Stability Results for a Coupled Viscoelastic Suspension Bridge Problem with Nonlinear Frictional Damping

Suspension bridges are essential in lifeline civil structures that have been constructed in many countries due to their superior effectiveness when it comes to long spans. In this paper, we study a mathematical model for a one-dimensional suspension bridge problem with viscoelastic damping and nonlinear frictional damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. Using the multiplier method, we establish an explicit formula for the energy decay rate and show that this rate depends on the rates of both the relaxation function and the nonlinear frictional damping. Our result improves and generalizes many existing results in the literature.