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

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-Karman equation, Hamilton's principle, and Galerkin method, two-degree-of-freedom non-linear ordinary differential governing equations are discretized.