In this paper, the stability of a spinning rotor loaded by a circumferentially distributed frictional traction is examined. Typical engineering applications include automotive and aircraft disc brakes and circular saws. The frictional traction, which is always directed tangent to the instantaneous deflection curve of the rotor, is decomposed into in-plane and transverse components. The in-plan component is equilibrated by the in-plane stresses while the transverse component is a slope-dependent nonconservative followertype force that is the major source of dynamic instability of the rotor in this study. The rotor is modeled as a spinning annular plate that includes the effects of rotary inertia and shear deformations in the context of the Mindlin thick plate theory. A thick plate model is employed to ensure an accurate estimation of the eigenvalues when the rotor vibration involves high circumferential modes (eighth or ninth) that are often observed in unstable automotive disc brakes. The pad or stator is represented as a viscoelastic subgrade that reacts to both transverse and shearing motion of the rotor. The degree of instability is measured by examining the resulting complex eigenvalues. Effects of various system parameters such as frictional traction, geometry of the rotor, pad size, spinning speed, and viscoelastic properties of the pad on the dynamic instability are discussed. Results, when compared with those from the classical thin plate model of the rotor, are significantly different.
Lithospheric flexure and deformation-induced gravity changes: effect of elastic compressibility and gravitation on a multilayered, thick-plate model