Acoustic Wave Modeling Research Articles

The effect of dust size distribution on quantum dust acoustic wave

Based on the quantum hydrodynamics theory, a proposed model for quantum dust acoustic waves (QDAWs) is presented including the dust size distribution (DSD) effect. A quantum version of Zakharov–Kuznetsov equation is derived adequate for describing QDAWs. Two different DSD functions are applied. The relevance of the wave velocity, amplitude, and width to the DSD is investigated numerically. The quantum effect changes only the soliton width. A brief conclusion is presented to the current findings and their relevance to astrophysics data is also discussed.

Analysis Technique for Asymmetrically Coupled Resonator Structures

Asymmetrical acoustically coupled structures are present in several acoustic applications. Specifically when they are used in filter design, some configurations provide unexplored and special response characteristics with high selectivity and relatively wide bandwidths. The relationships between geometries, configurations, and response specifications do not rely on a direct link. In this work, a novel approach to the analysis of these structures is presented as well as a model of an asymmetrical bulk acoustic wave coupled resonator filter obtained from the analysis presented.

Finite-Element Modeling of a Hexagonal Surface Acoustic Wave Device Based on ${\rm LiNbO}_{3}$ Substrate

We present a 3-D coupled-field finite-element model of a novel hexagonal surface acoustic wave (SAW) device which finds applications in materials characterization, as well as in chemical and biological sensing. Calculated frequency response as well as wave propagation characteristics along the three different delay paths corresponding to crystal orientations with Euler angles (0, 90, 90), (0, 90, 30), and (0, 90, 150) for a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> substrate are analyzed using this finite-element structural model. The transient response of the hexagonal SAW device upon application of an impulse electrical input at the transmitting interdigital transducer fingers is utilized to deduce its frequency response. The amplitude fields as well as displacement contours, generated in an AC analysis, along the SAW delay-line and substrate depth are analyzed and utilized to evaluate the wave propagation characteristics along the three propagation directions in this hexagonal SAW device. Our findings indicate that the acoustic waves generated in the three Euler directions are very different in character. The (0, 90, 30) and (0, 90, 150) directions have mixed modes with a prominent shear-horizontal component, whereas the (0, 90, 90) direction generates a Rayleigh wave. This allows the hexagonal device based on LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> to be used for rapid and simultaneous extraction of multiple parameters (film material density, Lame and shear modulii, sheet conductivity) of a thin-film material and achieve a more complete characterization in comparison to a conventional SAW device. Comparison of the simulation results with those obtained using perturbational models and experiments shows good agreement. This validation enables the consideration of such complicated device configurations for practical application, and allows for extending the developed models to analyze propagation characteristics in these SAW devices based on other bare and multilayered piezoelectric substrates prior to fabrication.

S0505-3-3 超音速ジェットから発生するマッハ波の周波数特性の解析(車両・機体・流体機械に関連した騒音問題へのアプローチと対策(3))

To understand the Mach wave frequency characteristics of a supersonic jet, normalization of pressure fluctuation at the source positions of a supersonic jet are conducted using the unsteady computational data. Normalization of frequency spectra based on the shear-layer thickness and time-averaged center jet-velocity works very well except for the temperature effects, as much as the empirical model of rocket acoustic waves build by NASA. This result will improve the prediction model of acoustic waves from a rocket plume.

Theoretical analysis of novel Brillouin scattering properties in photonic crystal fibers based on silica rod model

Based on an approximate model for acoustic waves in a silica rod with circular cross section, we theoretically investigated the dispersion properties of the hybrid acoustical modes and the acousto-optical interactions in the small core photonic crystal fiber. The calculation result shows that the dual-peaked Brillouin scattering gain coefficient spectrum is caused by the mode coupling of the hybrid acoustical modes in the small fiber core. Together with the dispersion properties of the acoustical modes, the influence of the pump wavelength and temperature on the dual-peaked Brillouin scattering gain coefficient spectrum are also calculated via their influences on the acoustic wave vector and material parameters. Our theoretical results agree with the experimental results well. And we also discuss the limit of application of this model through comparing the theoretical and experimental results.

