Dynamical behavior of networks of non-uniform Timoshenko beams system with boundary time-delay inputs

Abstract

The dynamical stability of planar networks of non-uniform Timoshenkobeams system is considered. Suppose that the displacement and rotational angle iscontinuous at the common vertex of this network and the bendingmoment and shear force satisfies Kirchhoff's laws, respectively.Time-delay terms exist in control inputs at exterior vertices. Thefeedback control laws are designed to stabilize this kind ofnetworks system. Then it is proved that the corresponding closedloop system is well-posed. Under certain conditions, the asymptoticstability of this system is shown. By a complete spectral analysis,the spectrum-determined-growth condition is proved to be satisfiedfor this system. Finally, the exponentialstability of this system is discussed for a special case and somesimulations are given to support these results.