Sonic Band Research Articles

Tunable Low Frequency Band Gap and Waveguide of Phononic Crystal Plates with Different Filling Ratio

Aiming at solving the NVH problem in vehicles, a novel composite structure is proposed. The new structure uses a hollow-stub phononic-crystal with filled cylinders (HPFC) plate. Any unit in the plate consists of a lead head, a silicon rubber body, an aluminum base as outer column and an opposite arranged inner pole. The dispersion curves are investigated by numerical simulations and the influences of structural parameters are discussed, including traditional hollow radius, thickness, height ratio, and the new proposed filling ratio. Three new arrays are created and their spectrum maps are calculated. In the dispersion simulation results, new branches are observed. The new branches would move towards lower frequency zone and the band gap width enlarges as the filling ratio decreases. The transmission spectrum results show that the new design can realize three different multiplexing arrays for waveguides and also extend the locally resonant sonic band gap. In summary, the proposed HPFC structure could meet the requirement for noise guiding and filtering. Compared to a traditional phononic crystal plate, this new composite structure may be more suitable for noise reduction in rail or road vehicles.

Bulk modulus for fluid-saturated rocks at intermediate frequencies: modification of squirt flow model proposed by Gurevich et al.

SUMMARY Squirt flow is an essential cause of wave dispersion and attenuation in saturated rocks. The squirt flow model, proposed by Gurevich et al., has been widely applied to explain the wave dispersion and associated attenuation for saturated rocks at sonic and seismic frequency bands. In this model, the saturated bulk modulus is obtained by taking the partially relaxed frame bulk modulus as the dry frame modulus into Gassmann's formula with the mineral bulk modulus as the matrix bulk modulus. However, because of the weakening effect of soft pores on rock matrix bulk modulus, the model cannot accurately predict the saturated bulk modulus when the soft-pore fraction (the ratio of the soft porosity to total porosity) becomes large. We modified this model following Gurevich et al. by setting a different boundary condition. The modified squirt flow model can obtain correct saturated bulk modulus for large soft-pore fractions in the full range of frequencies, showing excellent consistency with the predictions of Gassmann, Mavko & Jizba (modified) at both low- and high-frequency limits, respectively. Modelling results show that the saturated bulk moduli and their dispersions calculated by the original and modified models exhibit little difference when the soft-pore fraction is small. Under this condition, the original model is as effective and accurate as the modified one. When the soft-pore fraction becomes larger, the differences in the bulk moduli and their dispersions become substantial, suggesting the original model is not applicable any longer. Furthermore, the differences calculated for the intermediate frequency range is even more obvious than other ranges, suggesting that the modified model should be used to calculate the bulk modulus and the dispersion in this frequency range. In summary, the modified squirt flow model can extend the original model's applicable range in terms of soft-pore fraction and has a potential application in rocks having a relatively large amount of soft-pore fraction such as basalts.

Poles Extraction of Underwater Targets Based on Matrix Pencil Method

The majority of the sonic frequency bands used in active sonar detection and identification are within the resonance region of the target. The poles of target are very important characteristics of the resonance region. This paper analyzes and studies the method of extracting poles by using the matrix Pencil Method. A method which can determine the number of poles of underwater target automatically is proposed. It can average the poles that are gathered to synthesize a point as an alternative pole. Then by setting up a reasonable threshold. The poles with the higher energy in the target echo is extracted as the main pole. Aiming at the problem that the main poles of the target are missing or there are false poles in some directions, the main poles extracted from multiple directions of the target are integrated to obtain the final poles of the target. Finally, to prove the feasibility of proposed novel method echo pole extraction, the experiment was conducted in underwater spherical shell and thin rod in a silencing pool.

Bubbly Water as a Natural Metamaterial of Negative Bulk-Modulus

In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems.