Design, Modeling, and Characterization of a Novel Circular Surface Acoustic Wave Device

The design, modeling, and fabrication of a novel circular surface acoustic wave (SAW) device in complementary metal oxide semiconductor (CMOS) are introduced. The results obtained in authors' previous work demonstrated that it is possible to design and fabricate SAW-based sensors in CMOS with comparable performances to conventional devices. It is of great interest to improve the transfer characteristics and to reduce the losses of conventional rectangular SAW architectures for obtaining highly selective sensor platforms. Performance deficiencies of regular SAW devices in CMOS were addressed with this new architecture for improved performance. A 3-D model for the novel architecture was constructed. A detailed finite-element analysis was carried out to examine the transient, harmonic, and modal behavior of the new architecture under excitation. The devices were fabricated in 0.5 mum AMI semiconductor technology and the postprocessing was carried out using cost-effective CMOS compatible methods. The results demonstrate that it is possible to obtain highly oriented SAWs by using the novel circular architecture. A 12.24 dB insertion loss improvement was achieved when compared with a conventional rectangular device that was fabricated in the same technology.

High‐order parallel discontinuous Galerkin method for time‐domain acoustic simulations.

The modeling of acoustic waves in the time‐domain poses a significant challenge in scientific computing. A promising candidate for solving the three dimensional wave equation is the discontinuous Galerkin (DG) method. Advantages of the DG method are the easy parallelization and a special matrix structure which can reduce the overall time and the computer memory needed for solving the problem. In this study, a high order parallel DG method is investigated. The DG solver is implemented using the C++ programming language. Communication between processors of the parallel computer is performed using the message passing interface. In the solver, the polynomial degree of the basis functions is chosen individually for each element of the computation mesh (up to ninth order polynomials can be used). The unbounded problem is truncated using the perfectly matched layers. The method is evaluated with numerical simulations that are performed on a personal computer cluster.

Unified and stable scattering matrix formalism for acoustic waves in piezoelectric stacks

This paper presents a unified and full scattering matrix (s-matrix) formalism for modeling of acoustic waves in piezoelectric multilayered structures. A stable recursive algorithm is derived for computation of the total s-matrix of a stack in terms of the interface s-matrix, both referring to the eigenmode amplitudes. The derivation is direct and succinct, the deduced expressions of the s-matrix are terse and concise, and the recursion algorithm is efficient and convenient for implementation. The total s-matrix recursion scheme differs from the previously published partial matrix algorithms in that the recursions are conducted once for all independent of the stack boundary conditions and so the same results apply for any post-specified boundary condition. Numerical examples are given to show its numerical features that are superior to other currently used matrix formalisms, such as unconditional stability for both large and small thicknesses, being pole-free and branch point-sensitive, constant mean magnitude with stable phase, involving only dimensionless elements.

Acoustic waves in hydrogels: A bi-phasic model for ultrasound tissue-mimicking phantom

In the present paper a continuum poroelastic model for high frequency acoustic waves in hydrogels has been developed. The model has been used to obtain the acoustic longitudinal wave equation for ultrasound. In order to obtain a satisfactory model for hydrogels, a viscoelastic force describing the interaction between the polymer network of the matrix and the bounded water is introduced. The model is validated by means of ultrasound (US) wave speed and attenuation measurements in polyvinylalcohol (PVA) hydrogel samples as a function of their water volume fraction “β” and polymer matrix cross-linking. The model predicts that the law ∝ ν (1 + δ) for ultrasound attenuation can be applied as a function of the frequency ν, where δ is the frequency exponent of the polymer-bounded water viscosity. This outcome can well explain the attenuation of the US frequency in natural gels where δ is typically about 0.25÷0.50 while the value for pure water is 1. The theory and experiments show that US attenuation in hydrogels decreases steadily with the increase of its water volume fraction β in a linear. The new proposed dissipative mechanism leads to a US wave speed c that follows the law: c = c w( β − ϕ) − 3/2 , where c w is the US wave speed in water and ϕ is the volume fraction of the bounded water. Since 0 < β < 1 and ϕ > 0, the hydrogel US velocity is always higher than that of pure water. If β tends to 1 (100% water), then the US speed in hydrogels converges to a higher value than that of pure water. The US speed gap at β = 1, between hydrogels and water, is the direct consequence of the introduction of the polymer network-bounded water interaction. This is in line with the experimental results that show that the US speed gap at β = 1 decreases in the gel samples with a more cross-linked polymer matrix that has a lower bounded water volume fraction. On the contrary, if the water content is very low (i.e., β < 0.4), the measured US speed converges to that of the dry hydrogel matrix which increases in the samples with a higher degree of network cross-linking with greater elastic moduli.

