Plane Acoustic Wave Research Articles

Investigation on sound transmission through thick-wall cylindrical shells using 3D- theory of elasticity in the presence of external and mean air-gap flow

This paper studies the effects of an external mean flow and an internal air-gap mean flow on sound transmission through a double-wall thick cylindrical shell. Due to the major influence of some effective terms such as membrane, bending, transverse shearing and rotational inertia on thick-walled shell, three-dimensional theory of elasticity is used to obtain the governing equations of motion. Therefore, Newton’s second law is utilized to develop the equilibrium equations for an infinitesimal element in cylindrical coordinates. Then, the equations of motion related to the circular hollow cylinders are solved using Helmholtz potentials for arbitrary values of physical and geometrical parameters. In addition, by coupling of both inner and outer shells, a modal transfer matrix is created. This modal matrix stands for the global dynamic equilibrium of the double-wall cylinder. Moreover, the sound transmission Loss of the double-wall cylinder excited by an acoustic oblique plane wave with two angles of incident (i.e. elevation and azimuth angles) is predicted. Due to lack of studies in the field of sound transmission through the thick-walled shell, the results obtained in this study are compared with those from other researchers for a thin cylindrical shell. These results indicate an excellent agreement in comparison with each other. Furthermore, the results reveal that with thickening of the shell, critical and coincidence frequencies are getting closer to ring frequency. Moreover, the effects of external and air-gap flows on TL behave in similar way whereas the Mach number is positive. In addition, an improvement of transmission loss can be found whereas the Mach number is negative; particularly this enhancement is more specified for the external flow. Finally, the results indicate that where both external and air-gap fluids simultaneously flow in opposite directions the TL is significantly enhanced. However, for the case where these two fluids flow in the same direction the TL is decreased.

Feedback control of combustion instabilities from within limit cycle oscillations using [Formula: see text] loop-shaping and the ν-gap metric.

Combustion instabilities arise owing to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control, in which an actuator modifies some combustor input in response to a sensor measurement, can suppress combustion instabilities. Linear feedback controllers are typically designed, using linear combustor models. However, when activated from within limit cycle, the linear model is invalid, and such controllers are not guaranteed to stabilize. This work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations. A low-order model of a simple combustor, exhibiting the essential features of more complex systems, is presented. Linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame. The latter is determined numerically using a level set approach. Its implication is that the open-loop transfer function (OLTF) needed for controller design varies with oscillation level. The difference between the mean and the rest of the OLTFs is characterized using the ν-gap metric, providing the minimum required ‘robustness margin’ for an loop-shaping controller. Such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations.

On the Use of Transfer Approaches to Predict the Vibroacoustic Response of Poroelastic Media

The transfer matrix method (TMM) is a famous analytic method in the vibroacoustic community. It is classically considered as a high frequency approach, because of the hypothesis of acoustic plane waves impinging on a flat infinite panel. Thus, it cannot take into account directly finite-size effects or lateral boundary conditions (BCs), and it needs specific algorithms to correct its results in the low frequency range. Within the transfer matrix framework, the use of finite elements makes it possible to generalize the range of applications of transfer approaches. Thus, the study of wave propagation in poroelastic media, in presence of lateral BCs can be carried out. The links between theses waves and the acoustic response of a sample are investigated. Finally, it shows that transfer approaches are not limited in the low frequency range, as usually stated. In fact, the validity of analytic transfer approaches depends more on the material and on the geometry than on the frequency range.

Estimating frame bulk and shear moduli of two double porosity layers by ultrasound transmission

The acoustic plane wave transmission by water saturated double porosity media is investigated. Two samples of double porosity media assumed to obey Berryman and Wang (BW) extension (Berryman and Wang, 1995, 2000) of Biot’s theory in the low frequency regime are under consideration: ROBU® (pure binder-free borosilicate glass 3.3 manufactured to form the individual grains) and Tobermorite 11Å (the individual porous cement grains show irregular shapes). The de facto gap existing between theoretical and experimental data can be minimized by modifying adequately two of the parameters estimated from triaxial tests: the frame bulk and shear moduli. The frequency dependent imaginary parts that follow necessary from the minimization are in relation with the energy losses due to contact relaxation and friction between grains.

Localized acoustic surface modes

We introduce the concept of localized acoustic surface modes. We demonstrate that they are induced on a two-dimensional cylindrical rigid surface with subwavelength corrugations under excitation by an incident acoustic plane wave. Our results show that the corrugated rigid surface is acoustically equivalent to a cylindrical scatterer with uniform mass density that can be represented using a Drude-like model. This, indeed, suggests that plasmonic-like acoustic materials can be engineered with potential applications in various areas including sensing, imaging, and cloaking.

Experimental verification of acoustic trace wavelength enhancement.

