Nonlinear Acoustic Waves Research Articles

Non-destructive strength testing of microindented float glass by a nonlinear acoustic method

The present paper describes a method for non-destructive testing of the glass strength. Square 10 × 10 cm2 samples of annealed float glass was inflicted with a controlled defect in the centre of the atmospheric side using Vickers microindentation-induced cracking with a force of 2 N, 5 N and 10 N and compared to an un-indented reference. The samples were non-destructively tested using a nonlinear acoustic wave method resulting in defect values. The average of the defect values was found to linearly correlate to the indentation force in a log–log relationship. The samples were subsequently tested in a ring-on-ring setup that allows for an equibiaxial stress state. The indentation-induced cracking gave practically realistic strength values in the range of 45 to 110 MPa. The individual sample values for failure stress as a function of normalized defect value show linear trends with approximately half of the data within 95% confidence limit. In summary, this study provides an initial proof-of-concept for a non-destructive testing of the strength of glass.

Peculiarities in the Transformation of the Profile of Acoustic Nonlinear Waves Reflected from a Stepped Structure

The article presents the results of studying the reflection of an intense acoustic beam from stepped structures. The case of high Reynolds numbers is considered, when a sawtooth wave profile formed in the incident beam, and an obstacle in the form of a step was located normal to the acoustic axis and behind the discontinuity coordinate. When reflected from the obstacle, the acoustic beam incident on it splits into two parts, between which there is a path difference, specified by the stepped structure itself. The experiment focused on obstacles that create a path difference between the two parts of the beam during reflection, equal to 0, λ/3, λ/2, λ, etc. A broadband membrane hydrophone was used to record the shape of the profile of nonlinear waves of the incident and reflected acoustic beams at an arbitrary spatial point. This made it possible to analyze the evolution of the beam shape with increasing distance from the obstacle, as well as to study its transverse structure. The effect of doubling the characteristic frequency of a signal as an acoustic beam is reflected from a stepped structure is shown, which creates a path difference of λ/2 between the two parts of the reflected beam. It is demonstrated that the dynamics of nonlinear effects in intense beams reflected from stepped structures is similar to the transformation of the profile of acoustic waves generated by dual-frequency pump signals.

Parametric analysis of dust ion acoustic waves in superthermal plasmas through non-autonomous KdV framework

In the presence of superthermal plasma, propagation of non-linear dust ion acoustic waves has been studied in the framework of the Damped Forced Korteweg–de Vries (DFKdV) Equation. A feasible range is obtained for the existence of the solitary wave solutions in terms of the spectral index, and the unaffected dust-to-ion density ratio (denoted by κ and μ, respectively). It is observed that the transition of solitary wave structures from compressive to rarefactive can be completely determined by mainly these two parameters. The effects of all other parameters involved in the model, namely, the strength (f0) and frequency (ω) of the external periodic force, and damping coefficient (νid0) are studied using the bifurcation analysis; f0 and ω play a crucial role in the periodic and chaotic motions in the system. We also obtained certain critical values of the key parameters involved in the model for which the model exhibits periodic, quasi-periodic and chaotic behaviour.

Effect of the ion drag force on head‐on collisions between two nonlinear dust acoustic waves in a strongly coupled dusty plasma

AbstractThe effect of dust grain pressure on the head‐on collision of two dust‐acoustic solitary waves in non‐magnetized, collisionless, and strongly coupled dust plasma has been investigated [J. Plasma Phys. (2020), 86, 905,860,111]. In this paper, the model is augmented by incorporating the ion drag force on dust grains. By way of the extended perturbation method of Poincaré‐Lighthill‐Kuo, Korteweg‐de Vries equations are derived. The wave characteristics along with the phase shifts after the head‐on collision are analytically established and numerically assessed. It revealed a non‐negligible decrease in the wave amplitude and the phase shift.

Periodic solutions for the Blackstock–Crighton–Westervelt equation

We investigate the Blackstock–Crighton–Westervelt equation which models nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We prove existence and regularity, in a Lp−Lq setting, of time-periodic solutions for a given sufficiently small time-periodic forcing data, and homogeneous Dirichlet boundary conditions over a cylindrical domain. We show maximal Lp-regularity for the abstract linearized model. We use techniques of operator-valued Fourier multiplier theorems combined with a generalized version of the implicit function theorem.

