Non-linear free vibration analysis of point supported laminated composite skew plates

• Non-linear free vibration of skew plates with four types of point support arrangements is investigated.
• The effects of number of point supports, skew angle, fiber orientation and aspect ratio are reported.
• For the higher amplitude ratios, more nodes should be employed to achieve convergence.
• Aspect ratio has a significant effect on the non-linear frequency ratio.

The element-free Galerkin (EFG) method is employed to analyze the large amplitude free vibration of point supported laminated composite skew plates. The geometrical non-linearity is considered based on the von Karman’s assumptions and the point support boundary conditions are satisfied through the use of Lagrange multiplier method and orthogonal transformation technique. Assuming a periodic solution and applying the weighted residual method, the non-linear governing equations are used, and the problem is solved by direct iteration technique. The obtained results are first validated against the available solutions of simply supported and clamped plates, and then the point supported plates are dealt with. To this end, four types of point support arrangements are considered and non-linear frequency ratios for different numbers of point supports, amplitude ratios, skew angles, aspect ratios and fiber orientations are calculated which may serve as benchmarks for future research.