Free and forced vibration analyses of FGP doubly curved shells based on Chebyshev polynomials

The free and forced vibration behaviors of the functionally graded porous (FGP) doubly curved shell are investigated based on the Chebyshev polynomials. Three types of porosity distributions, including the symmetrical distribution, the uniform porosity distribution, and the non-uniform porosity distribution, are studied in this work. First, the Rayleigh–Ritz method and the multi-segments technology are employed to build the dynamic model of the doubly curved shell. Second, the third-kind Chebyshev polynomials are adopted to express the admissible displacement function of the doubly curved shell under vibration. Third, the general boundary conditions are described as a series of spring parameters via virtual spring technology. Then, the accuracy and efficiency of the proposed method are verified by comparing them with the results obtained from the finite element method and the open literature. Finally, the effect of the boundary condition, the geometrical parameter, and the porosity distribution on the free and forced vibration of the FGP doubly curved shell is investigated in details.