In search of optimal mode localization in two coupled mechanical resonators

Since thirty years ago in 1982 when the concept of mode localization of the two coupled mechanical structures was introduced, there have been many investigations on this phenomenon, leading to applications in various areas, one of which is focused on transducers. This phenomenon is linked closely to Anderson localization theory in condensed matter physics; in fact, it is regarded as one-dimensional representation of the Anderson localization. Later, the configuration of two coupled mechanical structures has been extended to multiple coupled structures having one or more localized modes. All these investigations have pointed out that a weaker coupling factor will result in stronger mode localization; sometimes, it was noted that the weakest coupling has the greatest localization effect. However, it is not sufficiently precise, as the “weakest” coupling is for the structures that are nearly separate. Here, in this article, we conduct a theoretical and experimental study to unveil that there exists an optimal coupling for coupled mechanical structures at which the energy localization effect reaches to the maximum.

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