Stochastic meshless method for nonlinear vibration analysis of composite plate reinforced with carbon fibers

With the aid of an efficient meshless numerical solution and the reproducing kernel particle method, the feasibility for investigating the nonlinear vibrations of the carbon fiber reinforced composite rectangular plate with the random material properties is studied in this paper. A geometrically nonlinear mathematical model is established based on the classical plate theory. According to the derived governing equation of motion by using the principle of virtual displacement, the nonlinear vibration behaviors of the carbon fiber reinforced composite plates with various edge supports are investigated. The linear and nonlinear eigenvalues and corresponding eigenvectors are calculated iteratively by using the dimensionless amplitude. The stochastic meshless method is proved to have a good computational accuracy for the composite plate, and exhibits an optimal choice for the shape function and constraint of the essential boundary conditions. The useful conclusions are obtained regarding the effect of the material and geometrical parameters including the boundary condition, length-width ratio, plate length and carbon fiber content on the nonlinear responses in the framework of the meshless method.