Vibration analysis of rotating combined thin-walled shells with multiple conical segments

In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on the Love's first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0° and 90° respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical-conical joined shell and cylindrical-conical-cylindrical-conical-cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown and the effects of rotating speed, circumferential wave number, spring stiffness and semi-vertex angles on the vibration behavior are given in detail.