Frequency response of spinning cylindrical shells with discontinuous boundary conditions: A semi-analytical method

Abstract

This paper develops a semi-analytical method for solving the frequency response of spinning cylindrical shells. The dynamic model of the spinning cylindrical shells with discontinuous boundary conditions is established. In the modeling, Sanders’ shell theory is employed and Chebyshev polynomials are adopted as the admissible displacement functions. By using the Lagrange equation, the equation of motion is obtained. Then, the equation is transformed into a state-space form, wherein the orthogonality of complex eigenvectors is derived. Further, the equation of motion is decoupled on the basis of the complex mode theory. Utilizing the reduced complex eigenvector, a semi-analytical method for solving the frequency response of the spinning shells is finally developed, wherein the point and distributed harmonic loads are all considered. The influences of the damping coefficient, the spinning speed, and the boundary spring stiffness on the frequency response of the shells are analyzed. The proposed method can conveniently predict the vibration characteristics of spinning cylindrical shells through a reduced-order dynamic model, which is much more efficient than numerical methods.