Stability of a tree-shaped network of strings and beams

2015/12/28 by Kaïs Ammari, Ammari, Kaïs, Farhat Shel +1
Mathematics · #35B40 #35M33 #35R02 #74K05 #74K10 #93D15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35M33 #msc:35R02 #msc:74K05 #msc:74K10 #msc:93D15

paper · pdf · doi:10.48550/arxiv.1512.08396

arxiv created 2015/12/28 · arxiv updated 2015/12/29

Abstract

In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there is no beam following a string ( from the root to the leaves) and decay polynomially if not. We use a frequency domain method from the semigroups theory.

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