Directivity is essentially a measure of a sonar array's beamwidth that can be obtained in a spherically isotropic ambient noise field; narrow array mainbeam widths are more directive than broader mainbeam widths. For common sonar systems, the directivity factor (or directivity index) is directly proportional to the ratio of an incident acoustic trace wavelength to the sonar array's physical length (which is always constrained). Increasing this ratio, by creating additional trace wavelengths for a fixed array length, will increase array directivity. Embedding periodic structures within an array generates Bragg scattering of the incident acoustic plane wave along the array's surface. The Bragg scattered propagating waves are shifted in a precise manner and create shorter wavelength replicas of the original acoustic trace wavelength. These replicated trace wavelengths (which contain identical signal arrival information) increase an array's wavelength to length ratio and thus directivity. Therefore, a smaller array, in theory, can have the equivalent directivity of a much larger array. Measurements completed in January 2015 at the Naval Undersea Warfare Center's Acoustic Test Facility, in Newport, RI, verified, near perfectly, these replicated, shorter, trace wavelengths.

Behavior of plane waves propagating through a temperature-inhomogeneous region

Description and analysis of acoustic waves in ducts with a region containing temperature-inhomogeneous fluid represent a significant problem of scientific and practical interest. This interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions. Most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature-homogeneous regions smoothly. In our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient. A polynomial character of the used temperature profile ensures smooth connection with constant-temperature regions. The one-dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically. The derived solutions based on Heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient. Due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature-homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method.

Retrieval of the equivalent acoustic constitutive parameters of an inhomogeneous fluid-like object by nonlinear full waveform inversion

This study addresses the problem of the acoustic characterization of an inhomogeneous object such as a soft-tissue organ containing a cyst or tumor whose size and/or composition evolve either negatively due to increased disease or positively due to increased response to treatment. The so-called ‘corrupted’ binary object, probed by a transient, acoustic plane wave, is a tube composed of a homogenous fluid-like (or assumed as such) mantle (medium 1: three acoustic constitutive parameters, one geometric parameter) surrounding a homogeneous fluid-like (or assumed as such) core (medium 2: three acoustic constitutive parameters, one geometric parameter), immersed in a spatially-infinite, homogeneous fluid (host medium 0: two acoustic parameters). The complete inversion of the diffracted acoustic field response of this object involves the retrieval of seven (six acoustic and one geometric) parameters, assuming we know beforehand the outer radius of the tube and acoustic parameters of the host. An alternative to this time-consuming, hazardous (due to the ill-posed nature of the) procedure, is to minimize the discrepancy, between the full waveform response of the binary object to a transient plane wave and the response of a homogeneous cylinder (medium characterized by three acoustic parameters, one geometric parameter) to the same transient plane wave, so as to retrieve the (three so-called equivalent) acoustic parameters of the homogeneous object. Thus, the first inverse problem is replaced by a second one (same assumptions concerning the outer radius of the objects, the host medium, the probe radiation and the sensing configuration as the first one) involving the retrieval of only three (instead of six) acoustic parameters. This procedure is potentially useful if the variation of at least one of the three equivalent parameters is sensitive to the variation of a key parameter of the inhomogeneous body (usually the characteristic dimension or the wavespeed of the core) and this variation can be expressed in a simple algebraic form (such as by a mixing formula). It is shown that this situation can arise if the average frequency of the acoustic probe radiation is sufficiently low. A sidelight of this investigation is the discovery that the equivalent constitutive parameters of the homogeneous cylinder are dispersive even when the component materials of the tube are not dispersive.

Transmission of a plane acoustic wave through a composite consisting of elastic and viscoelastic layers

Transmission of a plane acoustic wave through a composite consisting of elastic and viscoelastic layers

Receptivity of Hypersonic Boundary Layers over Straight and Flared Cones

The effects of adverse pressure gradients on the receptivity and stability of hypersonic boundary layers were numerically investigated. Simulations were performed for boundary-layer flows over a straight cone and two flared cones. The steady and the unsteady flowfields were obtained by solving the two-dimensional Navier–Stokes equations in axisymmetric coordinates using the fifth-order-accurate weighted essentially nonoscillatory scheme for space discretization and using a third-order total-variation-diminishing Runge–Kutta scheme for time integration. The mean boundary-layer profiles were analyzed using local stability and nonlocal parabolized stability equations methods. After the most amplified disturbances were identified, two-dimensional plane acoustic waves were introduced at the outer boundary of the computational domain and time-accurate simulations were performed. The adverse pressure gradient was found to affect the boundary-layer stability in two important ways. First, the frequency of the most amplified second-mode disturbance was increased relative to the zero-pressure gradient case. Second, the amplification of first- and second-mode disturbances was increased. Although an adverse pressure gradient enhances instability wave growth rates, small nose-tip bluntness was found to delay transition due to the low receptivity coefficient and the resulting weak initial amplitude of the instability waves. The computed and measured amplitude-frequency spectra in all three cases agree very well in terms of frequency and the shape except for the amplitude.

