Exponential stability and numerical computation for a nonlinear shear beam system

In this paper, we examine the stability of a nonlinear shear beam system. We demonstrate the well-posedness of the system using the Faedo-Galerkin method and establish exponential stability through the multiplier method. Our findings improve upon previously obtained stability results for certain nonlinear Timoshenko-type systems, as we do not require the use of two controls to achieve exponential stability. We also provide numerical experiments at the end to support our theoretical results.