Near-borehole characteristics of hydraulic fractures and fracturing-induced sonic-wave attenuation

The downhole hydraulic fracturing process, besides fracturing formation rocks, generates small, secondary fractures around the borehole, allowing evaluation of the result of fracturing using borehole sonic measurements. We analyzed the near-borehole fracture network from an existing laboratory hydraulic fracturing experiment to study the fracture distribution around the borehole. The result indicates that the fracture distribution exhibits fractal characteristics. The fractal dimension is high in the near-borehole region and decreases away from borehole. Because the fractal dimension increases with fracture density, this indicates that fracturing produces a high fracture-density zone in the near-borehole region. The high concentration of the hydraulic fractures in turn can causes significant attenuation in the sonic-logging waveforms acquired after fracturing. The fracturing-induced sonic attenuation, averaged over the sonic frequency band, can be estimated using a median frequency shift method. Comparison of the attenuation of the fracturing interval with that of an unfractured interval, or with that of the same interval before fracturing allows for evaluating the result of fracturing and the fracture extension along the borehole. The application of the method is demonstrated with field-data examples and validated by comparing results from existing borehole techniques, thus offering a useful technique for evaluating the result of hydraulic fracturing using the borehole sonic-wave attenuation.

On the Monotonicity of the CABARET Scheme Approximating a Scalar Conservation Law with an Alternating Characteristic Field and Convex Flux Function

The monotonicity of the CABARET scheme approximating the quasi-linear scalar conservation law with a convex flux is analyzed. The monotonicity conditions for this scheme are obtained in the areas where the propagation velocity of the characteristics has a constant sign, as well as in the areas of sonic lines, sonic bands, and shock waves, where the propagation velocity of the characteristics of the approximated divergent equation changes sign. The test computations are presented that illustrate these properties of the CABARET scheme.

Manipulating sonic band gaps at will: vibrational density of states in three-dimensional acoustic metamaterial composites

Vibrational properties of elastic composites containing a mass-in-mass microstructure embedded in a solid matrix are numerically studied. Using a lattice model, we investigate the vibrational density of states in three-dimensional composite structures where resonant particles are randomly dispersed. By dispersing such particles in the system, a sonic band gap appears. It is confirmed that this band gap can be introduced in a desired frequency regime by changing the parameters of resonant particles and the frequency width of this band gap can be controlled by varying the concentration of the resonant particles to be dispersed. In addition, multiple sonic band gaps can be realized using different species of resonant particles. These results enable us to suggest an alternative method to fabricate devices that can inhibit the propagation of elastic waves with specific frequencies using acoustic metamaterials.

Tuning sound with soft dielectrics

Soft dielectric tubes undergo large deformations when subjected to radial voltage. Using the theory of nonlinear electroelasticity, we investigate how voltage-controlled deformations of these tubes in an array alter acoustic wave propagation through it. We show that the propagation is annihilated across a certain audible frequency range, referred to as a sonic band gap. We carry out a numerical study, to find that the band gap depends nonlinearly on the voltage, owing to geometrical and material nonlinearities. By analyzing different mechanical constraints, we demonstrate that snap-through instabilities resulting from these nonlinearities can be harnessed to achieve sharp transitions in the gap width. Our conclusions hint at a new strategy to adaptively filter sound using a simple control parameter—an applied voltage.

Acoustic Measurements on a Sonic Crystals Barrier

This paper describes the measurements carried out over a sonic crystal at normal incidence according to EN 1793-6, which allows to cancel ground reflection and edge diffraction by applying suitable windowing techniques. The sample was made of hollow PVC pipes with an outer diameter of 160mm arranged in a square lattice with lattice constant 0.2 m. FE predictions were computed in order to verify the experimental campaign. A good match between simulations and measurements was found in the first sonic Bragg band gap. As expected, increasing the number of rows does not translate into a shift of the Bragg band gap but into an increase of the insulation properties.

