Effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration

For the purpose of understanding the effects of rotation on wave propagation within a tire’s treadband, the vibration of an inflated, circular cylindrical shell, rotating about a fixed axis has been considered here. The equations of motion of the rotating shell are formulated in a fixed reference frame (i.e., Eulerian coordinates). By assuming wave-like solutions for the free vibration case, the natural frequencies and corresponding wave-like basis functions can then be obtained. A natural frequency selection procedure is introduced that can be used to associate each of the basis functions with a single natural frequency. The basis functions are then superimposed to represent the forced response of the system when driven by a point harmonic force at a fixed location in the reference frame. By using the procedure described here, the coefficients of the basis functions can be obtained directly by solving an uncoupled ordinary differential equation. Finally, the resulting forced responses are presented in both the spatial and wave number domains, and the wave number spectrum of the rotating shell is compared with that of a stationary shell. Based on the results presented here, it is suggested that at typical rotational speeds it may be possible to use a stationary tire analysis to predict the characteristics of a rotating tire after performing a simple kinematic compensation. r 2003 Elsevier Ltd. All rights reserved.