Propagation Of Longitudinal Acoustic Waves Research Articles

Mathematical modeling of a new method for processing a seismic signal on the example of a section of the Saratov right bank. Part 2

This paper presents a new method of seismic exploration with two buried receivers on the same vertical, which helps in comparing the experimental seismogram cleared of non-vertical signals with the calculated theoretical seismogram, which depends on the parameters of the layered structure, such as the thickness of the layers, their density, velocity of propagation of longitudinal acoustic waves in rock, and seismic quality factors of media. The method of least squares aided in the search for the global minimum of the discrepancy function of the calculated and experimental seismic pulse waveforms. The implementation of the algorithm for solving the inverse seismic problem was carried out in the MatLab software package. The construction of a theoretical seismogram includes the calculation of the spectrum of the input impulse, calculation of the frequency dependences of the reflection coefficients and the passage of waves at the interfaces of rocks with different physical parameters, the calculation of the shape of the seismic impulses received by the receivers. A comparison of the calculated and real parameters of the geological structure obtained in the COMSOL Multiphysics software package shows that the developed algorithm results in obtaining a seismogram that practically coincides with the experimental seismogram corresponding to the real rock section, with appropriate geological parameters of media, such as thickness, density and propagation velocity of acoustic waves, as well as quality factors.

Non-contact vibration transmissibility measurements of an additively manufactured pentamode material

Pentamodal (PM) metamaterials are elastic structures that are designed to support purely longitudinal acoustic wave propagation over a wide band of frequencies. Further, these metamaterials can be designed to have anisotropic stiffness and be impedance matched to water [doi.org/10.1121/10.0009161]. Due to the complexity of three-dimensional (3D) PM microstructures, metal additive manufacturing techniques must be employed to physically realize these materials to achieve the specifically tailored impedance and anisotropic sound speeds over the desired frequency range. Previous work designed and built an additively manufactured titanium PM material measuring 98.9x 98.7x87.2 mm3 which was successfully characterized in a fresh-water tank. The current work presents vibration transmissibility measurements on the same PM sample. The structure was mounted on an electro-dynamic shaker which provided a broadband base excitation. Base acceleration and out-of-plane surface accelerations of each exposed face were then measured using point accelerometers and a scanning laser Doppler vibrometer, respectively, and the process was repeated for multiple sample orientations. The observed vibrational modes demonstrate the influence of geometric asymmetry introduced by the truncated domain of the PM lattice. Measurements were compared to a fully-featured finite element model of the sample using COMSOL Multiphysics showing good agreement in mode shapes. [Work supported by ONR]

Self-Similar Acoustic Waves in the Media with a Power-Law Hysteresis Nonlinearity

We present the results of the studies of propagation of longitudinal acoustic waves in the media with a power-law hysteresis nonlinearity. Exact analytical solutions for the self-similar periodic waves propagating in such media without changing their forms are given. The spectral characteristics of these waves are studied.

LASER-ULTRASONIC METHOD OF ACOUSTIC IMPEDANCE MEASUREMENT FOR QUANTITATIVE POROSITY ESTIMATION OF CROSS-PLY CARBON FIBER REINFORCED PLASTIC MATERIALS

A method of measuring the acoustic impedance of carbon fiber plastics based on the laser optoacoustic effect is proposed and experimentally realized. Measurement of the acoustic impedance of the studied composite is made by the value of the antiderivative of ultrasonic pulse reflected from the interface between the immersion liquid and the sample. A method for determining the porosity of a material by the measured value of the acoustic impedance, based on the dependence of the material density and the velocity of propagation of longitudinal acoustic waves in it on its porosity, is presented. Porous samples of crossply reinforced carbon plastics with three types of carbon fiber lay-up schemes were studied. It was found that the studied carbon fiber plastics have a non-uniform distribution of local porosity in the plane of carbon fabric stacking. It is also shown that the variation of the local porosity in the sample depends on the fiber laying scheme. It is shown that the porosity value obtained by X-ray computed tomography coincides with the results of laser-ultrasonic measurements. The advantage of the proposed method is the possibility of rapid diagnosis of porosity with one-way access to the object under study without measuring its dimensions and mass, which can be used for composite structures of complex shape.

