3104 G. G. Brown, Dept. of Mech. Eng. and Appl. Mech., Univ. of Michigan, Ann Harbor, MI 48109-2125
Matthew P. Castanier
Wan J. Chen
For disordered mono-coupled systems, wave localization causes an exponential spatial wave amplitude decay, with the associated decay constant known as the localization factor. In multi-coupled structural systems, with multiple wave types, wave conversions complicate the analysis of localization phenomena. In this work, Lyapunov exponents of the system wave transfer matrix are used to analyze localization in multi-coupled disordered systems. Lyapunov exponents are a measure of the exponential growth rate of wave vectors. In a mono-coupled system, the largest Lyapunov exponent is equivalent to the localization factor. Lyapunov exponents are calculated numerically and, for the case of weak disorder, approximated by perturbation techniques. Three examples are presented. First, a representative mono-coupled system is considered. The largest Lyapunov exponent is calculated and compared with localization factors found by Monte Carlo as well as perturbation methods. Then bi-coupled system, a multi-span beam resting on flexible supports, is examined. Lyapunov exponents are calculated and compared with the wave amplitude decay found in a single realization of the disordered system. Finally, a truss beam, which features four types of waves is examined, and the physical significance of the Lyapunov exponents is discussed.