Stabilization of a nonlinear rotating disk-beam system with localized thermal effect

Abstract

This article considers the stabilization problem of a rotating disk-beam system with localized thermal effect and torque control. Assume that the disk rotates with nonuniform angular velocity. A subdomain of the elastic beam is with thermoelastic damping, which is a kind of intrinsic one since thermoelasticity exists in almost all materials. Using only torque control, we prove that the system can be stabilized exponentially under certain condition on angular velocity, no matter how small the part with thermal effect of the beam is. The exponential stability is proved mainly by the resolvent estimate. Some numerical simulations are further given to support the theoretical results obtained in this paper.