Exact Boundary Controllability on a Tree-Like Network of Nonlinear Planar Timoshenko Beams

【Author】

Qilong GU;Günter LEUGERING;Tatsien LI;School of Mathematical Sciences, Shanghai Jiao Tong University;Department Mathematik, Friedrich-Alexander University Erlangen-Nuremberg;School of Mathematical Sciences, Fudan University;Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory;

【Institution】

School of Mathematical Sciences, Shanghai Jiao Tong University;Department Mathematik, Friedrich-Alexander University Erlangen-Nuremberg;School of Mathematical Sciences, Fudan University;Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory;

【Abstract】

This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3,American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.

【Keywords】

Nonlinear Timoshenko beams;;Tree-like networks;;Exact boundary controllability;;Semi-global classical solutions

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