VIBRATION MODE LOCALIZATION IN DISORDERED CYCLIC STRUCTURES, II: MULTIPLE SUBSTRUCTURE MODES

Vibration mode localization in disordered cyclic periodic structures with multiple substructure modes is studied. The localization factor characterizing the exponential rate of growth or decay of the amplitudes of vibration is related to the smallest positive Lyapunov exponent of the corresponding discrete dynamical system. Themultiplicative ergodic theoremof Oseledec is applied to determine the Lyapunov exponents and the localization factors. As a second approach, the Green function formulation is extended to a block matrix system to determine the localization factors for disordered periodic structures.