Phononic Plate Research Articles

Study of full band gaps and propagation of acoustic waves in two-dimensional piezoelectric phononic plates

Acoustic wave propagation in periodic structures composed of multi-constituents, namely the phononic crystals (PCs), has received much attention in the past decade. Recently, PCs constructed in the form of plate structures with two-dimensional lattices have been investigated, and some important phenomena, such as the full band-gap and waveguiding effects, induced by the periodicities of the phononic plates were reported. One of the virtues using Lamb waves is to perfectly confine the acoustic energy within the plate thickness and guided in structures with only 2D lattices rather than 3D lattices; however, the additional free surfaces derive much more complicated characteristics which are still awaiting study further. In this study, we investigate the band-gap and propagation properties of waves in two-dimensional phononic plates that consist of either elastic or piezoelectric materials by employing a revised full 3D plane wave expansion (PWE) method and so on. To apply the PWE method efficiently, Fourier expansions are performed in the thickness direction for an imaginary 3D periodic structure by stacking the phononic plates and vacuum layers alternatively. Moreover, effects of piezoelectricity, lattices, and filling ratios on band gaps are discussed.

Calculations of Lamb wave band gaps and dispersions for piezoelectric phononic plates using mindlin's theory-based plane wave expansion method

Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.

Large Lamb wave band gap in phononic crystals thin plates

We suggest that Lamb wave band gaps in one-dimensional phononic crystals can be substantially enlarged by using multiple heterostructures which consist of several pieces of phononic crystal with different ratios of the thickness to the lattice period. This is possible because each substructure shows a different band gap and the band structure of a Lamb wave is strongly affected by the ratio of the plate thickness to the lattice period. This effect has been demonstrated by using finite element simulations on two different one-dimensional systems.

Lamb waves in binary locally resonant phononic plates with two-dimensional lattices

The authors study the propagation of Lamb waves in two-dimensional locally resonant phononic-crystal plates, composed of periodic soft rubber fillers in epoxy host with a finite thickness. Our calculations are based on the efficient plane wave expansion formulation which utilized Mindlin’s plate theory. Calculated results show that the low-frequency gaps of Lamb waves are opened up by the localized resonance mechanism. The resonant frequencies of flexure-dominated plate modes are significantly dependent not only on the radius of circular rubber fillers but also on the plate thickness. The properties of localized resonance are qualitatively analogous to the vibration of a circular thin plate.

Large one-dimensional band gaps in three-component phononic crystals plates

Using the plane-wave expansion method, we study the propagation of Lamb wave mode in three-component phononic crystals plates. The influence of filling fraction, material parameters and especially the ratio of the thickness of the plates to the lattice period on the band gaps of Lamb wave mode are analyzed by numerical simulations. The optimum gap is obtained by tuning the thickness of the plates and the filling fraction.

Propagation of guided elastic waves in 2D phononic crystals

The phononic band structure of two-dimensional phononic guides is numerically studied. A plane wave expansion method is used to calculate the dispersion relations of guided elastic waves in these periodic media, including 2D phononic plates and thin layered periodic arrangements. We show that, for any guided elastic wave, Lamb or generalised Lamb modes, stop bands appear in the dispersion curves, displaying a phononic band structure in both cases.

VIBRATION PROPERTY OF TWO DIMENSION PHONONIC CRYSTALS THIN PLATE

Based on the vibrational equation of the thin plate, the band structure for the two-dimensional phononic crystals thin plate composed of two kind of material is provided by using plane wave expansion method. The composite materials thin plate exhibiting vibration band gap is found. But it is different from the xy mode band structure of two-dimensional phononic crystals. For the finite periodic structure thin plate, the vibration frequency response by finite element method is simulated. The frequency ranges of sharp drop in frequency response curve show good agreement with the band gaps. The wave field distribution of the frequency both in band gap and out of band gap is calculated in order to describe the vibration property of the phononic crystal thin plate. The existence of band gaps in the periodic structures thin plate gives a new idea in vibration control application of phononic crystals.

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We numerically investigate the propagation characteristics of Lamb waves in composite plate-type acoustic metamaterial constituted of one-side cylindrical stubs deposited on a two-dimensional binary locally resonant phononic plate. Numerical results show that, with the introduction of composite plate-type acoustic metamaterial, locally resonant band gap shifts to lower frequency, and a significant enlargement of the relative bandwidth by a factor of 3 can be obtained, compared to one-side locally resonant stubbed plates. We show that the band gap enlargement is attributed to the coupling between the local resonant Lamb modes of two-dimensional phononic plate and the resonant modes of the stubs.

Scandium: SIR W. Crookes. ( Phil. Trans. Roy. Soc., A2O9, 15.)

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80 μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.