Scattering from a finite ribbed plate with attached oscillators.

Double layer structures consisting of stainless steel and polymer rods are designed to blur and attenuate Bragg and Bloch-Floquet scattering from a periodically ribbed plate in a given frequency bandwidth. These structures can be considered as ribbed plate-spring-mass systems, the resonance frequencies of which are obtained from random and circular permutations of five basic oscillators. Analytical and finite element methods are used to find their parameters and tank tests have been carried out to ensure the accuracy of the numerical results and validate the relevance of such a model. It has been found that the typical features associated with the periodicity of the ribs are replaced by a "Christmas tree" appearance when the far field pressure backscattered from the model is displayed in the (frequency, aspect angle) plane. An analysis of backscattering patterns is presented and comparisons with Naval Research Laboratory results are made.

Electrical Evidence of the Tunable Electrical Bragg Bandgaps in Piezoelectric Plates.

A piezoelectric plate, poled along its thickness and supporting on its top and bottom surfaces a periodic grating of electrodes, is considered. An analytical model allowing band structure calculation is derived for the first symmetrical mode propagating along the length of the plate. Analytical results show that an electrical Bragg (EB) bandgap can be observed for this mode, depending on the electrical boundary conditions applied on the electrodes. This "EB bandgap" is associated with a discontinuity of the electric field between two successive unit cells. These results are validated with the numerical simulations based on the finite element method. Analytical and numerical results prove that the EB bandgap is highly tunable and can be optimized by changing the crystallographic orientation of the material. A simple tunable filter exploiting this bandgap is designed and fabricated. Experimental results of electrical impedance and electrical potential at the output together with a scanning laser vibrometer analysis are presented, which confirm the theoretical predictions.

Control of elastic wave propagation in one-dimensional piezomagnetic phononic crystals.

Two ways of controlling the acoustic waves propagation by external inductance or capacitance in a one-dimensional (1-D) piezomagnetic phononic crystal are investigated. The structure is made of identical bars, constituted of a piezomagnetic material, surrounded by a coil and connected to an external impedance. A model of propagation of longitudinal elastic waves through the periodic structure is developed and the dispersion equation is obtained. Reflection and transmission coefficients are derived from a 2 × 2 transfer matrix formalism that also allows for the calculation of elastic effective parameters (density, Young modulus, speed of sound, impedance). The effect of shunting impedances is numerically investigated. The results reveal that a connected external inductance tunes the Bragg band gaps of the 1-D phononic crystal. When the elements are connected via a capacitance, a hybridization gap, due to the resonance of the LC circuit made of the piezomagnetic element and the capacitance, coexists with the Bragg band gap. The value of the external capacitance modifies the boundaries of both gaps. Calculation of the effective characteristics of the phononic crystal leads to an analysis of the physical mechanisms involved in the wave propagation. When periodically connected to external capacitances, a homogeneous piezomagnetic stack behaves as a dispersive tunable metamaterial.

Tunable phononic crystals based on piezoelectric composites with 1-3 connectivity.

Phononic crystals made of piezoelectric composites with 1-3 connectivity are studied theoretically and experimentally. It is shown that they present Bragg band gaps that depend on the periodic electrical boundary conditions. These structures have improved properties compared to phononic crystals composed of bulk piezoelectric elements, especially the existence of larger band gaps and the fact that they do not require severe constraints on their aspect ratios. Experimental results present an overall agreement with the theoretical predictions and clearly show that the pass bands and stop bands of the device under study are easily tunable by only changing the electrical boundary conditions applied on each piezocomposite layer.

Theoretical and experimental analyses of tunable Fabry-Perot resonators using piezoelectric phononic crystals.

Theoretical and experimental analyses of piezoelectric stacks submitted to periodical electrical boundary conditions via electrodes are conducted. The presented structures exhibit Bragg band gaps that can be switched on or off by setting electrodes in short or open circuit. The band gap frequency width is determined by the electromechanical coupling coefficient. This property is used to design a Fabry-Perot cavity delimited by a periodic piezoelectric stack. An analytical model based on a transfer matrix formalism is used to model the wave propagation inside the structure. The cavity resonance tunability is obtained by varying the cavity length (i.e., by spatially shifting boundary conditions in the stack). 26% tuning of resonance and antiresonance frequencies with almost constant electromechanical coupling coefficient of 5% are theoretically predicted for an NCE41 resonator. To optimize the device, the influence of various parameters is theoretically investigated. The cavity length, phononic crystal (number and length of unit cells), and transducer position can be adapted to tune the frequency shift and the coupling coefficient. When the transducer is located at a nodal plane of the cavity, the value of the coupling coefficient is 30%. Experimental results are presented and discussed analyzing the effects of damping.

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.

Analysis of elastic waves transmitted through a 2-D phononic crystal exhibiting negative refraction.

A two-dimensional phononic crystal (PC) made of a square lattice of air holes in an aluminum matrix is studied. The band structure calculated in the irreducible Brillouin zone of the PC exhibits a branch with a negative slope that allows negative refraction. This phenomenon has been numerically verified using a prism-shaped PC for plane waves entering the PC with two different incidences. A detailed study of the waves at the exit of the PC shows that the plane wave is reconstructed after several wavelengths. Finally, the description of the refracted waves is interpreted using a point source array, giving information about the angular spreading and the relative amplitude of each refracted beam.