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Higher-order nonlinear dust ion acoustic (DIA) solitary waves in plasmas with weak relativistic effects in electrons and ions

Strongly focused nonlinear surface acoustic wave beams in isotropic solids

A promising direction in the tailored control of quantum materials is the modification of their structure-function relationship via engineered laser-driven shock waves. In order to inform how the laser excitation should be tailored to optimize the effect of the shock waves, a model is desired for strongly focused nonlinear surface waves in crystals. A model was developed previously in the paraxial approximation for weakly diffracting nonlinear surface wave beams in isotropic solids [Shull et al., JASA 97, 2126 (1995)]. Harmonic generation and shock formation were investigated numerically in that work for sources with uniform amplitude distributions, with analytical solutions for the fundamental and second harmonic obtained for weakly focused Gaussian beams. Here, numerical results are reported for shock formation in focused nonlinear surface waves obtained using a model unrestricted by the paraxial approximation in order to accommodate strong focusing in isotropic solids. Removal of the restriction to isotropic solids is work in progress based on representation of the wave field in terms of its angular spectrum and a model for planar nonlinear surface waves in crystals [Hamilton et al., JASA 105, 639 (1999)]. [Work supported by the IR&D Program at Applied Research Laboratories.]

Multiscale acoustics in dense granular media; geophysical implications

We overview sound interactions with dense granular packings, dry, wet or saturated by liquid, in which acoustic waves are served not only as a probe to monitor the fragile and heterogeneous contact networks, but also as a pump to fluidize the medium and trigger the shear instability. First, we describe the linear sound propagation in jammed granular solid: coherent waves and multiple scattering [1], as well as acoustic probing of elastic heterogeneities [2], and plastic rearrangements [3]. Then, we investigate the nonlinear acoustic waves dominated by the hysteresis due to micro-slips at contacts [4] and the huge softening of shear wave velocity in transient elastography [5]. Finally, we discuss the triggering of granular avalanches by high-amplitude ultrasound [6], through the acoustic lubrication of contacts (micro-plasticity) without visible grains motions. This work helps to understand landslides triggered by seismicity. [1] X. Jia, Phys. Rev. Lett. 93, 154303 (2004). [2] S. Wildenberg et al., Europhys. Lett. 115, 34005 (2016). [3] Y. Khidas and X. Jia, Phys. Rev. Express 85, 051304 (2012). [4] X. Jia, T. Brunet, and J. Laurent, Phys. Rev. Express 84, 020301(R) (2011). [5] J. Brum et al., Phys. Rev. Eexpress 99, 042902 (2019). [6] J. Léopoldès, X. Jia, A. Tourin, and A. Mangeney, Phys. Rev. Express 102, 042901 (2020).

Analytical study of ion-acoustic solitary waves in a magnetized plasma with degenerate electrons

The propagation of fully nonlinear ion acoustic solitary waves (IASW) in a magneto-plasma with degenerate electrons was investigated by Abdelsalam et al. [[1] Physics Letters A 372 (2008) 4923]. Based on their work in the present work, a rigorous and general analytical study is presented. This confirms their implied assumption that (i) only hump and no cavity is possible and (ii) for humps, the algebraic equation for the maximum density N obtained by them determines it uniquely (naturally assumes N > 1). Here we confirm analytically their assertion that N decreases with lx (the direction cosine of the wave vector k along the x-axis) and N increases with the increase of the Mach number (M).

Quantum Effects on Cylindrical Dust-ion Acoustic Waves in a Semiclassical Dense Dusty Plasma

The nonlinear cylindrical dust ion acoustic waves are studied in a collisional unmagnetized dense dusty plasma medium containing inertialess degenerated electrons and positrons, fluid ions, negatively charged dust fluid and neutrals in the background, including exchange-correlation effects of both electrons and positrons. Employing the reductive perturbation method, the damped Kadomstev–Petviashvili equation is derived in the framework of two-dimensional cylindrical geometry. An approximate analytical solution of this equation is also discussed. The quantum and geometrical effects on the dust ion acoustic waves have been investigated. It is found that the dust ion acoustic wave is modified by quantum diffraction, Fermi statistics and exchange-correlation potential. Moreover, it has been found that the nebulon structures of quantum dust ions acoustic wave are formed due to the Cartesian geometry and the transverse perturbation. It is also observed that the nebulon structure is significantly modified by the exchange-correlation effects.

Propagating characteristics of nonlinear dust acoustic solitary waves in multicomponent dusty plasma