Scattering and attenuation of surface acoustic waves in droplet actuation

This paper presents an analytical model for surface acoustic waves (SAW) in actuating a single liquid droplet on a piezoelectric substrate. Both scattering waves outside the droplet and attenuation waves beneath the droplet are obtained, and the energy transfer from SAW to droplet in the process of actuation is calculated. The results from this analytical model can provide qualitative explanations to some experimental observations, such as the weak actuation behind the droplet and flow patterns inside the droplet. It is found that effective actuation wavelength is around 1/5 of the droplet radius, at which the droplet absorbs the maximum incident SAW energy.

Legendre polynomial modeling of composite bulk acoustic wave resonators

The Legendre polynomial method has been extended to the modeling of bulk acoustic wave (BAW) resonators. Modifications have been made to the formulation in order to account for large differences in the physical properties of adjoining layers and to take into account the electric source. A unique formalism has been obtained which allows for both harmonic and modal analyses. Resonance and antiresonance frequencies, electric input impedance, electromechanical coupling coefficients, and quality factors have been obtained for an aluminum/zinc oxide/aluminum (Al∕ZnO∕Al) BAW resonator. The results are in excellent agreement with analytical results.

Friction Drive Simulation of Surface Acoustic Wave Motor Characteristics Based on Contact Mechanics

A physical analysis model of a surface acoustic wave (SAW) motor that is driven by frictional force resulting in nanometer elastic vibration has been proposed. In the case of the SAW motor, the vibration amplitude is from 3 to 30 nm at most. The vibration amplitude is almost the same as that of elastic deformation caused by the preload between a slider and a stator. In the analysis model, the elastic deformation, stick, and slip were considered. Numerical simulation was carried out successfully. Experimental results for the SAW motor at 9.6 MHz operation frequency were compared with simulation results. It was observed that a smaller projection slider with many projections has a high contact surface stiffness, thus, superior performances are obtained in terms of speed and thrust.

Application of the nearly perfectly matched layer in acoustic wave modeling

In this work, we successfully applied an alternative formulation of the perfectly matched layer (PML), the so-called nearly PML (NPML), to acoustic wave propagation modeling. The NPML formulation shows great advantages over the standard complex stretched coordinate PML. The NPML formulation deviates from the standard PML through an inexact variable change, but this fact only affects the wave behavior in the NPML layer, which is outside the region of interest. The equivalence of the wave-absorbing performance between these two PML formulations (the standard complex stretched coordinate PML formulation and the NPML formulation) in 3D Cartesian coordinates for acoustic wave propagation modeling is proved mathematically in this work. In time-domain methods, the advantages of the NPML over the standard PML were explained by both the analytical analysis and the numerical simulations in terms of implementation simplicity and computational efficiency. The computation time saving is up to 17% for the 2D example used in this work. For 3D problems, this computational saving is more significant. After theoretically analyzing the numerical reflections from the NPML and the standard PML, we concluded that these two PML formulations have exactly the same performance, even after spatial discretization. This conclusion is validated by numerical experiment. Finally, we tested the NPML in the Marmousi velocity model and found its wave-absorbing rate is high enough, even for this realistic structure.

Optimal blended spectral-element operators for acoustic wave modeling

Spectral-element methods, based on high-order polynomials, are among the most commonly used techniques for computing accurate simulations of wave propagation phenomena in complex media. However, to retain computational efficiency, very high order polynomials cannot be used and errors such as numerical dispersion and numerical anisotropy cannot be totally avoided. In the present work, we devise an approach for reducing such errors by considering modified discrete wave operators. We analyze consistent and lumped operators together with blended operators (weighted averages of consistent and lumped operators). Furthermore, using the operator-blending approach and a novel dispersion analysis method, we develop optimal spectral-element operators that have increased numerical accuracy, without resorting to very high order operators. The new operators are faster and computationally more efficient than consistent operators. Our approach is based on the tensor product decomposition of the element matrices into 1D factors. We apply standard lumping to the factor associated with the 1D mass matrix. A simplified numerical dispersion analysis of arbitrary order and spatial dimension provides a practical criterion for weighting consistent and lumped matrices. The approach is general and is valid for solving both the time-dependent and the stationary (Helmholtz) wave equations.

