Stability of Coupled Rayleigh Beams with Structural Damping

In this paper, we are concerned with the stability of a system of Rayleigh beam equations that are weakly coupled and partially damped, where the structural damping is actuated at only one of the Rayleigh beams. By estimating the growth of the resolvent on the imaginary axis, we obtain the polynomial decay rate of the weakly coupled Rayleigh system by virtue of the frequency domain approach. Finally, a numerical simulation is presented to verify the theoretical results.