Abstract This manuscript focuses on a suspension bridge system where the deck is modeled by the Timoshenko-Ehrenfest theory free of the second frequency spectrum. The existence and uniqueness of weak and strong solutions are proved by the Faedo-Galerkin method. The exponential decay is obtained without any restrictions on the coefficients of the system. The energy method is used for exponential stability, which consists of constructing a Lyapunov functional using suitable multipliers.
Raposo et al. (Fri,) studied this question.