Wave mixing in coupled phononic crystals via a variable stiffness mechanism

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels – primary and control ones – via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave transmission in the primary channel can be manipulated by the control channel's signal. We show that the application of control waves allows the selection of a specific mode through the primary channel. We also demonstrate that the mixing of two wave modes is possible whereby a modulation effect is observed. A detailed study of the design parameters is also carried out to optimize the switching capabilities of the proposed system. Finally, we verify that the system can fulfill both switching and amplification functionalities, potentially enabling the realization of an acoustic transistor.     

Acoustic axes in elasticity

New results are presented for the degeneracy condition of elastic waves in anisotropic materials. The condition for the existence of acoustic axes involves a traceless symmetric third order tensor that must vanish identically. It is shown that all previous representations of the degeneracy condition follow from this acoustic axis tensor. The conditions for existence of acoustic axes in elastic crystals of orthorhombic, tetragonal, hexagonal and cubic (RTHC) symmetry are reinterpreted using the geometrical methods developed here. Application to weakly anisotropic solids is discussed, and it is shown that the satisfaction of the acoustic axes conditions to first order in anisotropy does not in general coincide with true acoustic axes.     

On nonlinear energy flows in nonlinearly coupled oscillators with equal mass

Nonlinear Dynamics - Due to the near monopoly held by nonlinear energy sinks in the study of targeted energy transfer, little research has been done on the flow of mechanical energy between...     

Wave dispersion in randomly layered materials

Wave scattering in materials composed of two kinds of alternating layers with different elastic properties and randomly distributed thicknesses has been modeled. The general form of the dispersion equation is derived for the unbounded layered medium. It defines two basic macroscopic characteristics of the scattered wave: phase velocity and attenuation, which are explicit functions of wave frequency and microscopic parameters of the system: acoustic properties of the layers and stochastic characteristics of their thickness distributions. The analytical expressions are derived for three special cases: for long waves; for a periodic medium composed of layers with constant thicknesses and for random medium with uniform distribution of layer thicknesses. Special attention is paid to the analysis of the frequency dependence of the wave parameters. It was shown that the predictions of the model for long waves and for periodic medium are compatible with the results obtained in the literature.Moreover, comparison of theoretical results for frequency dependent wave parameters with numerical simulations of pulse transmission through the slab of the randomly layered medium shows good qualitative and quantitative agreement in wide frequency range.     

Acoustic emission monitoring of carbon-fiber-reinforced-polymer bridge stay cables in large-scale testing

This paper presents acoustic emission (AE) monitoring of damage initiation and progression in carbon-fiber-reinforced-polymer (CFRP) stay cables subject to largescale laboratory tests. The research is part of the University of California, San Diego (UCSD), larger project on the design and construction of a new cable-stayed bridge made of advanced composites. No previous use of AE on large-size CFRP stay cables appears in the literature. Three types of cables of potential use in the UCSD composite bridge were tested at lengths ranging from 5500 mm to 5870 mm. The AE events were monitored to detect damage and provide a qualitative correlation with the type of structural failure. The tests allowed a comparative characterization of the failure behavior of the three types of cables under investigation. An additional study was performed to characterize acoustic attenuation and dispersion phenomena that are relevant to AE testing of largescale CFRP cables. It is shown that despite their large size, these cables are excellent acoustic wave guides exhibiting very low attenuation. Finally, this study shows promising results for an effective use of in situ AE for health monitoring of these structural components in service.     

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux. A conformal mapping function for the coating and matrix is introduced, which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane. Using analytic continuation, we derive a general solution in terms of two auxiliary functions. The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface. Once the two auxiliary functions have been obtained in the elementary-form, the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined. The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition. Finally, the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.     

Acoustic streaming measurements in standing wave resonator using Particle Image Velocimetry

This paper experimentally investigates the measurement of acoustic streaming in a 7 m long-standing wave air-filled acoustic resonator. One can describe the acoustic streaming as a second-order steady flow, which is superimposed on the dominant acoustic velocity. It is induced by the nonlinearities of the acoustic propagation inside the resonator. The exploration of the acoustic velocity field by the synchronized PIV (stands for Particle Image Velocimetry) technique enabled to highlight and quantify these secondary flows. The PIV measurements of the acoustic velocity fields at different phases over the excitation signal period gave information on streaming profiles and the post processing applied allowed plotting the acoustic velocity over time. These results were compared to the outcome of a 2D numerical study performed with the commercial software Fluent, where good agreements were found. It indicates the ability of this method to accurately measure second order steady flow variations of the acoustic velocity field.     

