Evidence for complete surface wave band gap in a piezoelectric phononic crystal

Phononic-Crystal-Based SAW Magnetic-Field Sensors

In this theoretical study, we explore the enhancement of sensing capabilities in surface acoustic wave (SAW)-based magnetic field sensors through the integration of engineered phononic crystals (PnCs). We particularly focus on amplifying the interaction between the SAW and magnetostrictive materials within the PnC structure. Through comprehensive simulations, we demonstrate the synchronization between the SAWs generated by IDTs and the resonant modes of PnCs, thereby leading to an enhancement in sensitivity. Furthermore, we investigate the ΔE effect, highlighting the sensor's responsiveness to changes in external magnetic fields, and quantify its magnetic sensitivity through observable changes in the SAW phase velocity leading to phase shifts at the end of the delay line. Notably, our approach yields a magnetic field sensitivity of approximately S~138 °mT for a delay line length of only 77 µm in homogeneous magnetic fields. Our findings underline the potential of PnCs to advance magnetic field sensing. This research offers insights into the integration of engineered materials for improved sensor performance, paving the way for more effective and accurate magnetic field detection solutions.

Numerical Investigation of Phononic Crystal Based Film Bulk Acoustic Wave Resonators

Film bulk acoustic resonator (FBAR)-based filters have attracted great attention because they can be used to build high-performance RF filters with low cost and small device size. Generally, FBARs employ the air cavity and Bragg mirror to confine the acoustic energy within the piezoelectric layer, so as to achieve high quality factors and low insertion loss. Here, two-dimensional (2D) phononic crystals (PhCs) are proposed to be the acoustic energy reflection layer for an FBAR (PhC-FBAR). Four kinds of PhC structures are investigated, and their bandgap diagrams and acoustic wave reflection coefficients are analyzed using the finite element method (FEM). Then, the PhCs are used as the acoustic wave reflectors at the bottom of the piezoelectric stack, with high reflectivity for elastic waves in the specific frequency range. The results show that the specific PhC possesses a wide bandgap, which enables the PhC-FBAR to work at a broad frequency range. Furthermore, the impedance spectra of PhC-FBARs are very smooth with few spurious modes, and the quality factors are close to those of traditional FBARs with air cavities, showing the application potential of the PhC-FBAR filters with wide bandwidth and high power capability.

Tunable Graphene Phononic Crystal

In the field of phononics, periodic patterning controls vibrations and thereby the flow of heat and sound in matter. Bandgaps arising in such phononic crystals (PnCs) realize low-dissipation vibrational modes and enable applications toward mechanical qubits, efficient waveguides, and state-of-the-art sensing. Here, we combine phononics and two-dimensional materials and explore tuning of PnCs via applied mechanical pressure. To this end, we fabricate the thinnest possible PnC from monolayer graphene and simulate its vibrational properties. We find a bandgap in the megahertz regime within which we localize a defect mode with a small effective mass of 0.72 ag = 0.002 m_physical. We exploit graphene's flexibility and simulate mechanical tuning of a finite size PnC. Under electrostatic pressure up to 30 kPa, we observe an upshift in frequency of the entire phononic system by ∼350%. At the same time, the defect mode stays within the bandgap and remains localized, suggesting a high-quality, dynamically tunable mechanical system.

Narrow Band Solid-Liquid Composite Arrangements: Alternative Solutions for Phononic Crystal-Based Liquid Sensors

Periodic elastic composite structures attract great attention. They offer the ability to design artificial properties to advance the control over the propagation of elastic/acoustic waves. In previous work, we drew attention to composite periodic structures comprising liquids. It was shown that the transmission spectrum of the structure, specifically a well-isolated peak, follows the material properties of liquid constituent in a distinct manner. This idea was realized in several liquid sensor concepts that launched the field of phononic crystal liquid sensors. In this work we introduce a novel concept—narrow band solid-liquid composite arrangements. We demonstrate two different concepts to design narrow band structures, and show the results of theoretical studies and results of experimental investigations that confirm the theoretical predictions. This work extends prior studies in the field of phononic crystal liquid sensors with novel concepts and results that have a high potential in a field of volumetric liquid properties evaluation.

