Free vibration analysis of coupled structures of laminated composite conical, cylindrical and spherical shells based on the spectral-Tchebychev technique

Abstract

In this article, a numerical spectral-Tchebyshev (ST) technique is applied to solve the free vibration strong solution of the coupled structures of laminated composite conical, cylindrical and spherical shells under various boundary conditions. The artificial spring technique is introduced to realize the coupling connection of substructures and simulate the arbitrary boundary conditions. Considering the first-order shear deformation shell theory (FSDST), and using Hamilton variational analysis under its framework to derive the governing equations of motions of three coupled structures: coupled conical-cylindrical shells, coupled spherical-cylindrical shells and coupled spherical-cylindrical-conical shells. The solution of the governing equations of motions is obtained using the spectral-Tchebyshev technique. The variables along the generatrix direction are discretized based on the Gauss-Lobatto nodes, while the Tchebyshev polynomials are used for spectral approximation. The variables along the circumferential direction are approximated by Fourier series. The calculated free vibration characteristics of the coupled structures are compared with the numerical results based on previous references and the finite element method, which completely reflects the excellent convergence and calculation accuracy of the spectral-Tchebyshev technique. On this basis, the effect of the material properties and geometric dimensions of the substructures (conical, cylindrical and spherical shells) on the free vibration frequencies of the coupled structure is further studied.