Do Shape Memory Alloy Cables Restrain the Vibrations of Girder Bridges? A Mathematical Point of View

We study the energy decay of a damped Euler-Bernoulli beam which is subject to point-wise feedback force representing Shape Memory Alloy (SMA) cable. The problem we consider that paper by [Liu et al. Int. J. Struct. Stab. Dyn. 17 (2017) 1750076] but, for simplicity, our mod-elization does not take into account additional stiffness term they considered. An explicit expression given resolvent underlying operator as well its eigenvalues and eigenfunctions. show exponential energy. fastest rate supremum real part spectrum infinitesimal generator semigroup since prove existence Riesz basis. To question ”Do cables restrain vibrations girder bridges?”, experiments in answer positively. Our allow give definite yet. only presence these may be enough. Some physical parameters have chosen carefully.