Spectral-Tchebychev technique for the free vibration analysis of composite laminated stepped and stiffened cylindrical shells with arbitrary boundary conditions

Abstract

By combining the first-order shear deformation theory (FSDT) with the spectral-Tchebychev (ST) technique, including the arbitrary boundary conditions, this paper analyzes the free vibration characteristics of composite laminated stepped and stiffened cylindrical shells. Based on artificial spring technique, the boundary conditions at both ends of the structure and the coupling continuity conditions between the shell segments are simulated. Then the Hamilton’s principle is applied to obtain the governing differential equations of each shell segments, the governing equations of the boundary conditions at both ends of the structure and the elastic coupling governing equations between adjacent shell segments. The displacement components of the composite laminated stepped and stiffened cylindrical shells are spectrally expanded into the finite terms of Tchebyshev polynomials, and then discretized according to Gauss-Lobatto points to obtain the matrix form characteristic equations of the structure. The frequency of free vibration of the structure and the corresponding mode shape can be obtained by solving the characteristic equation. In the numerical example, the convergence analysis of the model established by the technique in this paper is carried out, and then the frequency results of composite laminated stepped and stiffened cylindrical shells under arbitrary boundary conditions calculated in this paper are compared with the calculation results of related literature and finite element software. It is fully verified that the proposed spectral-Tchebychev technique not only has the characteristics of rapid convergence, but also can accurately analyze the free vibration behaviors of composite laminated stepped and stiffened cylindrical shells under arbitrary boundary conditions. After proving its effectiveness and accuracy, the parameter studies are finally carried out to analyze the influence of material parameters and rib geometric parameters on the free vibration behaviors of composite laminated stiffened cylindrical shells.