An analytical method for vibration analysis of cylindrical shells coupled with annular plate under general elastic boundary and coupling conditions

Abstract

A unified solution for coupled cylindrical shell and annular plate systems with general boundary and coupling conditions is presented in the study by using a modified Fourier-Ritz method. Under the framework, regardless of the boundary and continuity conditions, each displacement for the cylindrical shell and the annular plate is invariantly expressed as the modified Fourier series composed of the standard Fourier series and auxiliary functions. The introduction of the auxiliary functions can not only remove the potential discontinuities at the junction and the extremes of the combination but also accelerate the convergence of the series expansion. All the expansion coefficients are determined by the Rayleigh-Ritz method as the generalized coordinates. The arbitrary axial position of the annular plate coupling with the cylindrical shell considered in the theoretical formulation makes the present method more general. The theoretical model established by present method can be conveniently applied to cylindrical shell-circular plate combinations just by varying the inner radius of the annular plate. The convergence and accuracy of present method are tested and validated by a number of numerical examples for coupled annular plate-cylindrical shell structures with various boundary restraints and general elastic coupling conditions. The effects of the axial position of the annular plate and elastic coupling conditions on the vibration behavior of the coupled system are also investigated. The power of present method compared to conventional finite element method is demonstrated with less computation cost. Some new results are presented to provide useful information for future researchers.