Vibration mode localization in disordered large planar lattice trusses

Vibration mode localization in large randomly disordered planar lattice trusses is studied in this paper. The equations of motion of a general ns-storey and nb-bay truss are formulated using a finite element method. The localization factor, which characterizes the exponential rate of growth or decay of amplitudes of vibration of a randomly disordered periodic structure, is related to the smallest positive Lyapunov exponent for the corresponding random discrete dynamical system. A numerical algorithm for determining all the Lyapunov exponents for a discrete random dynamical system is presented. As a second approach, Greenʹs function formulation for a block tridiagonal matrix system is applied to determine the localization factors for disordered periodic trusses. Numerical results of vibration mode localization for single-bay and double-bay trusses are obtained by using the method of transfer matrix and the method of Greenʹs function.