Acoustic wave propagation in inhomogeneous,layered waveguides based on modal expansions and hp-FEM

A new model is presented for harmonic wave propagation and scattering problems in non-uniform, stratified waveguides, governed by the Helmholtz equation. The method is based on a modal expansion, obtained by utilizing cross-section basis defined through the solution of vertical eigenvalue problems along the waveguide. The latter local basis is enhanced by including additional modes accounting for the effects of inhomogeneous boundaries and/or interfaces. The additional modes provide implicit summation of the slowly convergent part of the local-mode series, rendering the remaining part to be fast convergent, increasing the efficiency of the method, especially in long-range propagation applications. Using the enhanced representation, in conjunction with an energy-type variational principle, a coupled-mode system of equations is derived for the determination of the unknown modal-amplitude functions. In the case of multilayered environments, h$h$- and p$p$-FEM have been applied for the solution of both the local vertical eigenvalue problems and the resulting coupled mode system, exhibiting robustness and good rates of convergence. Numerical examples are presented in simple acoustic propagation problems, illustrating the role and significance of the additional mode(s) and the efficiency of the present model, that can be naturally extended to treat propagation and scattering problems in more complex 3D waveguides.     

Acoustic emission assessment of interface cracking in thermal barrier coatings

In this paper, acoustic emission (AE) and digital image correlation methods were applied to monitor interface cracking in thermal barrier coatings under compression. The interface failure process can be identified via its AE features, including buckling, delamination incubation and spallation. According to the Fourier transformation of AE signals, there are four different failure modes: surface vertical cracks, opening and sliding interface cracks, and substrate deformation. The characteristic frequency of AE signals from surface vertical cracks is 0.21 MHz, whilst that of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. The energy released of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. Based on the energy released from cracking and the AE signals, a relationship is established between the interface crack length and AE parameters, which is in good agreement with experimental results.     

Acoustic damping rate measurements in binary mixtures of atomic species via transient-grating spectroscopy

The objective of this work is to investigate the ability of transient-grating spectroscopy (TGS) to measure accurately the acoustic damping rate by analyzing the temporal behavior of laser-induced gratings. Experiments are performed in a binary gaseous mixture, with a trace amount of NO₂, as a function of both composition and pressure. Measured and theoretically calculated acoustic damping rates are compared using both a classical model and a more comprehensive model that included additional diffusive mechanisms. The TGS technique demonstrated here provides a nearly instantaneous measurement with reasonably high spatial resolution. The experimental data agree well with theoretical predictions.     

Acoustic emission monitoring of crack propagation in additively manufactured and conventional titanium components

Additive manufacturing (AM) is a novel and innovative production technology that can produce complex and lightweight engineering products. In AM components, as in all engineering materials, fatigue is considered as one of the principle causes of unexpected failure. In order to detect, localise and characterise cracks in various material components and metals, acoustic emission (AE) is used as a non-destructive monitoring technique. One of the main advantages of AE is that it can be also used for dynamic damage characterisation and specifically for crack propagation monitoring. In this research, we use AE to monitor the fatigue crack growth behaviour of Ti6Al4V components under four-point bending. The samples were produced by means of AM as well as conventional material. Notched and unnotched specimens were investigated with respect to the crack severity and crack detection using AE. The main AE signal parameters –such as cumulative events, hits, duration, average frequency and rise time– were evaluated and indicate sensitivity to damage propagation in order to lead to a warning against the final fracture occurrence. This is the first time that AE is applied in AM components under fatigue.     

Acoustic radiation force of a solid elastic sphere immersed in a cylindrical cavity filled with ideal fluid

An expression for the acoustic radiation force function on a solid elastic spherical particle placed in an infinite rigid cylindrical cavity filled with an ideal fluid is deduced when the incident wave is a plane progressive wave propagated along the cylindrical axis. The acoustic radiation force of the spherical particle with different materials was computed to validate the theory. The simulation results demonstrate that the acoustic radiation force changes demonstrably because of the influence of the reflective acoustic wave from the cylindrical cavity. The sharp resonance peaks, which result from the resonance of the fluid-filled cylindrical cavity, appear at the same positions in the acoustic radiation force curve for the spherical particle with different radii and materials. Relative radius, which is the ratio of the sphere radius and the cylindrical cavity radius, has more influence on acoustic radiation force. Moreover, the negative radiation forces, which are opposite to the progressive directions of the plane wave, are observed at certain frequencies.     

Chaos in Acoustic Subspace Raised by the Sommerfeld–Kononenko Effect

This paper deals with vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a point excitation by an electric motor of limited power-supply. The whole system is divided into two “exciter - foundation” and “foundation-plate-medium”. In the system “motor-foundation” three classes of steady state regimes are determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions, in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they correspond to chaotic functions. In another mathematical model where the exciter stands directly on an infinite plate (without foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydro-elastic subsystem in the regime of motor shaft rotation. In this case the process of rotation can be approximately described as a solution of the fourth order nonlinear differential equation and may have the same three classes of steady state regimes as the first model. That is the electric motor may generate periodic acoustic waves, modulated waves with an infinite number of frequencies or chaotic acoustic waves in a fluid.     

