Free and forced vibration analysis of coupled conical–cylindrical shells with arbitrary boundary conditions

• Vibration analysis of conical–cylindrical shells via a modified Fourier–Ritz method.
• The proposed method is applicable to arbitrary boundary conditions.
• The present method is feasible to analyze coupled conical–cylindrical–conical shells.
• Effects of dimensional and elastic restraint parameters are studied.
• Forced vibration behaviors of the shell subjected to point loads are presented.

This paper presents a free and forced vibration analysis of coupled conical–cylindrical shells with arbitrary boundary conditions using a modified Fourier–Ritz method. Under the current framework, regardless of the boundary conditions, each of the displacement components of both the conical and cylindrical shells are expanded invariantly as a modified Fourier series, which is composed of a standard Fourier series and closed-form supplementary functions introduced to accelerate the convergence of the series expansion and remove all the relevant discontinuities at the boundaries and the junction between the two shell components. All the expansion coefficients are determined by using the Rayleigh–Ritz method as the generalized coordinates. By using the present method, a unified solution for the coupled conical–cylindrical shells with classical and non-classical boundary conditions can be directly derived without the need of changing either the equations of motion or the expressions of the displacements. The reliability and accuracy of the present method are validated by comparison with FEM results and those from the literature. Studies on the effects of dimensional and elastic restraint parameters on the free vibrations are also reported. Investigation on vibration of the conical–cylindrical–conical shell combination shows the extensive applicability of present method for more complex shell combinations. New numerical examples are also conducted to illustrate the forced vibration behavior of the coupled conical–cylindrical shell subjected to the excitation forces in different directions.