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 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 deg and 90 deg, 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.

A finite element model of an aero-engine dual-rotor system with intermediate bearing supported by six bearings is set up. Three modes of non-concentricity caused by the assembly process are defined, namely parallel non-concentricity, front deflection angle non-concentricity and rear deflection angle non-concentricity. The influence of the non-concentricity on the vibration characteristics of the dual-rotor system is investigated in detail. The results show that the parallel non-concentricity and the front deflection angle non-concentricity have a significant influence on the bending vibration modals of the high-pressure rotor and the low-pressure rotor, but have little influence on the local vibration modals of the rotors. With the increase in the magnitude of the non-concentricity, the natural frequencies of the bending modals decrease continuously, and the mode shapes of bending modals and that of local modals may be interchanged, leading to the emergence of bending modals in advance. Therefore, the key parameters to be controlled in the assembly process are the parallel non-concentricity and the front deflection angle non-concentricity. In order to prevent the bending modal of the dual-rotor system from appearing in advance, it is necessary to control the parallel non-concentricity within 2 mm and the front deflection angle non-concentricity amount within 0.18°.

The aerothermoelastic behavior of a conical shell in supersonic flow is studied in the paper. According to Love’s first approximation shell theory, the kinetic energy and strain energy of the conical shell are expressed and the aerodynamic model is established by using the linear piston theory with a curvature correction term. By taking the characteristic orthogonal polynomial series as the admissible functions, the mode function of conical shell under different boundary conditions can be obtained using the Rayleigh–Ritz method. Then, the dynamic model of the conical shell is derived by using the Lagrange equation. Based on the model, variations in the natural frequencies with respect to temperature and free-stream static pressure are analyzed. Additionally, the effects of the length-to-radius ratio, the thickness-to-radius ratio, and semi-vertex angle, as well as the thermal and aerodynamic loads on the aerothermoelastic stability of the structure are investigated in detail.