Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam | Zendy

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Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Author(s) -

Sebti Kerbal,

Nassereddine Tatar

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1811-87

Subject(s) - viscoelasticity , mathematics , timoshenko beam theory , exponential stability , beam (structure) , type (biology) , displacement (psychology) , mathematical analysis , exponential function , control theory (sociology) , classical mechanics , physics , nonlinear system , thermodynamics , computer science , optics , psychology , ecology , control (management) , quantum mechanics , artificial intelligence , biology , psychotherapist

A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.

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