New general decay properties of a rotating beam

In this paper, we study a rotating Euler–Bernoulli beam with memory. One end fixed to a rotated motor in a horizontal plane and to a tip mass at the other end. The coupled dynamic model is modelled by infinite-dimensional partial differential equations (PDEs) coupled with finite-dimensional ordinary differential equations (ODEs). Under the suitable control force applying at the motor, we establish some decay results for the associated energy with general assumptions on the memory kernel. We also give some numerical illustrations to show the effectiveness of the boundary control law. This new results substantially improve several earlier related results in the literature.