A meshless method for thermal vibration analysis of curved-edge trapezoidal plates made of laminated materials

Abstract This paper reports a meshless method for stochastic vibration analysis of trapezoidal composite laminates with curvilinear bound. The basis functions used in this meshless method are Chebyshev polynomials, which are adapted to the defining domain of the Chebyshev polynomials by transforming the curved-edge plate into a square plate using a coordinate mapping technique. The developed vibration analysis model combines the first-order shear deformation theory (FSDT) and thermos-elasticity theory using the Hamiltonian variational principle. The displacement tolerance function of the square plate is approximated by a two-dimensional meshless Chebyshev-radial basis point interpolation method. Gaussian Lobato sampling points are used to discretize the square domain. The correctness and efficiency of the model is verified by comparison with finite element results and published literature. The effects of temperature, geometry, and stochastic loading on the vibration characteristics of curved edge trapezoidal plates are also carried out. The results show that the existing Chebyshev-radial basis point interpolation method can accurately and efficiently calculate the vibration characteristics of curved-edge trapezoidal plates under different boundary conditions.