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Stability of a tree‐shaped network of strings and beams
Author(s) -
Ammari Kaïs,
Shel Farhat
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5255
Subject(s) - mathematics , string (physics) , stability (learning theory) , tree (set theory) , domain (mathematical analysis) , beam (structure) , exponential stability , zero (linguistics) , energy (signal processing) , exponential growth , root (linguistics) , mathematical analysis , stability theory , control theory (sociology) , mathematical physics , physics , computer science , quantum mechanics , optics , statistics , nonlinear system , linguistics , philosophy , control (management) , machine learning , artificial intelligence
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. Our technique is based on a frequency domain method.