Acoustic radiation force on an elastic cylinder in a Gaussian beam near an impedance boundary

Acoustic radiation force (ARF) is studied by considering an infinite elastic cylinder near an impedance boundary when the cylinder is illuminated by a Gaussian beam. The surrounding fluid is an ideal fluid. Using the method of images and the translation-addition theorem for the cylindrical Bessel function, the resulting sound field including the incident wave, its reflection from the boundary, the scattered wave from the elastic cylinder, and its image are expressed in terms of the cylindrical wave function. Then, we deduce the exact equations of the axial and transverse ARFs. The solutions depend on the cylinder position, cylinder material, beam waist, reflection coefficient, distance from the impedance boundary, and absorption in the cylinder. To analyze the effects of the various factors intuitively, we simulate the radiation force for non-absorbing elastic cylinders made of stainless steel, gold, and beryllium as well as for an absorbing elastic cylinder made of polyethylene, which is a well-known biomedical polymer. The results show that the impedance boundary, cylinder material, absorption in the cylinder, and cylinder position in the Gaussian beam significantly affect the magnitude and direction of the force. Both stable and unstable equilibrium regions are found. Moreover, a larger beam waist broadens the beam domain, corresponding to non-zero axial and transverse ARFs. More importantly, negative ARFs are produced depending on the choice of the various factors. These results are particularly important for designing acoustic manipulation devices operating with Gaussian beams.     

Acoustic, thermal and flow processes in a water filled nanoporous glass by time-resolved optical spectroscopy

We present heterodyne detected transient grating measurements on water filled Vycor 7930 in the range of temperature 20-90 °C. This experimental investigation enables to measure the acoustic propagation, the average density variation due to the liquid flow and the thermal diffusion in this water filled nano-porous material. The data have been analyzed with the model of Pecker and Deresiewicz which is an extension of Biot model to account for the thermal effects. In the whole temperature range the data are qualitatively described by this hydrodynamic model that enables a meaningful insight of the different dynamic phenomena. The data analysis proves that the signal in the intermediate and long time-scale can be mainly addressed to the water dynamics inside the pores. We proved the existence of a peculiar interplay between the mass and the heat transport that produces a flow and back-flow process inside the nano-pores. During this process the solid and liquid dynamics have opposite phase as predicted by the Biot theory for the slow diffusive wave. Nevertheless, our experimental results confirm that transport of elastic energy (i.e. acoustic propagation), heat (i.e. thermal diffusion) and mass (i.e. liquid flow) in a liquid filled porous glass can be described according to hydrodynamic laws in spite of nanometric dimension of the pores. The data fitting, based on the hydrodynamic model, enables the extraction of several parameters of the water-Vycor system, even if some discrepancies appear when they are compared with values reported in the literature.     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

Bulk and surface acoustic wave phenomena in crystals: Observation and interpretation

Crystal acoustics is a field that has engaged the attention of theoreticians and experimentalists alike for decades and more. Many striking effects have been revealed, and elegant analytical techniques applied to their interpretation. This article is oriented towards the experimental aspects of the field and the interpretation of the phenomena that have been observed. Particular attention is given to reviewing the techniques that have probed the intricacy of acoustic wave propagation in crystals, including phonon imaging, laser- and capillary-fracture-generated ultrasound, transmission acoustic microscopy and surface Brillouin scattering, and a selection of results obtained with these techniques is presented. Some of these studies pertain to bulk waves and others to surface acoustic waves. The interpretation of far-field observations is carried out within the ray approximation, and elastodynamic Green’s functions are invoked in the interpretation of near-field results. Extensive use is made of the acoustic-slowness and wave surfaces, in particular features such as acoustic axes, with their attendant polarization singularities, and folds in the wave surface.     

Optimization of a ribbon diode with magnetic insulation for increasing the current density in a high-current relativistic electron beam

The geometry of the ribbon diode of the U-2 accelerator is optimized to increase both the current density and the total current of the relativistic electron beam for its subsequent injection into the plasma of a multimirror GOL-3 trap. Beam simulation in the diode was performed using the POISSON-2 applied software modified on the basis of the results obtained using the theory of a planar diode in an inclined magnetic field. As a result of the optimization, the diode geometry and the magnetic field configuration were found that should provide a factor of 1.5–2 increase in the current density in experiments with a small angular divergence of electron velocities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 25–35, May–June, 2009.