Plane Vibration Characteristics of a Pneumatic Tire Model 650492
An elastically supported cylindrical shell is used to represent the motion of a pneumatic tire in the plane of the wheel. This is an attempt to utilize shell motion as an analog to the plane motion of the pneumatic tire tread. The idea is suggested by the constructional features of a pneumatic tire, both from the point of view of mass distribution and the distribution of elastic stiffness.
The equations of motion for such a model are derived by reference to conventional energy methods. In this derivation, the influence of internal pressure and elastic support of the shell is taken into account. The frequencies are determined as functions of the mode shape, and it is shown that nodes, as well as antinodes, rotate with an angular velocity somewhat less than the angular velocity of the rotating pneumatic tire, to an extent determined by the particular mode shape in question. It is hoped that these phenomena may be useful in explaining or understanding some vibratory or acoustic interactions between a tire and suspension system.