One-step polymeric phononic crystal manufacture

A versatile system to construct bulk polymeric phononic crystals by using acoustic waves is described. In order to fabricate this material, a customised cavity device fitted with a ∼2 MHz acoustic transducer and an acoustic reflector is employed for the acoustic standing wave creation in the device chamber. The polymer crystal is formed when the standing waves are created during the polymerisation process. The resulting crystals are reproduced into the shape of the tunable device cavity with a unique periodic feature. The separation is related to the applied acoustic wave frequency during the fabrication process and each unit cell composition was found to be made up to two material phases. To assess the acoustic properties of the polymer crystals their average acoustic velocity is measured relative to monomer solutions of different concentrations. It is demonstrated that one of the signature characteristics of phononic crystal, the slow wave effect, was expressed by this polymer. Furthermore the thickness of a unit cell is analysed from images obtained with microscope. By knowing the thickness the average acoustic velocity is calculated to be 1538 m/s when the monomer/cross-linker concentration is 1.5 M. This numerical calculation closely agrees with the predicted value for this monomer/cross-linker concentration of 1536 m/s. This work provides a methodology for rapid accessing a new type of adaptable phononic crystal based on flexible polymers.

Wide Acoustic Bandgap Solid Disk-Shaped Phononic Crystal Anchoring Boundaries for Enhancing Quality Factor in AlN-on-Si MEMS Resonators

This paper demonstrates the four fold enhancement in quality factor (Q) of a very high frequency (VHF) band piezoelectric Aluminum Nitride (AlN) on Silicon (Si) Lamb mode resonator by applying a unique wide acoustic bandgap (ABG) phononic crystal (PnC) at the anchoring boundaries of the resonator. The PnC unit cell topology, based on a solid disk, is characterized by a wide ABG of 120 MHz around a center frequency of 144.7 MHz from the experiments. The resulting wide ABG described in this work allows for greater enhancement in Q compared to previously reported PnC cell topologies characterized by narrower ABGs. The effect of geometrical variations to the proposed PnC cells on their corresponding ABGs are described through simulations and validated by transmission measurements of fabricated delay lines that incorporate these solid disk PnCs. Experiments demonstrate that widening the ABG associated with the PnC described herein provides for higher Q.

Lithium Niobate Phononic Crystals for Tailoring Performance of RF Laterally Vibrating Devices

This paper reports the first demonstration of phononic crystals (PnCs) in suspended lithium niobate thin films, which exhibit band gaps for tailoring the performance of laterally vibrating devices. Transmission and reflection properties of lithium niobate PnCs for both shear-horizontal (SH0) and length-extensional (S0) modes have been investigated and subsequently explored in two applications. In the first case, PnC-embedded delay lines were designed for filtering with stopbands, while in the second case, PnC-bounded resonators were implemented for spurious mode suppression. Equivalent circuit models incorporating acoustic scattering parameters of the designed PnCs and Mason's model of the transducers have been built for each application. Benchmarked to reference devices without PnCs, the measured PnCs embedded in delay lines show 20-dB attenuation in the stopbands and less than 2-dB loss in the passbands for the SH0 mode, and 30-dB attenuation in the stopbands and less than 10-dB loss in the passbands for the S0 mode. The fabricated piezoelectric PnC-bounded resonator has shown a quality factor of 434 at 142.7 MHz with undesired spurious modes significantly suppressed. These demonstrations show that lithium niobate PnCs for laterally vibrating devices can potentially lead to wideband and low-loss acoustic functions for radio frequency signal processing.

A highly attenuating and frequency tailorable annular hole phononic crystal for surface acoustic waves

Surface acoustic wave (SAW) devices are widely used for signal processing, sensing and increasingly for lab-on-a-chip applications. Phononic crystals can control the propagation of SAW, analogous to photonic crystals, enabling components such as waveguides and cavities. Here we present an approach for the realisation of robust, tailorable SAW phononic crystals, based on annular holes patterned in a SAW substrate. Using simulations and experiments, we show that this geometry supports local resonances which create highly attenuating phononic bandgaps at frequencies with negligible coupling of SAWs into other modes, even for relatively shallow features. The enormous bandgap attenuation is up to an order-of-magnitude larger than that achieved with a pillar phononic crystal of the same size, enabling effective phononic crystals to be made up of smaller numbers of elements. This work transforms the ability to exploit phononic crystals for developing novel SAW device concepts, mirroring contemporary progress in photonic crystals.

