Studies On The Band Structure Properties Of Elastic Waves Propagating In The Nanoscaled Layered Nearly Periodic Structures

It has been more than fifty years for the studies on the elastic wave’s propagation in the layered media. It has been found that there are band gaps and pass bands in the dispersion curves of the layered periodic complex materials, but this did not catch enough attention. It was after the proposing of the conception of phononic crystals and the extensive engineering applications of its band gap properties in acoustic detectors, filters, waveguides, transducers, etc., that the scientists paid more and more attention on the band gap properties. It is well known that the layered periodic structure is the one-dimensional phononic crystal.With the rapid development of the technology in the fields of communication information, medical engineering, etc., the size of acoustic devices is required to be smaller and smaller. The nano acoustic devices or nano phononic crystals emerged. However in practical cases, disorder in certain degree or completely disorder always exists due to randomly distributed material defaults or manufacture errors during production process. Disorder in the phononic crystals will lead to the wave localization phenomenon which can be used to control the wave propagation. In addition, the quasi-periodic and defected layered structures can be treated as disordered ones deviating quasi-periodically or defect from periodic ones. So in theory, these structures named as nearly periodic structures also can tune the wave propagation.In this thesis, the transfer matrix method based on the nonlocal elastic continuum theory is developed to study the band gap properties for the elastic waves propagating in the nanoscaled layered randomly disordered/quasi-periodic and defected structures. By using the localization factor the following questions are studied:1) Both the anti-plane and mixed in-plane wave modes propagating in arbitrary directions are considered for the nanoscaled layered randomly disordered systems. The disorders in the layer thickness and mass density are discussed. The influence of the disorder degree on the band structures and cut-off frequency are analyzed. The influence of the ratio of the internal to external characteristic lengths on the band structures are also discussed in case of the disorder in the layer thickness.2) The P wave propagating normally in the nanoscaled layered quasi-periodic system which arranged as the Fibonacci sequence are studied. The influences of the layer numbers on the localization factors and the band structures are discussed. New layered systems or arrangement types can be obtained by introducing translational symmetry or/and mirror symmetry. The influences of the arrangement types on the band structures and the cut-off frequency are talked about. At last, for the systems with the defect layer the influences of the location and the ratio of the internal to external characteristic lengths of the defect layer on the band structures are analyzed.