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


Qilong GU,Gunter LEUGERING,Tatsien LI.Exact Boundary Controllability on a Tree-Like Network of NonlinearPlanar Timoshenko Beams[J].Chinese Annals of Mathematics B,2017,38(3):711~740
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Qilong GU; Gunter LEUGERING;Tatsien LI


This work was supported by the National Basic Research Program of China (No.2103CB834100), the National Science Foundation of China (No.11121101), the National Natural Sciences Foundation of China (No.11101273) and the DFG-Cluster of Excellence: Engineering of Advanced Materials.
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.


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


35L70, 93B05, 49J40
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