A-Li Chen

Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures

In this paper, anti-plane transverse wave propagation in nanoscale periodic layered piezoelectric structures is studied. The localization factor is introduced to characterize the wave propagation behavior. The transfer matrix method based on the nonlocal piezoelectricity continuum theory is used to calculate the localization factor. Additionally, the stiffness matrix method is applied to compute the wave transmission spectra. A cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure. The size effect or the influence of the ratio of the internal to external characteristic lengths on the cut-off frequency and the wave propagation behavior are investigated and discussed.

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.

Elastic Wave Propagation in Anisotropic and Functionally Graded Layered Phononic Crystals: Band-Gaps, Pass-Bands and Low Transmission Pass-Bands

This paper describes a mathematical model of plane wave propagation in anisotropic and functionally graded layered phononic crystals with finite and infinite number of unit-cells. Classification of pass-bands and band-gaps is presented based on asymptotic analysis of the wave-fields in periodic layered structures. Two kinds of band-gaps where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges in which the transmission is low enough for engineering applications, but it does not tend to zero exponentially with the number of unit-cells approaching infinity. The results of the numerical simulation are presented in order to demonstrate wave propagation phenomena. The influence of the anisotropy and functionally graded interlayers on the band-gaps and pass-bands is analysed.

Wave motion in piezoelectric layered phononic crystals with and without electroded surfaces

Plane wave excitation and propagation in layered piezoelectric phononic crystals with and without given electric potentials at the metallic interfaces is studied in the present work. Two kinds of piezoelectric layered phononic crystals are considered: an infinite periodic structure and a periodic structure surrounded by two half-spaces. The influences of electrodes on wave transmission, band-gaps and pass-bands are investigated.

Band-gaps and low transmission pass-bands in layered piezoelectric phononic crystals

In-plane wave propagation in layered piezoelectric phononic crystals composed of functionally graded interlayers arisen from the solid diffusion is considered in the present work. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered piezoelectric functionally graded phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the wave transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of the unit-cells tends to infinity. Wave-fields, low transmission pass-bands and band-gaps in layered and functionally graded piezoelectric phononic crystals are analyzed.

Influence of disorder on the defect states of a phononic crystal with a point defect

The supercell-based plane wave expansion method is used to study the effects of random disorders on the defect states of a two-dimensional solid-solid phononic crystal with a point defect. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The radius disorder and location disorder are concerned. The influences of the disorder degree on the defect states for both anti-plane and in-plane wave modes are investigated and discussed. It is found that, with increase of the disorder degree, the frequencies and localization degree of the defect bands will change. The influence of the disorder on the defect states is more pronounced for the in-plane modes than for the anti-plane modes. Radius disorder has more influences on the defect bands than the location disorder does. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on behaviors of elastic wave propagating in wave filters, as well as the tuning of the point defect states.

Study on band structures and localization phenomenon of twodimensional phononic crystals with one-dimensional quasi-periodicity

By viewing the quasi-periodicity as the deviation from the periodicity in a particular way, the quasi phononic crystal that has quasi-periodicity (Fibonacci sequence) in one direction and translational symmetry in the other direction is considered. The band structures are characterized by localization factors which are calculated by using the plane-wave-based transfer-matrix method. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional phononic crystals with one-dimensional quasi-periodicity. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.