### ASA 125th Meeting Ottawa 1993 May

## 2aPA1. Localization and wave conversion phenomena in multi-coupled nearly
periodic structural systems.

**Christophe Pierre
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*3104 G. G. Brown, Dept. of Mech. Eng. and Appl. Mech., Univ. of Michigan,
Ann Harbor, MI 48109-2125
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**Matthew P. Castanier
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Wan J. Chen
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*ADDRESS MISSING
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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.