Local thin plate spline collocation for free vibration analysis of laminated composite plates

This paper focuses for the first time on free vibration analysis of laminated composite plates by a meshless local collocation method based on thin plate spline radial basis function. This method approximates the governing equations using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties, and lamination schemes are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method.

► Local thin plate spline for free vibration of laminated composite plates.
► The method to circumvent the singularity of the thin plate spline is proposed.
► Thin plates spline with shape parameter k   = 3 produces the better results.
► Dimensionless sizes of the support domain αs=5αs=5 produces the better results.