Abstract

A non-periodic multilayer film was analyzed to show that, despite its non-periodicity, the film exhibits full band-gaps and localized modes at its interfaces, as well as in the sonic composites. The film consists of alternating layers of two different materials that follow a triadic Cantor sequence. The Cantor structure shows extremely low thresholds for subharmonic generation of ultrasonic waves, compared with homogeneous and periodic structures. The coupling between the extended-mode (phonon) and the localized-mode (fracton) vibration regimes explains the generation of full band-gaps, for which there are no propagating Lamb waves. The large enhancement of the nonlinear interaction results from a more favorable frequency and spatial matching of coupled modes. A full band-gap that excludes Love waves is also analyzed.

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