Analysis of a thermoelastic Timoshenko beam model

In this paper, we analyze a linear problem describing the vibrations of a coupled suspension bridge. The single-span roadbed is modeled as an extensible thermoelastic beam of Timoshenko type. The main cable is modeled as an elastic string and is connected to the roadbed by a distributed system of elastic springs. For this linear model, we obtain the existence and uniqueness of solutions by using the semigroup theory. The exponential decay property is also proved. Then, through a variational formulation, the model is numerically analyzed and some numerical experiments are performed to verify the behavior of the numerical method.