THE IN-PLANE STEADY-STATE RESPONSE OF A RING IN RELATIVE MOTION TO A CONSTANT LOAD

Abstract

Ring-like structures are very commonly used in civil, mechanical and aerospace engineering. Typical examples of such structures are components in turbomachinery, compliant gears, conventional pneumatic tires and more recent non-pneumatic tires, to name a few. In this paper, a ring on elastic foundation is considered. The foundation, modelled as distributed springs, connects the inner surface of the ring to an immovable axis. Focus is placed on the in-plane response of the ring subjected to in-plane load only. A high-order ring model, which accounts for the through-thickness variations of displacements is adopted for the study. Two loading situations of a ring structure are of interest in practice: (i) a stationary ring subjected to a circumferentially moving constant load; and (ii) a rotating ring under a stationary constant load. For the first situation, it is well-known that resonances occur when the rotational speeds of the load satisfy certain conditions. In a series of recent investigations, such resonance speeds have been predicted for a rotating ring subjected to a stationary load. In this paper the case of the rotating ring under a stationary constant load and that of a stationary ring subjected to a moving load are compared in terms of their resonance speeds, as well as the steady-state responses for various parameters. It is found that these two cases are distinguishable even for system parameters which result at similar critical speeds.