Nowadays, the dusty plasma has become an interesting new branch of the plasma physics. As is well known, the dusty plasmas play a significant role in the space, astrophysical and laboratory environments. In these days, the studying of the nonlinear waves in dusty plasma has attracted researchers’ attention, in order to explain many basic phenomena in the plasma physics. The nonlinear waves play an important role in studying dusty plasma environments, such as the aster-oid zones, the earth’s mesosphere, and the planetary rings. In this work, the propagating characteristics of nonlinear dust acoustic solitary waves in a multicomponent dusty plasma which is composed of positively charged dust particles, streaming protons and electrons, Kappa distributed electrons and ions are studied in detail. The Sagdeev potential method is employed to investigate the large amplitude dust acoustic waves. It has an evidence for the existence of compressive and rarefractive solitary waves. With the help of the Sagdeev potential method, the Sagdeev potential function and the bifurcation analysis of phase-portrait are obtained. Firstly, the Sagdeev potential function is obtained by the Sagdeev potential method. Then, the variations of phase diagram with different parameters in a two-dimensional autonomous system in the multicomponent dusty plasma system are investigated. It is found that the system has the linear wave solutions, nonlinear wave solutions, and solitary wave solutions at the same time. Meanwhile, the existence of different wave behaviors is closely related to various system factors. Moreover, it is found that only the rarefractive solitary waves exist in the multicomponent dusty plasma system by using the numerical simulation technique. Finally, the important influence of system parameter on the phase diagram, the Sagdeev potential function and the propagating characteristics of nonlinear dust acoustic solitary waves are discussed clearly. The results show that the different system parameters such as Mach number <i>M</i>, the masses, the temperatures, the number densities, the charge numbers of multiple particles and the Kappa distribution parameters for ions and electrons have important effects on the amplitudes, the widths and the waveforms of nonlinear dust acoustic solitary waves.

INVESTIGATION OF NEW SOLITARY WAVE SOLUTIONS OF THE GILSON–PICKERING EQUATION USING ADVANCED COMPUTATIONAL TECHNIQUES

This study focuses on employing recent and accurate computational techniques, specifically the Sardar-sub equation [Formula: see text] method, to explore novel solitary wave solutions of the Gilson–Pickering [Formula: see text] equation. The GP equation is a mathematical model with implications in fluid dynamics and wave phenomena. It describes the behavior of solitary waves, which are localized disturbances propagating through a medium without changing shape. The physical significance of the [Formula: see text] equation lies in its ability to capture the dynamics of solitary waves in various systems, including water waves, optical fibers, and nonlinear acoustic waves. The study’s findings contribute to the advancement of mathematical modeling approaches and offer valuable insights into solitary wave phenomena. The stability of the constructed solutions is investigated using the properties of the Hamiltonian system. The accuracy of the computational solutions is demonstrated by comparing them with approximate solutions obtained through He’s variational iteration [Formula: see text] method. Furthermore, the effectiveness of the employed computational techniques is validated through comparisons with other existing methods.

Nonlinear ion acoustic wave structure in electron–ion plasma in presence of fully relativistic electron beam

Analytical description of large amplitude nonlinear ion acoustic (IA) waves in the presence of a cold relativistic electron beam is presented. The pseudopotential method is adopted to observe the effects of various parameters like beam density, ion temperature, etc. on the IA wave structures. Furthermore, the maximum amplitude of the IA wave is estimated, and its variation with fully relativistic electron beam parameters is investigated. The maximum allowed amplitude of the wave is found to decrease with the increase in the electron beam density as well as in the ion temperature. The Mach number has the effect to increase the maximum amplitude of the electric field.

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.

Amplitude reflections and interaction solutions of linear and nonlinear acoustic waves with hard and soft boundaries

In this study, the propagation of a fundamental plane mode in a bifurcated waveguide structure with soft–hard boundaries is analyzed by using the Helmholtz equation. The explicit solution is given to this bifurcated spaced waveguide problem by means of matching the potential across the boundary of continuity. Amplitudes of the reflected field in all those regions have been evaluated, and the energy balance has been derived. We have observed the reflection of the acoustic wave against the wavenumber and shown its variation with the duct width. Convergence of the problem has been shown graphically. In our analysis, we notice that the reflected amplitude decreases as the duct spacing increases; as a result, the acoustic energy will increase as the duct spacing increases. It is expected that our analysis could be helpful to give better understanding of wave reflection in an exhaust duct system. We then reduce the linear acoustic wave equation to the Kadomtsev–Petviashvili (KP) equation. Multiple-periodic wave interaction solutions of the KP nonlinear wave equation are investigated, and the energy transfer mechanism between the primary and higher harmonics is explained, which, to the best of our knowledge, is overlooked.

An arbitrary Lagrangian-Eulerian method for nonlinear structural-acoustic interaction of hyperelastic solid and compressible viscous fluid

This paper develops a numerical method for predicting the nonlinear structural-acoustic interactions of a hyperelastic solid immersed in an unbounded compressible viscous fluid. The nonlinear acoustic wave model with perfectly matched layers adopted is proposed in an arbitrary Lagrangian-Eulerian frame to absorb acoustic waves at truncated fluid boundaries, whereas the geometric and material nonlinearities of the hyperelastic solid are characterized in a total Lagrangian form. Both the fluid and the solid are discretized by the finite element method, and both models are coupled together by the momentum equilibrium and kinematic compatibility on the common interface. The convergence and accuracy of the proposed method are assessed by comparing the computed results with existing solutions. A hyperelastic ring in a viscous fluid is analyzed to provide physical insights into the nonlinear dynamics behaviors of the coupled hyperelastic solid and acoustic fluid system. The hyperelastic ring in acoustic fluid exhibits deformation instability under a uniform distributed excitation load, producing a series of subharmonics, ultrasubharmonics, and superharmonics in the structural and acoustic responses. Nonlinear internal resonance and bifurcation phenomena in the vibration of the ring and the acoustic waves of the fluid are also discussed.