Vibrational properties of acoustic metamaterial multilayers

The vibrational properties of acoustic metamaterial multilayers, which are made of a periodic arrangement of clusters of mass and mass-in-mass microstructure, were numerically studied. The dispersion relations of one-dimensional multilayers and two-dimensional periodic structures with square lattices were clarified. It was confirmed that flat modes appear in a sonic band gap, and that the number of such in-gap modes can be controlled by changing the structure of a multilayer. The physical origin of the flat modes is also discussed.

Enlargement of locally resonant sonic band gap by using composite plate-type acoustic metamaterial

Abstract 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.

Dynamic characterization of shale systems by dispersion and attenuation of P- and S-waves considering their mineral composition and rock maturity

The dynamical elastic effective properties of gas–oil shale systems are found by using the self-consistent method and from them, dispersion and attenuation of P- and S-waves are calculated for a wide range of frequencies including seismic, sonic and ultrasonic bands. The mathematical model has the virtue of considering solid and fluid inclusions embedded in a matrix solid taking into account the volume fraction of each one. The mineral composition estimated from geological and petrophysical data is fed into the theoretical model in order to calculate the effective mechanical properties. The solid frame may be composed of clay, quartz or carbonate dominated lithotype; and the complement volume is occupied by pore fluids (water, heavy oil or dry gas), kerogen or solid inclusions. From that, typical patterns are established by the dispersion and attenuation of elastic waves in shale systems considering their mineralogy and maturity. In the acoustical branch, the results of the modeling have already been validated with laboratory data. Quartz and carbonate dominated lithologies exhibit very similar elastic responses and clay dominated lithotype shows a reverse reaction. These results are very useful tools to analyze and interpret the seismic response of target zones in oil and gas shale formations. Also, they aim to discriminate: drained, water-saturated, immature, mature or post-mature shale systems.

Lamb wave band gaps in a homogeneous plate with inclined cylindrical dots

We report on the theoretical analysis of locally resonant sonic band gaps (BGs) in a phononic crystal (PC) structure constituted by a square array of inclined cylindrical dots deposited on a thin homogeneous plate. Based on an efficient finite element method (FEM), we show that the PC plate with inclined dots can lower Lamb wave BGs due to a weak localized resonance of the edge of the upper surface of the inclined dots. The BGs can be effectively shifted by changing the value of the incline. The total displacement fields are computed to explain how the inclined dot induces the lowering of the locally resonant BGs. Transmission power spectra (TPS) are calculated to demonstrate the existence of the BGs and it matches well with the band structure. BGs evolution as a function of geometrical parameters of the PC plate with inclined dot is also studied.

Manipulating the extraordinary acoustic transmission through metamaterial-based acoustic band gap structures

We report theoretical predictions and experimental results on the formation of pass bands and stop bands of extraordinary acoustic transmission in multilayer structures based on alternating layers of acoustic metamaterial and air. The metamaterial layers can be made of any acoustically hard material perforated with a two-dimensional array of subwavelength apertures. In this way, it is possible to tailor the density and speed of sound of an otherwise acoustically bulk hard material with fixed properties. The sonic band structure allows transmission passband and stop bandgaps that depend on the layer thicknesses and effective properties of the metamaterials. In addition, we show the existence of resonant tunneling due to the formation of an acoustic passband in a spectral region of low transmission for a single layer. This opens the possibility to engineer different types of phononic materials to manipulate and control acoustic waves.

Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates

We report on the theoretical analysis of the enlargement of locally resonant acoustic band gap in two-dimensional sonic crystals based on a double-side stubbed plate. A significant enlargement of the relative bandwidth by a factor of 2 compared to the classical one-side stubbed plates is obtained and discussed. Based on an efficient finite element method, we show that this band gap enlargement is due to the coupling between the same nature of the resonant eigenmodes (in-plane or out-of-plane) of the stubs located in each plate side, producing a strong interaction with the plate’s Lamb modes. Acoustic displacement fields are computed to illustrate such mechanism and to discuss the physics behind it.