DIRECT AND INVERSE ACOUSTIC SCATTERING BY A COMBINED SCATTERER

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by a union of a crack and a penetrable inhomogeneous medium with compact support. The well-posedness of the direct problem is established by the variational method. An uniqueness result for the inverse problem is proved, that is, both the crack and the inhomogeneous medium can be uniquely determined by a knowledge of the far-field pattern for incident plane waves. The linear sampling method is employed to recover the location and shape of the combined scatterer. It is worth noting that we make the first step on reconstructing a mixed-type scatterer of a crack and an inhomogeneous medium by the linear sampling method.

Finite element method to fluid–solid interaction problems with unbounded periodic interfaces

Consider a time‐harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by its Lamé constants. This article is concerned with a variational approach to the fluid–solid interaction problems with unbounded biperiodic Lipschitz interfaces between the domains of the acoustic and elastic waves. The existence of quasiperiodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. A finite element scheme coupled with Dirichlet‐to‐Neumann mappings is proposed and the convergence analysis is performed. The Dirichlet‐to‐Neumann mappings are approximated by truncated Rayleigh series expansions. Finally, numerical tests in 2D are presented to confirm the convergence of solutions and the energy balance formula. In particular, the frequency spectrum of normally reflected signals is plotted for water–brass and water–brass–water interfaces. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 5–35, 2016

Scattering of plane acoustic waves at elastic particles with rough surfaces

A comprehensive theoretical and numerical study of the influence of surface roughness of elastic particles in water on the scattering of ultrasonic waves has been carried out. For near spherical shape of the particles and with small rms-roughness heights, a perturbation method has been developed. In this method, the first-order perturbation contribution predicts the contribution to the incoherently scattered acoustic field due to surface roughness, and the second-order perturbation contribution predicts the change in the coherent field and will satisfy the requirement of energy conservation. The second-order perturbation contribution is evaluated by use of the form function concept, while the first-order perturbation to the total scattered acoustic field is evaluated by use of the scattering cross-section. As a function of the ka-value and for different rms-roughness heights a numerical study of the forward and backward scattering from rough, elastic particles has been carried out and a substantial roughness influence on the scattered field has been verified. Some experimental results from measurements of scattering from glass and cast iron spheres have given evidence to the numerical predictions.

On the interaction of composite plate having a vibration-absorbing covering with incident acoustic wave

We formulate the coupled problem of planar acoustic wave propagation through the composite plate which contains in its second layer a damping material possessing large logarithmic decrement. Aero-hydrodynamical interaction between plate and external acoustic environment is defined by three-dimensional wave equations, whilst mechanical behavior of double-layered plate is examined with a model based on classical Kirchhoff-Love’s hypothesis. Exact analytical solutions were given for plates with simply supported edges. Based on given solutions we find parameters for second layer which lead to substantially damping of plate vibrations in the case of acoustic loading at resonant modes.

First-principles study on the elastic and thermal properties of Ca0.5Sr0.5TiO3

In this paper, Ca/Sr atoms are confirmed to have symmetric distributions on 4c sites by using the minimum energy principle, and the stable crystal structure of Ca0.5Sr0.5TiO3 is built. The lattice parameters, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio of Ca0.5Sr0.5TiO3 (CST50) are investigated by the plane wave pseuedopotential method based on the first-principles density functional theory within the local density approximate (LDA) and generalized gradient approximation. The properties of planar acoustic velocity are studied by Christoffel equation, and the minimum thermal conductivity is investigated with Cahill and Cahill-Pohl models. The results show that the calculated lattice parameters are consistent with the corresponding experimental values. The larger calculated elastic constasnts C11, C22, and C33 suggest the incompressibility along the principle axes. The bulk modulus B is larger than the shear modulus G; G/BLDA = 0.5789 and G/BGGA = 0.5999, indicating that CST50 is a brittle material. The three-dimensional image of Young's modulus along [100], [010], and [001] crystal orientations shows the anisotropic elasticity of CST50. The planar projections of Young's modulus in (001) and (010) planes show the stronger anisotropy than in (100) plane and all the planar projections have two-fold symmetry. The Poisson's ratio exhibits the incompressbility of CST50. The universal elastic anisotropy indexes ALDAU = 0.0235 and AGGAU= 0.0341 indicate the weak anisotropy of CST50. The planar acoustic wave which has a branch of longitudinal wave and two branches of transverse wave is anisotropic along (010) and (001) planes and isotropic along (100) plane, and all the corresponding planar projections have two-fold symmetry. The minimum thermal conductivity calculated in Cahill model is isotropic in each plane, while the minimum thermal conductivity calculated in Cahill-Pohl model is proportional to the second power of T under low temperatures and reaches a constant at high temperatures. In the quasi harmonic Debye model, the molar heat capacity and thermal expansion coefficient of CST50 are close to those of calcium titanate, indicating that CST50 has the stable thermal expansion property at high temperatures. The direct band gap of CST50 is 2.19 eV and the bottom of the valence band is mainly determined by the electron orbitals of Ti-3d and O-2p. The analysis of the charge populations shows that the covalence of Ti–O is stronger than those of Sr–O and Ca–O, and the band length of Ti–O is shorter than those of Sr–O and Ca–O; (200), (110) and (002) planar contour charge densities indicate that Ti atoms interact strongly with O atoms. The charge population and contour charge density prove that CST50 has a stable Ti–O octahedral structure.

Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (μ,λ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method.

Detection of Small Stress Relaxation in Tightened Metallic Structures by Ultrasounds

Experimental data are presented here to highlight the performances of ultrasounds for the control or the better understanding of the quality of the mechanical contact between tightened plates. Thus, variations of the mechanical load as small as those induced by creep or stress relaxation are potentially detectable by simply monitoring the amplitude of the reflected acoustic plane wave reflected at this interface.To illustrate this, two 3cm thick aluminium plates are firstly tightened with a given torque and next, the amplitude of the acoustic wave is monitored for several days. All long this test, the temperature of the sample is controlled as well as the compression load applied to the plates using a thermocouple and a bolt gauge sensor. The reflected amplitude decreases quickly during first hours and then stabilises after a week approximately. The total variation reaches –28% of the initial value of the reflected amplitude. During this test, temperature is remained almost constant and its fluctuation around the ambient temperature is not correlated with the reflected amplitude. As expected from classic stress relaxation tests, the compression load has slowly decreased by an amount of only –1% but this should have logically increased the reflected amplitude. Further investigations have shown that instrumentation drift were negligible. Consequently, this large decrease of the reflected amplitude has been interpreted as the indication of the increase of the contact area between the two tightened plates. This test attests the high sensitivity of ultrasonic reflection measurement to investigate quality of mechanical contacts for non destructive testing.

Passage of a plane acoustic wave through a layered composite with components of elastic and viscoelastic materials

The problem of passage of a plane acoustic wave through a flat composite layer of finite thickness is considered. It is assumed that the composite consists of mutually alternate layers of elastic and viscoelastic materials, and all composite layers are either parallel or perpendicular to the incident-wave front. In addition, the thickness of each separate layer of the composite is considered to be much smaller than both the acoustic wavelength and the composite thickness. The formulated problem is investigated using an averaged composite model, which helps to determine the reflection and transmission factors and the change in the sound-intensity level during sound propagation through a composite layer.

Diffraction of a Plane Acoustic Wave from a Finite Soft (Rigid) Cone in Axial Irradiation

The problem of diffraction of a plane acoustic wave by a finite soft (rigid) cone is investigated. This one is formulated as a mixed boundary value problem for the three-dimensional Helmholtz equation with Dirichlet (Neumann) boundary condition on the cone surface. The diffracted field is sought as expansion of unknown velocity potential in series of eigenfunctions for each region of the existence of sound pressure. The solution of the problem then is reduced to the infinite set of linear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality properties of the Legendre functions. The main part of asymptotic of ISLAE matrix element determined for large indexes identifies the convolution type operator amenable to explicit inversion. This analytical treatment allows one to transform the initial diffraction problem into the ISLAE of the second kind that can be readily solved by the reduction method with desired accuracy depending on a number of truncation. All these determine the analytical regularization method for solution of wave diffraction problems for conical scatterers. The boundary transition to soft (rigid) disc is considered. The directivity factors, scattering cross sections, and far-field diffraction patterns are investigated in both soft and rigid cases whereas the main attention in the near-field is focused on the rigid case. The numerically obtained results are compared with those known for the disc.

Acoustoelastic Behaviour of Double-Layer Plates Accounting Internal Damping of Layer Materials

In this paper, the coupled problem of planar acoustic wave propagation through the double-layer composite plate containing the second layer from damping material with high logarithmic decrement is examined. Aerohydrodynamic interaction between plate and external acoustic environment is defined by three-dimensional wave equations, whilst mechanical behaviour of double-layered plate is examined with model based on classical Kirchhoff-Love's hypothesis. Exact analytical solutions are given for plates with simply supported edges. On the basis of given solutions, parameters for second layer, which lead substantially damping of plate vibrations are found in the case of acoustic loading at resonant modes.