On acoustic band gaps in homogenized piezoelectric phononic materials (original) (raw)
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Numerical simulation of acoustic band gaps in homogenized elastic composites
International Journal of Engineering Science, 2009
The dispersion of acoustic or elastodynamic waves in elastic composites are studied using the homogenized model. We consider heterogeneous periodic structures consisting of soft but heavy inclusions embedded in a stiffer matrix. By virtue of the asymptotic homogenization technique in conjunction with an appropriate scaling of the elasticity coefficients in the inclusions, the limit model exhibits the band gaps in wave propagation due to the negative effective mass. This phenomenon can be revealed by studying guided waves in discrete mass-spring structures with scaledependent parameters. The main purpose of the paper is to justify the applicability of the homogenized model of the heterogeneous elastic continuum for prediction of the band gaps in structures featured by a finite scale of heterogeneities. We show the band gaps numerical identification and discus aspects of anisotropy, microstructure geometry and material contrast between the constituents in the context of the long wave dispersion.
Acoustic wave transmission through piezoelectric structured materials
Ultrasonics, 2009
This paper deals with the transmission of acoustic waves through multilayered piezoelectric materials. It is modeled in an octet formalism via the hybrid matrix of the structure. The theoretical evolution with the angle and frequency of the transmission coefficients of ultrasonic plane waves propagating through a partially depoled PZT plate is compared to finite element calculations showing that both methods are in very good agreement. The model is then used to study a periodic stack of 0.65PMN-0.35PT/0.90PMN-0.10PT layers. The transmission spectra are interpreted in terms of a dispersive behavior of the critical angles of longitudinal and transverse waves, and band gap structures are analysed. Transmission measurements confirm the theoretical calculations and deliver an experimental validation of the model.
Modeling wave dispersion and band gaps in heterogeneous elastic media
Applied and Computational Mechanics, 2007
In this paper we report recent developments and results concerning validation of the homogenization approach applied in modeling waves in strongly heterogeneous elastic media. The homogenization limit model is obtained for stationary waves, but can also be used to estimate dispersion properties for long guided waves propagation. Band gaps distribution depends on the material contrast and on the geometrical arrangements in the microstructure. Similarity between discrete structures and heterogeneous continua is used to demonstrate the dispersion phenomena. The modeling approach has been extended to the piezo-phononic materials, which may be useful in designing smart materials. Also problems of optimal shape design at the microscopic level were pursued.
Dispersion features of elastic waves in phononic crystals: finite element analysis
Ferroelectrics, 2019
In this report, we present an investigation of the dispersion properties of the phononic crystal in different lattice, geometries for various piezoelectric materials. We study dispersion properties of the epoxy resin/ piezoelectric based phononic structures in the frequency range by using the finite element method for various lattices, piezoelectric materials and cross-sectional inclusions. The effect of the cross-section of piezoelectric inclusions, lattice geometry and filling factor on the phononic band gap is illustrated. A numerical approach is used to obtain the dispersion properties of the 2D piezoelectric phononic crystals which yields further insight into the phenomenon of the reflection from different families of piezoelectric in relation to the presence of phononic gaps.
Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions
Crystals, 2021
The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and...
Homogenized Phononic Plates and Wave Dispersion
We consider the problem of wave propagation in periodically heterogeneous composite plates with high contrasts in elastic coefficients. The unfolding method of homogenization is applied to obtain limit plate models. Due to the high contrast ansatz in scaling the elasticity coefficients of compliant inclusions, the dispersion properties are retained in the limit when the scale of the microstructure tends to zero. We study two plate models based on the Reissner-Mindlin theory and on the Kirchhoff-Love theory. We show that, when the size of the microstructures tends to zero, the limit homogeneous structure presents, for some wavelengths, a negative "mass density" tensor. This means that there exist intervals of frequencies in which there is no propagation of elastic waves, the so-called band-gaps.
Acoustic band structure of periodic elastic composites
Physical Review Letters, 1993
%'e present the first full band-structure calculations for periodic, elastic composites. For transverse polarization of the vibrations we obtain a "phononic" band gap which extends throughout the Brillouin zone. A complete acoustic gap or a low density of states should have important consequences for the suppression of zero-point motion and for the localization of phonons, and may lead to improvements in transducers and in the creation of a vibrationless environment.
Physical Review E, 2002
The propagation of acoustic waves in a two-dimensional composite medium constituted of a square array of parallel copper cylinders in air is investigated both theoretically and experimentally. The band structure is calculated with the plane wave expansion ͑PWE͒ method by imposing the condition of elastic rigidity to the solid inclusions. The PWE results are then compared to the transmission coefficients computed with the finite difference time domain ͑FDTD͒ method for finite thickness composite samples. In the low frequency regime, the band structure calculations agree with the FDTD results indicating that the assumption of infinitely rigid inclusion retains the validity of the PWE results to this frequency domain. These calculations predict that this composite material possesses a large absolute forbidden band in the domain of the audible frequencies. The FDTD spectra reveal also that hollow and filled cylinders produce very similar sound transmission suggesting the possibility of realizing light, effective sonic insulators. Experimental measurements show that the transmission through an array of hollow Cu cylinders drops to noise level throughout frequency interval in good agreement with the calculated forbidden band.
In this paper, plane wave expansion and stiffness matrix methods are adopted to analyze the dispersion relation of Rayleigh surface acoustic waves in a piezoelectric phononic composite composed of two homogeneous layers (ZnO and AlN) deposited on a onedimensional piezoelectric (111) Si/AlN phononic substrate. The effect of crystallographic orientation of silicon on the dispersion relation is discussed. We found that the width of the gap became larger when the middle layer was introduced. The influence of filling fraction, thicknesses of the film and the middle layer on the band gap width is discussed. In addition, the phase velocity and the electromechanical coupling coefficient for Rayleigh surface modes are calculated versus the filling fraction. A comparison of phononic composite with ZnO/AlN/(111)Si layered structure is presented to deduce the interest of introduction of the phononic substrate.
Phononic band gaps of elastic periodic structures: A homogenization theory study
Physical Review B, 2007
In this study, we investigate the band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry ⌫.