【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

To explore the background and basis of the node document

Total: 17 articles

- [1] Zhiqiang WANG School of Mathematical Sciences, Fudan University, Shanghai 200433, China., Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems, Chinese Annals of Mathematics(Series B), 2006 (06)
- [2] Ke WANG 11 School of Mathematical Sciences,Fudan University,Shanghai 200433,China., Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems, Chinese Annals of Mathematics(Series B), 2011 (06)
- [3] Gnter R.LEUGERING1 E.J.P.Georg SCHMIDT21Department of Mathematics,Friedrich-Alexander University,Erlangen-Nuremberg,Martensstrasse 3,D 91085 Erlangen,Germany.2Department of Mathematics and Statistics,McGill University,805 Sherbrooke Street West,Montreal,H3A 2K6,Canada., On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space, Chinese Annals of Mathematics(Series B), 2012 (01)
- [4] M. Asghari;;M.H. Kahrobaiyan;;M.T. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science, 2010 (12)

Documents that have the similar content to the node document

Total: 23 articles

- [1] Cross-cultural study on neighborhood noise problems——results of students, Chinese Journal of Acoustics, 1990 (01)
- [2] On the Neighborhood in Stabilizing Period-T Orbits for Chaotic m Degree Polynomial Dynamical System, Communications in Nonlinear Science & Numerical Simulation, 1998 (04)
- [3] Modified DM Models for Aging Networks Based on Neighborhood Connectivity, Communications in Theoretical Physics, 2008 (01)
- [4] Information from the Kinematics of F and G Stars in the Solar Neighborhood, Chinese Journal of Astronomy and Astrophysics, 2002 (05)