Non-linear parametric vibration of the laminated composite shallow shells including primary and 1:2 internal resonances

Abstract

This research aims to study the non-linear parametric vibration of laminated composite shallow (LCS) shells with the optimal fiber angles exposed to external and parametric excitations, including primary and 1:2 internal resonances. In this regard, optimal fiber angles are found with implementations of the P-T method for the objective functions and utilization of the particle swarm optimization (PSO). Also, the non-linear model of the shallow shells is established based on the stress function and the first-order shear deformation theory (FSDT). According to FSDT, Hooke’s law, von-Kármán equation, Hamilton’s principle, and Galerkin method, two-degree-of-freedom non-linear ordinary differential governing equations are discretized.

Keywords:

• Laminated composite shallow shells
• non-linear parametric vibration
• chaos
• primary and internal resonances
• PSO algorithm
• P-T method
• multiple scales method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors greatly appreciate the supports of the Natural Sciences and Engineering Research Council of Canada (NSERC), Qinghai Normal University (Project 111 D20035) and the University of Regina to the present research.