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

The propagation of linear and nonlinear electron acoustic waves (EAWs) in an unmagnetized plasma, comprising dynamical inertial electrons, hot (r, q) distributed electrons, warm electron beam, and immobile ions is studied. The linear dispersion relation is investigated for varying beam velocity. The Korteweg-de Vries (KdV) equation for EAWs is derived in the small amplitude limit. Depending on the beam density, temperature and velocity, we get a critical condition for which the quadratic nonlinearity vanishes from the plasma system. For such a condition, the modified Korteweg de Vries (mKdV) equation, with cubic nonlinearity, is derived, which admits both negative and positive potential solitary structures. It is noted that the spectral indices r and q of the generalized (r, q) distribution, the concentration of the cold, hot and the beam electrons, and the temperature ratios, significantly affect the fundamental properties of the propagation and interaction of electron acoustic solitary waves (EASWs). The types of possible overtaking interaction of two mKdV solitons are investigated. The spatial regime for the two soliton interaction is found to vary in accordance with the variation of single soliton for various plasma parameters. The results of present study may be beneficial to comprehend the interaction between two EASWs in laboratory, space and astrophysical plasmas.

Acoustic black hole analogy to analyze nonlinear acoustic wave dynamics in accelerating flow fields

We present a physical model and a numerical method based on a space- and time-dependent Galilean-type coordinate transformation to simulate acoustic waves in the presence of an accelerating background flow field with sonic transition. Kinematically, the coordinate transformation is designed so as to maintain the well-posedness of the transformed wave equation, which is solved in a fixed computational domain using standard finite differences. Considering an acoustic black hole analogy, we analyze the nonlinear dynamics of acoustic waves in a stationary but non-uniformly accelerating flow field under the assumption of spherical symmetry. The choice of the acoustic black hole analogy is motivated by the fact that the steady-state spherical sonic horizon allows us to parameterize the wave-flow configuration in terms of a Helmholtz number He=c2/(λagh), which is expressed as a function of the speed of sound c, the emitted wavelength λa, and the flow acceleration at the sonic horizon, that is, the acoustic surface gravity gh. The results of the numerical simulations show that He describes geometrically similar sets of wave characteristics for different combinations of gh and λa. However, we also observe nonlinear variations of the wave amplitude along the wave characteristics, which are attributed to nonlinear Doppler modulations. It appears that these amplitude modulations depend on the acceleration of the flow field and can, therefore, differ for geometrically similar characteristics.

The Westervelt–Pennes model of nonlinear thermoacoustics: Global solvability and asymptotic behavior

In this work, we investigate the global well-posedness and asymptotic behavior of a mathematical model of ultrasound-induced heating based on a coupled system of Westervelt's nonlinear acoustic wave equation and Pennes bioheat equation. To this end, under Dirichlet–Dirichlet boundary conditions, we prove global existence for sufficiently small and smooth solutions of the nonlinear model using an energy method. In addition, we show that the energy norm of the resulting pressure and temperature decays to the steady state exponentially fast.

Nonlinear sound absorption of Helmholtz resonators with serrated necks under high-amplitude sound wave excitation

This paper focuses on the design and sound absorption analysis of Helmholtz resonators with serrated necks inspired by the leading edges of owl wings. Numerical models for predicting the sound absorption and the flow field of the resonators are established by a finite element method based on nonlinear acoustic wave equations. The thermal conduction and vortex energy dissipation of resonators with straight and serrated necks are evaluated. The effects of the geometrical parameters including the neck diameter, the serration height, and the serration pitch on the sound absorption behaviors of the resonator are discussed. It is found that for a lower-intensity acoustic excitation, the serration leads to periodic oscillations of the fluid in the resonator neck, and increases the acoustic resistance of the resonator. For a high-intensity sound excitation, the distributions of the velocity and vorticity in the resonator neck show that the serrated structure can produce more vorticities, which is beneficial for acoustic energy dissipation. The resistance of the resonators grows significantly and the reactance decreases slightly with an increase in intensity of the sound excitation. Sound absorption coefficients of resonators fabricated by three-dimensional (3D) printing are tested in an impedance tube for a large range of sound pressure excitations. The computed results of the sound absorption coefficients are in good agreement with the experimental data, and the superior sound absorption performance of the resonator with a serrated neck is confirmed.