Three-dimensional free vibration analysis of functionally graded cylindrical panels with cut-out using Chebyshev–Ritz method

The free vibration analysis of functionally graded (FG) cylindrical panels with a cut-out and under thermal environment is studied using the three-dimensional Chebyshev–Ritz method. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The formulation is based on the elasticity theory, which includes the effects of initial thermal stresses induced by the thermal environment. Chebyshev polynomials in conjunction with suitable boundary functions are used as admissible functions of the Ritz method. The convergence behavior of the method is demonstrated and to validate the results, comparisons are made with the available solutions for isotropic homogeneous and FG curved panels without cut-out. In addition, the solution for homogeneous panels with cut-out are compared with those obtained via the commercial finite element package 'ABAQUS'. Then, the effects of volume fraction index, different types of temperature distributions through the panel thickness, dimensions of the cut-out and the geometrical parameters of the panels on their free vibration behaviors are studied.