The control and manipulation of propagating sound waves on a surface has applications in on-chip signal processing and sensing. Here, Ash et al. deviate from standard designs and fabricate frequency tailorable phononic crystals with an order-of-magnitude increase in attenuation.

Engineered metabarrier as shield from seismic surface waves

Resonant metamaterials have been proposed to reflect or redirect elastic waves at different length scales, ranging from thermal vibrations to seismic excitation. However, for seismic excitation, where energy is mostly carried by surface waves, energy reflection and redirection might lead to harming surrounding regions. Here, we propose a seismic metabarrier able to convert seismic Rayleigh waves into shear bulk waves that propagate away from the soil surface. The metabarrier is realized by burying sub-wavelength resonant structures under the soil surface. Each resonant structure consists of a cylindrical mass suspended by elastomeric springs within a concrete case and can be tuned to the resonance frequency of interest. The design allows controlling seismic waves with wavelengths from 10-to-100 m with meter-sized resonant structures. We develop an analytical model based on effective medium theory able to capture the mode conversion mechanism. The model is used to guide the design of metabarriers for varying soil conditions and validated using finite-element simulations. We investigate the shielding performance of a metabarrier in a scaled experimental model and demonstrate that surface ground motion can be reduced up to 50% in frequency regions below 10 Hz, relevant for the protection of buildings and civil infrastructures.

Level repulsion of GHz phononic surface waves in quartz substrate with finite-depth holes

This paper presents numerical and experimental results on the level repulsion of gigahertz surface acoustic waves in an air/ST-cut quartz phononic structure with finite-depth holes. The colorful dispersion with the parameter of the in-plane (sagittal plane) ratio of polarization was adopted to determine the Rayleigh wave bandgap induced by the level repulsion. The results of numerical analyses showed that the frequency and width of the bandgap induced by the level repulsion strongly depend on the geometry of the air holes in the phononic structure. In the experiment, a pair of slanted interdigital transducers with frequency in the gigahertz range was designed and fabricated to generate and receive broadband Rayleigh waves, whereas the reactive ion etching process with electron-beam lithography was used to fabricate submicrometer phononic structures. The measured results of the bandgap induced by the level repulsion agreed favorably with the numerical prediction.

Investigation of complete bandgaps in a piezoelectric slab covered with periodically structured coatings

The propagation of elastic waves in a piezoelectric slab covered with periodically structured coatings or the so-called stubbed phononic crystal slab is investigated. Four different models are selected and the effects of distribution forms and geometrical parameters of the structured coatings on complete bandgaps are discussed. The phononic crystal slab with symmetric coatings can generate wider complete bandgaps while that with asymmetric coatings is favorable for the generation of multi-bandgaps. The complete bandgaps, which are induced by locally resonant effects, change significantly as the geometry of the coatings changes. Moreover, the piezoelectric effects benefit the opening of the complete bandgaps.

Propagation of shear elastic and electromagnetic waves in one dimensional piezoelectric and piezomagnetic composites

Coupled shear (SH) elastic and electromagnetic (EM) waves propagating oblique to a one dimensional periodic piezoelectric and piezomagnetic composite are investigated using the transfer matrix method. Closed-form expression of the dispersion relations is derived. We find that the band structures of the periodic composite show simultaneously the features of phononic and photonic crystals. Strong interaction between the elastic and EM waves near the center of the Brillouin zone (i.e., phonon-polariton) is revealed. It is shown the elastic branch of the band structures is more sensitive to the piezoelectric effect while the phonon-polariton is more sensitive to the piezomagnetic effect of the composite.

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

We propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars' head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes.

Monolithic phononic crystals with a surface acoustic band gap from surface phonon-polariton coupling

We theoretically and experimentally demonstrate the existence of complete surface acoustic wave band gaps in surface phonon-polariton phononic crystals, in a completely monolithic structure formed from a two-dimensional honeycomb array of hexagonal shape domain-inverted inclusions in single crystal piezoelectric Z-cut lithium niobate. The band gaps appear at a frequency of about twice the Bragg band gap at the center of the Brillouin zone, formed through phonon-polariton coupling. The structure is mechanically, electromagnetically, and topographically homogeneous, without any physical alteration of the surface, offering an ideal platform for many acoustic wave applications for photonics, phononics, and microfluidics.

