MODE LOCALIZATION UP TO HIGH-FREQUENCIES IN COUPLED ONE-DIMENSIONAL SUBSYSTEMS

Mode localization in two coupled one-dimensional subsystems is investigated using a wave technique. This approach allows the study of localization behavior at both low and high frequencies, and it leads to a number of new results regarding the frequency dependence of this phenomenon. It is found that upper and lower bounds on the degree of localization (defined as the ratio of the subsystem vibration amplitudes) may be expressed very simply in terms of the reflection coefficient of the coupling element. It is shown that the plot of the degree of localization against frequency consists of a series of phase-shifted interlacing curves that exhibit a cyclic behaviour. It follows that both global and local modes can occur over the whole frequency range. For nearly identical subsystems, modes of each type tend to occur in groups, which has significant implications for high-frequency vibration analysis methods such as Statistical Energy Analysis. The analytical predictions are compared with finite element computations for two coupled beams, and excellent agreement is found. (C) 1995 Academic Press Limited