Vibration and sound radiation of a cylindrical shell under a circumferentially moving load

Abstract

A theoretical model is developed to evaluate the vibration and sound radiation of a thin cylindrical shell excited by a constant point load continuously traveling along the circumferential direction at a rotational speed Ω. This rotating load model takes into account the exterior fluid loading due to the sound pressure radiated by the shell. The three equations of the vibroacoustic problem are the shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid–shell interface. The rotating load model is based on a frequency-domain solution which is convenient for the interpretation of the vibratory and acoustic responses in terms of shell modes. The equations of motion are expanded over the shell modes to give the modal equations of motion. A frequency-domain representation of the rotating load shows that its frequency content is a series of equal amplitude harmonics NΩ. Each harmonic excites exclusively the circumferential mode N. For this rotating excitation, vibration and radiation critical speeds are identified. They give, respectively, an indication at which rotational speeds high vibration levels and sound radiation efficiency are expected. Finally, a good correlation between the rotating load model and experiments are obtained.