Non-reciprocal behavior of one-dimensional piezoelectric structures with space-time modulated electrical boundary conditions

Propagation of longitudinal acoustic waves in a one-dimensional piezoelectric structure with space-time modulated electrical boundary conditions is investigated. An analytical model allowing the calculation of eigenmodes for spatially continuous shifts of electrical boundary conditions is compared with finite difference time domain simulation results for a discrete set of time-varying spatially fixed conditions. Both models predict that such a structure behaves as a nonreciprocal device exhibiting unidirectional propagation properties in some frequency ranges. The modulus and direction of the modulation speed vector strongly affect this nonreciprocal behavior. Moreover, other nonlinear phenomena such as frequency up and down conversions, wave packet distortion, and parasitic echoes occurring in such systems are investigated in detail. The importance of these phenomena is discussed in the context of nonlinear acoustic wave-based components for radio-communication systems.

Microfluidic Bulk-Modulus Measurement by a Nanowavelength Longitudinal-Acoustic-Wave Microsensor in the Nonreflective Regime

Investigating the physical mechanisms of interaction between acoustic waves and fluids is significant for the detection of the properties of liquids. Researchers in this field have mainly used shear-mode acoustic wave sensors to measure fluid density and viscosity, but not the bulk modulus. Using an immersed gigahertz-range microsensor, one can obtain compressional information about a liquid from the observed propagation of longitudinal acoustic waves in the nonreflective regime. This work fills a gap by enabling measurement of a liquid's bulk modulus in a microfluidic setting, with an eye toward physiological fluids in particular.

Investigation on Characteristics of Longitudinal Acoustic Wave Propagation in Coal Mine Drill Rods

In order to investigate the feasibility of drill rods used for wireless data transmission in coal mine, the properties of longitudinal acoustic wave propagation in drill string are studied. The results show that: the spectral properties of drill string for coal mine show like a comb filter with wide passbands; when single drill rod become longer, numbers of passbands become more, the width of total passband become narrower; bigger diameter of drill rod makes the width of total passband narrower and amplitudes lower; for integral type and joint-connection type drill rod with same diameter and length, they have little difference in total passband width; the drill strings with different total length have almost same spectral characteristics. In the drill strings investigated, the drill strings composed by drill rods with 42mm diameter and 1m length has the widest passband which occupy 70% of the whole frequency scope. All results indicate that drill rods can be used as channel in data transmission in coal mine gallery.

Acoustic Wave Sensor Based on Piezomagnetic Phononic Crystal

The propagation of longitudinal acoustic waves in a 1D phononic crystal (PnC) contains a piezomagnetic material (Terfenol-D) as a defect layer is analyzed and discussed theoretically. A resonant mode was generated inside the phononic band gap when the piezomagnetic material thickness becomes around its half wavelength. The present results revealed that the frequency of the generated resonant mode can be controlled by applying an external magnetic field. In addition, the resonant mode is shifted towards higher and lower frequencies by applying an external pressure on the PnC structure. The simulated results are very valuable in the application of sensors measuring magnetic fields and in the early detection of building cracks.

Photoelastic and acousto-optic effects in 65GeS2-25Ga2S3-10CsCl glass

The peculiarities of photoelastic and acousto-optic effects are first tested in chalcohalide 65GeS2-25Ga2S3-10CsCl glass exploring the interferometry method. The determined piezo-optic coefficients occur to be (in Br) π11=2.8±0.6, π12=6.0±0.9 and π44=−3.2±1.1. In respect to maximal acousto-optic figure of merit М2=55.6·10−15s3/kg proper for longitudinal acoustic wave propagation and polarization along X2 (і=2) direction, this glass seems more perspective for photoelastic and acousto-optic modulation in visible and near IR ranges, than many alternative candidates, such as crystalline quartz, LiNbO3, CaWO4, PbMoO4, β-BaB2O4, etc. For the first time it has been shown that piezo-optic effect of isotropic solids is anisotropic, and the degree of anisotropy is the difference of π11–π12 coefficients.

