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The miniaturization of electronic devices is an important trend in the development of modern microelectronics information technology. However, when the size of the component or the material is reduced to the micro/nano scale, some size-dependent effects have to be taken into account. In this paper, the wave propagation in nano phononic crystals is investigated, which may have a potential application in the development of acoustic wave devices in the nanoscale. Based on the electric Gibbs free energy variational principle for nanosized dielectrics, a theoretical framework describing the size-dependent phenomenon was built, and the governing equation as well as the dispersion relation derived; the flexoelectric effect, microstructure, and micro-inertia effects are taken into consideration. To uncover the influence of these three size-dependent effects on the width and midfrequency of the band gaps of the waves propagating in periodically layered structures, some related numerical examples were shown. Comparing the present results with the results obtained with the classical elastic theory, we find that the coupled effects of flexoelectricity, microstructure, and micro-inertia have a significant or even dominant influence on the waves propagating in phononic crystals in the nanoscale. With increase in the size of the phononic crystal, the size effects gradually disappear and the corresponding dispersion curves approach the dispersion curves obtained with the conventional elastic theory, which verify the results obtained in this paper. Thus, when we study the waves propagating in phononic crystals in the micro/nano scale, the flexoelectric, microstructure, and micro-inertia effects should be considered.

Waves Propagating in Nano-Layered Phononic Crystals with Flexoelectricity, Microstructure, and Micro-Inertia Effects