Frequency-dependent velocity prediction theory with implication for better reservoir fluid prediction

A series of experiments have shown that the elastic wave velocities and attenuation are dependent on frequency (Jones, 1986; Sams et al., 1997; Batzle et al., 2006). Velocity dispersion and attenuation may make it difficult to match different frequency bands of geophysical data such as surface seismic and VSP (∼5 to 300 Hz), sonic log (1 kHz to 20 kHz), and ultrasonic core survey (>[Formula: see text] Hz). For example, sonic log data are often used to constrain seismic inversion on the assumption that log velocity equals to seismic velocity at well locations. However, these two sets of velocities are different due to the effect of velocity dispersion, especially in reservoirs. Therefore, if we could develop a proper frequency-dependent rock physics model to correct the data at the sonic frequency band to that at the seismic frequency band, it would be useful for the solution to the data-matching problem.

Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates

We provide experimental evidence of the existence of a locally resonant sonic band gap in a two-dimensional stubbed plate. Structures consisting of a periodic arrangement of silicone rubber stubs deposited on a thin aluminium plate were fabricated and characterized. Brillouin spectroscopy analysis is carried out to determine the elastic constants of the used rubber. The constants are then implemented in an efficient finite-element model that predicts the band structure and transmission to identify the theoretical band gap. We measure a complete sonic band gap for the out-of-plane Lamb wave modes propagating in various samples fabricated with different stub heights. Frequency domain measurements of full wave field and transmission are performed through a scanning laser Doppler vibrometer. A complete band gap from 1.9 to 2.6 kHz is showed using a sample with 6-mm stub diameter, 5-mm thickness, and 1-cm structure periodicity. Very good agreement between numerical and experimental results is obtained.

A sonic band gap based on the locally resonant phononic plates with stubs

Using the finite element method, we have studied the acoustic properties of a novel phononic crystal (PC) structure constructed by periodically depositing single-layer or two-layer stubs on the surface of a thin homogeneous plate. Numerical results show that the extremely low frequency band gap (BG) of the Lamb waves can be opened by the local resonance (LR) mechanism. We found that the width of such a BG depends strongly on the height and the area of cross section of the stubs. The displacement field distribution of the oscillating modes is given to explain how the coupling of the modes induces the opening of the BG. The physics behind the opening of the LRBG in our phononic structures can be understood by using a simple ‘spring-mass’ model.

Three-Dimensional Sonic Band Gaps Tunned by Material Parameters

In this paper, band gaps tunned by material parameters in three-dimensional fluid-fluid sonic crystals are studied. From the basic wave equation, it is found that the material parameters directly determining the three-dimensional sonic band gaps are the mass density ratio and bulk modulus ratio. The calculation of the sonic band gaps is completed by the plane-wave expansion method. The effects of these parameters on sonic band gaps are discussed in details for the simple-cubic (sc), face-centered cubic (fcc) and body-centered cubic (bcc) lattices. The results show that the first potential sonic band gap easily appears at both small mass density ratio and bulk modulus ratio, and becomes wider with both of these two parameters decreasing. The bulk modulus ratio plays a more important role than the mass density ratio in tuning the sonic band gaps. The present analysis can be applied to artificially design band gaps.

Numerical and experimental results on sonic band gaps in 1‐D phononic crystals with a symmetric stub

The wave propagation in periodic systems has received a great deal of attention during the last years. By analogy with the studies driven on photonic crystals, many works were conducted on phononic crystals. In this paper the propagation of elastic waves through a one dimensional chain of beads with grafted stubs is experimentally as well as numerically investigated. The results obtained by both approaches are well correlated and show that the stub introduces a dip in the spectral response of the chain. The numerical analysis shows that this dip is due to the excitation of a stub mode that cancels the transmission from one extremity of the chain to the other. The position and the shape of the dip in the response are related to the geometry and nature of the stub. The results show that it is possible to adjust the position of the dip and open potential applications of these structures for filtering or demultiplexing. Finally first results on periodically grafted stubs in the chain are presented.