35209

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