A meshless collocation method based on radial basis functions for free and forced vibration analysis of functionally graded plates using FSDT

The current study presents a meshless collocation method based on radial basis functions (MC-RBF) to analyze the free and forced vibration of functionally graded plates. We used the first-order shear deformation plate theory for the displacements and strains. The governing equations are discretized via the MC-RBF method to obtain the natural frequencies. We suggested a new algorithm (modified LOOCV) to acquire the shape parameters of the radial basis function in the free and forced vibration problems. The discretized equations are converted to reduced equations via the proposed transformation matrix. The run-time of this method is significantly lower than the other methods. In particular, the accuracy of the proposed algorithm is acceptable. The discretized equations are reduced by eigenvectors and are converted to state-space form and solved using the numerical Runge-Kutta method. The various boundary conditions are taken into account, such as their clamped, simply supported, free and mixture, and various power-law indices. The results show that the MC-RBF method using a modified LOOCV algorithm is a convenient method for free and forced vibration of FG plates.

Automated summary

The study introduces a meshless collocation method based on radial basis functions for analyzing the free and forced vibration of functionally graded plates. A new algorithm is proposed to determine the shape parameters of the radial basis function and discretize the governing equations for obtaining natural frequencies. The reduced equations are solved using eigenvectors and numerical methods, providing a convenient and accurate approach for vibration analysis.