Measurement of acoustic velocity in the stack of a thermoacoustic refrigerator using particle image velocimetry

Thermoacoustic refrigeration systems generate cooling power from a high-amplitude acoustic standing wave. There has recently been a growing interest in this technology because of its simple and robust architecture and its use of environmentally safe gases. With the prospect of commercialization, it is necessary to enhance the efficiency of thermoacoustic cooling systems and more particularly of some of their components such as the heat exchangers. The characterization of the flow field at the end of the stack plates is a crucial step for the understanding and optimization of heat transfer between the stack and the heat exchangers. In this study, a specific particle image velocimetry measurement is performed inside a thermoacoustic refrigerator. Acoustic velocity is measured using synchronization and phase-averaging. The measurement method is validated inside a void resonator by successfully comparing experimental data with an acoustic plane wave model. Velocity is measured inside the oscillating boundary layers, between the plates of the stack, and compared to a linear model. The flow behind the stack is characterized, and it shows the generation of symmetric pairs of counter-rotating vortices at the end of the stack plates at low acoustic pressure level. As the acoustic pressure level increases, detachment of the vortices and symmetry breaking are observed.

A Novel Saw Device in CMOS: Design, Modeling, and Fabrication

The design, finite element modeling, fabrication, and characterization of a novel surface acoustic wave (SAW) delay line for bio/chemical and telecommunication applications in CMOS technology are introduced. A full modeling was carried out. The devices are designed in a standard semiconductor foundry 1.5-mum two-metal two-poly process. A unique maskless postprocessing sequence is designed and completed. The three postprocessing steps are fully compatible with any standard integrated circuit technology such as CMOS. This allows any signal control/processing circuitry to be easily integrated on the same chip. ZnO is used as the piezoelectric material for SAW generation. A thorough characterization and patterning optimization of the sputtered ZnO was carried out. The major novelties that are introduced in the SAW delay line features are the embedded heater elements for temperature control, compensation, and acoustic absorbers that are designed to eliminate edge reflections and minimize triple transit interference that is amplified by edge reflections. Both of these attributes are designed by using CMOS materials without disturbing SAW performance

A semi-analytic model for localized variable charge dust acoustic waves

A semi-analytic model for nonlinear variable charge dust acoustic waves is outlined. It is shown that rarefactive variable charge dust acoustic solitons involving cusped density humps can exist. The effects of dust dynamics as well as equilibrium dust charge on these nonlinear localized structures are briefly discussed.

Poroacoustic acceleration waves

A model for acoustic waves in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment, such models for poroacoustic waves are of much interest to the building industry. The model has been investigated in some detail by P. M. Jordan. Here we present a rational continuum thermodynamic derivation of the Jordan model. We then present results for the amplitude of an acceleration wave making no approximations whatsoever.

Facet Growth of 4He Crystal Induced by Acoustic Waves

Very fast growth of the c-facet of a 4 He crystal was induced by acoustic waves. The growth velocity was larger at lower temperatures and saturated below about 400 mK. The velocity was proportional to the acoustic wave power. This fast growth cannot be explained by the spiral growth mechanism for the known value of the step mobility. We developed a step multiplication model for high-power acoustic waves and found reasonable agreement with the observed temperature and power dependence of the growth velocity.

3D FE simulation of H 2 SAW gas sensor

In this work, a three-dimensional finite element (3D FE) model of a two-port surface acoustic wave (SAW) delay line based hydrogen sensor on XY lithium niobate (LiNbO 3) substrate with a palladium thin film is developed and simulated. This simulation is performed using ANSYS Version 6.1 platform. Changes in the propagation characteristics of the SAW in terms of the time delay in the voltage and particle displacements due to exposure of palladium thin film to hydrogen and insertion loss of the device are studied. Also, the impulse response of the device is simulated, from which the frequency response and hence the center frequency and insertion loss of the sensor is determined. The 3D representation of the surface acoustic wave propagation on the substrate is demonstrated.