Energy decay for a suspension bridge problem with variable exponent and time dependent nonlinear damping

In this paper, we study a mathematical model for a one-dimensional suspension bridge problem with variable exponent nonlinear damping modulated by a time dependent coefficient. 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. We use the multiplier method to establish general energy decay results depending on both the range of the variable exponent functions and the time dependent coefficients. Our results substantially improve, extend, and generalize some earlier related results in the literature.