On the physical origin of conical bubble structure under an ultrasonic horn.

The cavitation field generated by an ultrasonic horn at low frequency and high power is known to self-organize into a conical bubble structure. The physical mechanism at the origin of this bubble structure is investigated using numerical simulations and acoustic pressure measurements. The thin bubbly layer lying at horn surface is shown to act as a nonlinear thickness resonator that amplifies acoustic pressure and distorts acoustic waveform. This mechanism explains the self-stabilization of the conical bubble structure as well as the generation of shock wave and the focusing at very short distance.

Modeling of bulk acoustic wave devices built on piezoelectric stack structures: impedance matrix analysis and network representation.

The fundamental electro-acoustic properties of a solid layer are deduced in terms of its impedance matrix (Z) and represented by a network for modeling the bulk acoustic wave devices built on piezoelectric stacked structures. A piezoelectric layer is described by a three-port equivalent network, a nonpiezoelectric layer, and a short- or open-circuit piezoelectric layer by a two-port one. Electrical input impedance of the resonator is derived in terms of the Z-matrix of both the piezoelectric layer and an external load, the unique expression applies whether the resonator is a mono- or electroded-layer or a solidly mounted resonator (SMR). The loading effects of Al-electrodes on the resonating frequencies of the piezoelectric ZnO-layer are analyzed. Transmission and reflection properties of Bragg mirrors are investigated along with the bulk radiation in SMR. As a synthesizing example, a coupled resonator filter (CRF) is analyzed using the associated two-port equivalent network and by calculating the power transmission to a 50Omega-load. The stacked crystal filter is naturally included in the model as a special case of CRF. Combining a comprehensive matrix analysis and an instructive network representation and setting the problem with a full vectorial formalism are peculiar features of the presented approach.

Piezoacoustic wave spectra using improved surface impedance matrix: application to high impedance-contrast layered plates.

Starting from the general modal solutions for a homogeneous layer of arbitrary material and crystalline symmetry, a matrix formalism is developed to establish the semianalytical expressions of the surface impedance matrices (SIM) for a single piezoelectric layer. By applying the electrical boundary conditions, the layer impedance matrix is reduced to a unified elastic form whether the material is piezoelectric or not. The characteristic equation for the dispersion curves is derived in both forms of a three-dimensional acoustic SIM and of an electrical scalar function. The same approach is extended to multilayered structures such as a piezoelectric layer sandwiched in between two metallic electrodes, a Bragg coupler, and a semi-infinite substrate as well. The effectiveness of the approach is numerically demonstrated by its ability to determine the full spectra of guided modes, even at extremely high frequencies, in layered plates comprising up to four layers and three materials. Negative slope in f-k curve for some modes, asymptotic behavior at short wavelength regime, as well as wave confinement phenomena made evident by the numerical results are analyzed and interpreted in terms of the surface acoustic waves and of the interfacial waves in connection with the bulk waves in massive materials.

Ultrasonic cavitation in thin liquid layers.

The generation of ultrasonic cavitation in a thin liquid layer trapped between a large radiating surface and a hard reflector and bounded laterally by a gas-liquid interface is investigated. The theoretical analysis predicts that a large amplification of the acoustical pressure is obtained with this configuration. Experiments are conducted by driving the layer with horn-type transducers having a large emitting surface. Ultrasonic cavitation is obtained in a broad frequency range at low input intensity due to the amplification effect. Erosion tests on metallic foils demonstrate the existence of a region of intense cavitation activity which can be localised by controlling the input intensity.

Experimental and theoretical investigation of the mean acoustic pressure in the cavitation field.

The cavitation field radiated by a 20 kHz sonotrode-type transducer is experimentally and theoretically analyzed. Special interest is paid to the origin of the strong fluid streaming appearing in low frequency sonoreactors. A new experimental procedure is proposed to evaluate the mean acoustic pressure inside the fluid. This parameter has been quantified for different points and amplitudes. The velocity of the radiating surface is controlled by a laser interferometer and is always sinusoidal. Train wave excitation is used. The pressure wave and amplitude are measured in the tank with a calibrated hydrophone. The acoustic mean pressure is estimated from the total pressure value at the end of the pulse after an adequate filtering. An analytical nonlinear second order model based on the coupling of the equations of the fluid mechanics with the Rayleigh-Plesset equation is developed in order to relate the measured acoustic parameters to the cavitation state of the fluid. The distributions of the fundamental amplitude and mean pressure are calculated as a function of bubble density and bubble size. A qualitative theoretical description of the experimental data is presented. Quantitative differences and model limitations are commented.

Cone-like bubble formation in ultrasonic cavitation field.

A new phenomenon in ultrasonic cavitation field is reported. Cavitation bubbles are observed to self-arrange in a cone-like macrostructure in the vicinity of transducer radiating surface. The cone-like macrostructure is stable while its branch-like pattern microstructure changes rapidly. The structure is constituted by moving bubbles which undergo attractive and repulsive Bjerknes forces caused by high acoustic pressure gradients and strongly nonlinear oscillations of cavitation bubbles. The cone-like bubble structure is a chemically active formation. Its remarkably high activity is confirmed by chemiluminescence experiments.