Hybridization and regularization schemes applied to identify rough acoustic impedance profiles in slender structures with noisy data.

The modified sequential algebraic algorithm (MSAA) is a routine developed to solve the longitudinal acoustic wave propagation problem in inhomogeneous media. This method accurately predicts the echo generated by the inhomogeneities, particularly when the acoustic impedance variation profile in the damaged part of the structure is non-smooth. Used for solving the inverse problem by a stochastic optimization approach, MSAA efficiently identifies rough profiles of impedance with low noise level in the input data. As noise level increases, the inverse problem turns out to be "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to apply a regularization scheme and to use a hybrid optimization strategy to reduce the error in the damage estimation. In the numerical examples, 40 parameters are successfully identified for a signal to noise ratio of 20 dB. For all tested damage profiles, the regularization and hybridization procedures decreased the maximum absolute error to levels lower than 4%, and for the roughest impedance profile, the mean squared error was reduced by more than one order of magnitude and the error propagation was avoided. In an experimental validation, a pulse-echo essay was successfully conducted with the recovery of a damage with 264 parameters.

The Wave Processes in Micro-Inhomogeneous Media with Different-Modulus Nonlinearity and Relaxation

We present the results of analytical and numerical studies of propagation of longitudinal acoustic waves in micro-inhomogeneous media with different-modulus nonlinearity and relaxation. The solutions for evolution of the profiles and spectral characteristics of the initially harmonic waves are obtained.

A modified sequential algebraic algorithm applied to identify rough acoustic impedance profiles in slender structures.

This paper develops and examines a modified technique for identifying damage in slender structures. An algorithm, called modified sequential algebraic algorithm, is presented to solve the longitudinal acoustic wave propagation problem in inhomogeneous media. This method accurately predicts the echo generated by the inhomogeneities when the acoustic impedance variation profile in the damaged part of the structure is non-smooth. For these cases, the available algorithms fail to provide the actual regressive wave component. In the following, a stochastic optimization scheme, the differential evolution method, is applied to solve the inverse problem. Numerical examples with smooth and non-smooth impedance profiles are considered. It is shown that, for smooth profiles, both the available techniques and the modified algorithm succeed in identifying the actual damage. Nevertheless, in situations where a rough profile is to be reconstructed, only the modified algorithm succeeds. The technique is found to be robust with respect to additive noise in the signals.

Localization of acoustic modes in periodic porous silicon structures.

The propagation of longitudinal acoustic waves in multilayer structures based on porous silicon and the experimental measurement of acoustic transmission for the structures in the gigahertz range are reported and studied theoretically. The considered structures exhibit band gaps in the transmission spectrum and these are localized modes inside the band gap, coming from defect layers introduced in periodic systems. The frequency at which the acoustic resonances appear can be tuned by changing the porosity and/or thickness of the defect layer.

Tunable passband in one-dimensional phononic crystal containing a piezoelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 single crystal defect layer

Longitudinal acoustic wave propagation in one-dimensional phononic crystal containing a 0.2mol% Fe-doped relaxor-based ferroelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 (PMN–0.38PT) single crystal defect layer is theoretically studied using the transfer matrix method. A passband can be produced in the stopband when the inserted PMN–0.38PT layer with thickness around its half wavelength. The frequency of the passband is closely dependent on the PMN–PT strain coefficient, suggesting that the band structure of phononic crystal is tunable by applying external electric field onto the piezoelectric crystal. Also, we investigated the influence of acoustic impedance of periodic constitutive materials (layers A and B) on the passband, where the bandwidth of the new passband becomes narrower as the acoustic impedance ratio of layer A and B (ZA/ZB) increase. The simulated results provide valuable guidance for designing tunable acoustic filters and switches made of phononic crystal consisting of the piezoelectric defect layer.