Phonon waveguides for electromechanical circuits

Nanoelectromechanical systems (NEMS), utilizing localized mechanical vibrations, have found application in sensors, signal processors and in the study of macroscopic quantum mechanics. The integration of multiple mechanical elements via electrical or optical means remains a challenge in the realization of NEMS circuits. Here, we develop a phonon waveguide using a one-dimensional array of suspended membranes that offers purely mechanical means to integrate isolated NEMS resonators. We demonstrate that the phonon waveguide can support and guide mechanical vibrations and that the periodic membrane arrangement also creates a phonon bandgap that enables control of the phonon propagation velocity. Furthermore, embedding a phonon cavity into the phonon waveguide allows mobile mechanical vibrations to be dynamically switched or transferred from the waveguide to the cavity, thereby illustrating the viability of waveguide-resonator coupling. These highly functional traits of the phonon waveguide architecture exhibit all the components necessary to permit the realization of all-phononic NEMS circuits.

Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves

We demonstrate the experimental realization of a multiresonant metamaterial for Lamb waves, i.e., elastic waves propagating in plates. The metamaterial effect comes from the resonances of long aluminum rods that are attached to an aluminum plate. Using time-dependent measurements, we experimentally prove that this metamaterial exhibits wide band gaps as well as sub- and suprawavelength modes for both a periodic and a random arrangement of the resonators. The dispersion curve inside the metamaterial is predicted through hybridizations between flexural and compressional resonances in the rods and slow and fast Lamb modes in the plate. We finally underline how the various degrees of freedom of such system paves the way to the design of metamaterials for the control of Lamb waves in unprecedented ways.

Experiments on seismic metamaterials: molding surface waves

Materials engineered at the micro- and nanometer scales have had a tremendous and lasting impact in photonics and phononics. At much larger scales, natural soils civil engineered at decimeter to meter scales may interact with seismic waves when the global properties of the medium are modified, or alternatively thanks to a seismic metamaterial constituted of a mesh of vertical empty inclusions bored in the initial soil. Here, we show the experimental results of a seismic test carried out using seismic waves generated by a monochromatic vibrocompaction probe. Measurements of the particles' velocities show a modification of the seismic energy distribution in the presence of the metamaterial in agreement with numerical simulations using an approximate plate model. For complex natural materials such as soils, this large-scale experiment was needed to show the practical feasibility of seismic metamaterials and to stress their importance for applications in civil engineering. We anticipate this experiment to be a starting point for smart devices for anthropic and natural vibrations.

A GaAs phononic crystal with shallow noncylindrical holes

A square lattice of shallow, noncylindrical holes in GaAs is shown to act as a phononic crystal (PnC) reflector. The holes are produced by wet-etching a GaAs substrate using a citric acid:H2O2 etching procedure and a photolithographed array pattern. Although nonuniform and asymmetric etch rates limit the depth and shape of the phononic crystal holes, the matrix acts as a PnC, as demonstrated by insertion loss measurements together with interferometric imaging of surface acoustic waves propagating on the GaAs surface. The measured vertical displacement induced by surface phonons compares favorably with finite-difference time-domain simulations of a PnC with rounded-square holes.

25th anniversary article: ordered polymer structures for the engineering of photons and phonons

The engineering of optical and acoustic material functionalities via construction of ordered local and global architectures on various length scales commensurate with and well below the characteristic length scales of photons and phonons in the material is an indispensable and powerful means to develop novel materials. In the current mature status of photonics, polymers hold a pivotal role in various application areas such as light-emission, sensing, energy, and displays, with exclusive advantages despite their relatively low dielectric constants. Moreover, in the nascent field of phononics, polymers are expected to be a superior material platform due to the ability for readily fabricated complex polymer structures possessing a wide range of mechanical behaviors, complete phononic bandgaps, and resonant architectures. In this review, polymer-centric photonic and phononic crystals and metamaterials are highlighted, and basic concepts, fabrication techniques, selected functional polymers, applications, and emerging ideas are introduced.

Analysis of signals propagating in a phononic crystal PZT layer deposited on a silicon substrate

The design of a stop-band filter constituted by a periodically patterned lead zirconate titanate (PZT) layer, polarized along its thickness, deposited on a silicon substrate and sandwiched between interdigitated electrodes for emission/reception of guided elastic waves, is investigated. The filter characteristics are theoretically evaluated by using finite element simulations: dispersion curves of a patterned PZT layer with a specific pattern geometry deposited on a silicon substrate present an absolute stop band. The whole structure is modeled with realistic conditions, including appropriate interdigitated electrodes to propagate a guided mode in the piezoelectric layer. A robust method for signal analysis based on the Gabor transform is applied to treat transmitted signals; extract attenuation, group delays, and wave number variations versus frequency; and identify stop-band filter characteristics.

