Asymptotic frequency distributions for variable coefficients Rayleigh beams under boundary feedback control

The analysis of the boundary damping rate for eigenmodes of a Rayleigh Beam with variable coefficients is usually difficult because explicit solution formula are hard to come by. In this paper, by using the estimating devices of , we can carry out an asymptotic analysis and conclude that there is a uniform damping rate for the high frequency modes. As a result, Riesz basis property and exponential stability can be deduced and a conjecture in is settled.