Nonlinear dynamics of doubly curved shallow microshells

Mergen H. Ghayesh*, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)803-814
Number of pages12
JournalNonlinear Dynamics
Volume92
Issue number3
Early online date30 Jan 2018
DOIs
Publication statusPublished - May 2018
Externally publishedYes

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