Split-mode ultrasonic transducer

A split-mode ultrasonic transducer is investigated in both theory and experiment. This transducer is a two-dimensional structure of periodically poled domains in a ferroelectric wafer with free surfaces. The acoustic vibrations are excited by a radio frequency electric current applied along the length of the wafer, which allows the basal-plane surfaces to be free of metal coatings and thus ready for further biomedical applications. A specific physical property of this transducer consists of the multiple acousto-electric resonances, which occur due to an acoustic mode split when the acoustic half-wavelength is equal to the domain length. Possible applications include ultrasonic generation and detection at the micro-scale, intravascular sonification and visualization, ultrasound therapy of localized small areas such as the eye, biomedical applications for cell cultures, and traditional nondestructive testing including bones and tissues. A potential use of a non-metallized wafer is a therapeutic application with double action that is both ultrasound itself and an electric field over the wafer. The experimental measurements and theoretical calculations are in good agreement.

Experimental and numerical study of evanescent waves in the mini stopband of a 1D phononic crystal

This paper deals with the analysis of the guided evanescent waves in stopbands of a 1D phononic crystal (PC). A new numerical implementation is shown in order to get the complex values of the wavenumbers in a frequency range where a gap occurs. The considered phononic system is an aluminum plate with a one-dimensional sinusoidal grating. For this structure a mode-gap (mini stopband) occurs at low frequency: it involves the two fundamental Lamb modes A(0) and S(0). The numerical study is performed by using a finite element method (ATILA code). The experiments deal with a finite length grating and evanescent waves are characterized at the vicinity of the mini stopband.

Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted considerable interest because of the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures have started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works related to phononic plate waves which have recently been published by the authors and coworkers. Theoretical and experimental studies of Lamb waves in 2-D PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2-D PC plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are addressed. These methods were applied to study the complete band gaps of Lamb waves, characteristics of the propagating and localized wave modes, and behavior of anomalous refraction, called negative refraction, in the PC plates. The theoretical analyses demonstrated the effects of PC-based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and on the frequencies of waveguide and cavity modes. On the experimental side, the design and fabrication of a silicon-based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity are discussed. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.

Controlling the transmission of ultrahigh frequency bulk acoustic waves in silicon by 45° mirrors

In this paper, we present a feasible microsystem in which the direction of localized ultrahigh frequency (∼1GHz) bulk acoustic wave can be controlled in a silicon wafer. Deep etching technology on the silicon wafer makes it possible to achieve high aspect ratio etching patterns which can be used to control bulk acoustic wave to transmit in the directions parallel to the surface of the silicon wafer. Passive 45° mirror planes obtained by wet chemical etching were employed to reflect the bulk acoustic wave. Zinc oxide (ZnO) thin film transducers were deposited by radio frequency sputtering with a thickness of about 1μm on the other side of the wafer, which act as emitter/receptor after aligned with the mirrors. Two opponent vertical mirrors were inserted between the 45° mirrors to guide the transmission of the acoustic waves. The propagation of the bulk acoustic wave was studied with simulations and the characterization of S(21) scattering parameters, indicating that the mirrors were efficient to guide bulk acoustic waves in the silicon wafer.

Plate wave stop-bands in periodically poled lithium niobate

The dispersion curves of four lowest plate acoustic waves (PAWs) in the ZX cut of a periodically poled lithium niobate (PPLN) wafer are computed numerically and investigated experimentally. Experiment is in agreement with simulated dispersion curves. Calculations and measurements reveal the stop-bands in the dispersion curves of the PAW modes in PPLN despite a wafer that has uniform mechanical properties. At a specific wave number, within the frequencies of the stop-bands, the acoustic modes do not propagate.