Propagation of nonlinear acoustic waves in bimodular media with linear dissipation

Results of a theoretical study and numerical simulation of the propagation of longitudinal acoustic waves in a medium with bimodular nonlinearity and linear dissipation are presented. The exact analytical solutions are derived for stationary and self-similar waves. Numerical simulation of the propagation of initially harmonic waves was carried out using the spectral method.

Transmission gaps and Fano resonances in an acoustic waveguide: analytical model

A simple acoustic device consisting of two dangling side resonators grafted at two sites on aslender tube is designed possibly to obtain transmission stop bands (where the propagationof longitudinal acoustic waves is forbidden). In contrast to all known systems ofthis kind, a spectral transmission gap of nonzero width occurs here even withthis simple structure. This is obtained by combining appropriately the zeros oftransmission of the side resonators. Sharp resonant states inside the gaps canbe achieved without introducing any defects in the structure. This results froman internal resonance of the structure when such a resonance is situated in thevicinity of a zero of transmission or placed between two zeros of transmission, theso-called Fano resonances. A general analytical expression for the transmissioncoefficient is given for various systems of this kind within the framework of theGreen’s function method. The amplitude and the phase of the transmission arediscussed as a function of frequency and it is shown that the width of the stopbands is very sensitive to the number of side resonators. These results should haveimportant consequences for the suppression of low-frequency noise and for designingfilters.

Transmission gaps and Fano resonances in a simple acoustic waveguide: Analytical model

A simple acoustic device consisting of two dangling side resonators grafted at two sites on a slender tube is designed to obtain possibly transmission stop bands where the propagation of longitudinal acoustic waves is forbidden. Contrary to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for these systems within the framework of the Green's function method. The amplitude and the phase time of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of the side resonators. These results should have important consequences for the suppression of low-frequency noise and for designing filters.

Simplified experimental technique to extract the acoustic radiation induced static strain in solids

A simplified experimental technique to measure the acoustic radiation induced static strain during the longitudinal acoustic wave propagation in solids is proposed. Experiments have been carried out to extract the static displacement (dc) component without resorting to electronic filters, as in the case of previously reported experimental measurements. This prevents the influence of the filter time response characteristics on the measurement. The dependence of the static displacement amplitude on the square of the fundamental amplitude of the input wave, its being independent of the burst width of the tone burst, and its abnormal variation at low input amplitudes are reported.

Acoustic Localization in Weakly Compressible Elastic MediaPermeated with Air Bubbles

The propagation of longitudinal acoustic waves in weakly compressibleelastic media permeated with air bubbles is investigated on the basisof the radial pulsation equation of a single bubble. The multiplescattering of waves in such media is rigorously described by using aself-consistent approach. Theoretical results show that there existsstrong acoustic localization in a range of frequency slightly above thebubble resonance frequency, even for a very small volume fraction ofbubbles. Further study reveals that the localization is in factattributed to collection behaviour of bubbles, allowing for anefficient cancellation of propagating waves. This is essentiallyconsistent with the known conclusions recently drawn for bubbly liquidby Kou et al. [2003 Appl. Phys. Lett. 83 4247]

R-axis sound speed and elastic properties of sapphire single crystals

The sound speed was measured for plane wave propagation along the normal to the (11̄02) plane of sapphire single crystals. The measured r-axis sound speed is significantly different (∼7%) from measured c- and a-axis sound speeds. These results contradict the previous assumption that the mechanical response of sapphire is nearly isotropic. Also, the r axis is not a pure mode direction for longitudinal acoustic wave propagation. The measured r-axis sound speed was not consistent with calculations using the elastic constants reported for sapphire. This discrepancy arises because the elastic constants determined previously used crystallographic conventions different from those in current use. By rotating the coordinate system used for describing the material properties of sapphire in earlier work, consistency is achieved with the current crystallographic conventions. The effect of this coordinate transformation on the second-order elastic constants, the third-order elastic constants, and the photoelastic constants of sapphire is discussed.