An analytic method for free and forced vibration analysis of stepped conical shells with arbitrary boundary conditions

An analytic method is presented for free and forced vibration analysis of stepped conical shells with general boundary conditions. The method is involved in dividing the stepped shells into segments according to the locations of discontinuities, such as thickness and semi-vertex angle. Combining Flügge shell theory with power series method, displacements and forces at cross-section of conical segments are expressed in terms of eight unknown coefficients. Meanwhile, by employing artificial springs to restrain edge displacements, arbitrary boundary conditions, including classic and elastic ones, can be analyzed. All separate segments are assembled together through displacement continuity conditions and equilibriums of forces at junctions of discontinuities. To test the validity of present method, comparisons of some stepped conical shells subjected to classic and elastic boundary conditions are firstly presented. The results of present method agree fairly well with those in literature and calculated by finite element method. Furthermore, influences of semi-vertex angle, elastic boundary conditions, discontinuity, excitation and damping are investigated. Parametric studies reveal that meridional and circumferential displacements have significant effects on fundamental and beam mode frequency parameters, and effects of the location of discontinuity and semi-vertex angle depend on boundary conditions and thickness ratios.