Band gaps of lamb waves in one-dimensional piezoelectric composite plates: effect of substrate and boundary conditions

We theoretically study the band structures of Lamb waves in one-dimensional phononic crystal plates consisting of piezoelectric ceramics placed periodically in epoxy with epoxy or piezoelectric ceramic substrate by the virtual plane wave expansion method. The dependences of the widths and starting frequencies of first band gaps (FBG) on the substrate's thickness, the filling fraction, and the lattice spacing are calculated for different materials of substrate under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). The FBG width decreases gradually as the substrate's thickness increases and the FBG starting frequency increases progressively as the thickness increases on the whole. The FBG widths and starting frequencies with SC are always larger than with OC. Our research shows that it is possible to control the width and starting frequency of the FBG in the engineering according to need by choosing suitable values of the substrate's thickness, the filling fraction, and the lattice spacing.

Phononic crystals based on LiNbO3 realized using domain inversion by electron-beam irradiation

We report in this paper about the realization of domain inversion in z-cut lithium niobate by electron beam irradiation in order to perform phononic crystals. The fabrication of these phononic crystals on z-cut LiNbO3, which is, in our case, a periodic repetition of voids and LiNbO3, was achieved by domain inversion followed by wet etching, taking advantage of the large difference in etching rate between z+ and z- faces. A pertinent choice of irradiation conditions such as accelerating voltage, beam current, and charge density was determined and optimized. Two-dimensional structures at the micrometer scale were then realized on z-cut LiNbO3. We demonstrate the achievement of hexagons with diameters between 2 microm and 18 microm, with a very important depth close to 30 microm, which depends on the etching time and the hole size. The obtained structures, which exhibit a filling fraction varying from 1% to 64%, were characterized before etching by polarizing microscope to visualize the inverted domains. After HF etching, scanning electron microscopy was used to observe the obtained phononic structures. Taking into account the obtained filling fraction values and the size of created hexagons, the frequency band gap of these structures is expected at a range of 200 to 350 MHz. As expected in this frequency range, we have proven experimentally the existence of the phononic band gap on z-cut LiNbO3 by combination of a realized phononic crystal with a surface acoustic wave (SAW) device.

Waveguiding inside the complete band gap of a phononic crystal slab

The propagation of acoustic waves in a square-lattice phononic crystal slab consisting of a single layer of spherical steel beads in a solid epoxy matrix is studied experimentally. Waves are excited by an ultrasonic transducer and fully characterized on the slab surface by laser interferometry. A complete band gap is found to extend around 300 kHz, in good agreement with theoretical predictions. The transmission attenuation caused by absorption and band gap effects is obtained as a function of frequency and propagation distance. Well confined acoustic wave propagation inside a line-defect waveguide is further observed experimentally.

The band gaps of plate-mode waves in one-dimensional piezoelectric composite plates: polarizations and boundary conditions

Theoretical studies are presented for the band structures of plate-mode waves in a one-dimensional (1-D) phononic crystal plate consisting of piezoelectric ceramics placed periodically in an epoxy substrate. The dependences of the widths and starting frequencies of first band gaps (FBG) on the filling fraction and the thickness to lattice pitch ratio are calculated for different polarizations of piezoelectric ceramics under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). We found that the FBG always is broadened by polarizing piezoelectric ceramics, and the FBG widths with SC always are larger than that with OC for the same polarization. Our research shows that there are three critical parameters which determine the FBG: the polarized directions, the filling fraction, and the ratio of the plate thickness to the lattice pitch, respectively. Therefore, we can control the width and starting frequency of the FBG in the engineering according to need by choosing these parameters of the system.

Increased efficiency of surface wave stimulation on the inaccessible side of a thick isotropic plate with superimposed periodicity

Because of the growing number of applications of phononic crystals and other periodic structures, there is a renewed and growing interest in understanding the interaction of ultrasound with periodically corrugated surfaces. This paper presents a theoretical investigation of the transformation of ultrasound incident from the solid side onto a solid-liquid periodically corrugated interface. It is shown that it is possible to tailor the shape of a corrugated surface with given periodicity such that there is a significant amount of energy transformed into Scholte-Stoneley waves than if pure saw-tooth or sine-shaped surfaces were used. This permits the fabrication of periodic structures that can be patched on or engraved in body parts of a construction and enables efficient generation of Scholte-Stoneley waves. The study is performed for incident homogeneous plane waves as well as for bounded beams. Incident longitudinal waves are studied as well as incident shear waves.

Complete band gaps in two-dimensional phononic crystal slabs

The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, d, to the lattice period, a. Especially, we have explored how these absolute band gaps close up as the parameter d/a increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.