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Nonlinear Dynamics

, Volume 92, Issue 3, pp 803–814 | Cite as

Nonlinear dynamics of doubly curved shallow microshells

  • Mergen H. Ghayesh
  • Hamed Farokhi
Original Paper
  • 287 Downloads

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.

Keywords

Nonlinear dynamics Microshells Modified couple stress theory Modal interactions Nonlinear resonant response 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of AdelaideAdelaideAustralia
  2. 2.Department of AeronauticsImperial College LondonLondonUK

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