Nonlinear Acoustic Response Research Articles

A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads

In this investigation, the analysis of the nonlinear vibroacoustic and sound transmission loss behaviors of nanoplates made of functionally graded materials considering the nonlocal strain gradient theory is presented. It is presumed that the properties of the functionally graded nanoplate are in the form of the simple power law scheme and continuous along the thickness, under nonlinear temperature rise and incident oblique acoustic wave as well as the first-order shear deformation theory. For this purpose, applying Hamilton’s principle, the nonlinear partial differential equations of motion are derived by the displacement field function approach and by considering the von Kármán nonlinear strain-displacement relations. To solve the equations, using the Galerkin method, the nonlinear partial differential equations of motion lead to the Duffing equation. Then, applying the homotopy analysis method, the equation of the transverse movement of the nanoplate is solved semi-analytically to obtain the nonlinear frequencies. Lastly, the nonlinear vibration and acoustic response of functionally graded nanoplate are investigated by considering the variation of the significant factors such as material gradient indices, nonlocal parameters, length scale parameters, aspect ratio, dimensionless amplitude, nonlinear temperature changes, and sound characteristics of the functionally graded nanoplate.

Modulating Nonlinear Acoustic Response of Phospholipid-Coated Microbubbles with pH for Ultrasound Imaging.

Activatable microbubble contrast agents for contrast-enhanced ultrasound have a potential role for measuring physiologic and pathologic states in deep tissues, including tumor acidosis. In this study, we describe a novel observation of increased harmonic oscillation of phosphatidylcholine microbubbles (PC-MBs) in response to lower ambient pH using a clinical ultrasound scanner. MB echogenicity and nonlinear echoes were monitored at neutral and acidic pH using B-mode and Cadence contrast pulse sequencing (CPS), a harmonic imaging technique at 7.0 and 1.5 MHz. A 3-fold increase in harmonic signal intensity was observed when the pH of PC-MB suspensions was decreased from 7.4 to 5.5 to mimic normal and pathophysiological levels that can be encountered in vivo. This pH-mediated activation is tunable based on the chemical structure and length of phospholipids composing the MB shell. It is also reliant on the presence of phosphate groups, as the use of lipids without phosphate instead of phospholipids completely abrogated this phenomenon. The increased harmonic signal likely is the result of increased MB oscillation caused by a decrease of the interfacial tension induced at a lower pH, altering the lipid conformation. While relative signal changes are interpreted clinically as mostly related to blood flow, pH effects could be significant contributors, particularly when imaging tumors. While our observation can be used clinically, it requires further research to isolate the effect of pH from other variables. These findings could pave the way toward for the development of new smart ultrasound contrast agents that expand the clinical utility of contrast-enhanced ultrasound.

Nonlinear acoustic response in nanoparticle-dielectric systems and nondestructive assessment of particle agglomeration

Nanoparticle agglomeration reduces the modification effect of nanocomposites, and there is a need to investigate a technique for evaluating the overall particle dispersion within the material, which in turn ensures the modification effect of the material. In this paper, a non-destructive testing technique for nanoparticle dispersion based on nonlinear ultrasonic (NLUS) is proposed to rapidly assess the overall nanoparticle dispersion within a material. An interfacial mismatch model describing different degrees of nanoparticle agglomeration was firstly developed, and then the nonlinear acoustic response of the nanoparticle-dielectric system was quantitatively solved, and the theoretical model was validated in conjunction with NLUS tests. The experimental results show that agglomerated interfaces are the source of the nonlinear response of nanodielectrics and that the microscopically generated nonlinear effects can be equivalently accumulated to the mesoscopic domain, with the error in the theoretically calculated values of the two being less than 5%; The NLUS technique eliminates the need for cumbersome steps such as particle size counting, and its small number of rapid detection results are close to the statistical convergence of the particle size of the 250 particles accumulated in the imaging image of the scanning electron microscope, with an error of between 3% ∼ and 13%. With a single inspection area of 339 mm3, the NLUS technology significantly reduces evaluation time and cost while expanding the inspection area, offering the combined advantages of speed, wide field of view, and non-destructiveness.

Hydrophobin-Coated Perfluorocarbon Microbubbles with Strong Non-Linear Acoustic Response

Gas-filled microbubbles are well-established contrast agents for ultrasound imaging and widely studied as delivery systems for theranostics. Herein, we have demonstrated the promising potential of the hydrophobin HFBII—a fungal amphiphilic protein—in stabilizing microbubbles with various fluorinated core gases. A thorough screening of several experimental parameters was performed to find the optimized conditions regarding the preparation technique, type of core gas, HFBII initial concentration, and protein dissolution procedure. The best results were obtained by combining perfluorobutane (C4F10) gas with 1 mg/mL of aqueous HFBII, which afforded a total bubble concentration higher than 109 bubbles/mL, with long-term stability in solution (at least 3 h). Acoustic characterization of such microbubbles in the typical ultrasound frequency range used for diagnostic imaging showed the lower pressure resistance of HFBII microbubbles, if compared to conventional ones stabilized by phospholipid shells, but, at the same time, revealed strong non-linear behavior, with a significant harmonic response already at low acoustic pressures. These findings suggest the possibility of further improving the performance of HFBII-coated perfluorinated gas microbubbles, for instance by mixing the protein with other stabilizing agents, e.g., phospholipids, in order to tune the viscoelastic properties of the outer shell.

Characterization of acoustic droplet vaporization in tissue-mimicking, fibrin-based hydrogels for microrheology applications

Ultrasound-induced vaporization of phase-shift droplets (PSDs) into microbubbles, termed acoustic droplet vaporization (ADV), has expanded biomedical applications. Here, we explored the potential of ADV as a high-resolution, on-demand microrheometer using theoretical and experimental methodologies. This approach could be used to characterize tissue elasticity at spatial resolutions unrealizable with conventional in situ techniques, thus assisting with identification of underlying pathologies. For theoretical studies, bubble dynamics were combined with appropriate material constitutive models accounting for viscoelasticity of the surrounding tissue. Experiments were conducted on submicron- and micron-sized, perfluoropentane PSDs embedded in fibrin-based hydrogels with varying shear elastic moduli (0.2 kPa–11 kPa) to mimic soft tissues. Experimental studies included optical high-speed imaging and acoustic interrogations to record radial dynamics and acoustic emissions of the ADV-bubbles, respectively. Radial dynamics and the acoustic emissions of microbubbles produced by ADV depended significantly on fibrin elasticity. For example, an increase in fibrin elastic modulus from ∼0.8 kPa to ∼6 kPa reduced the maximum expansion radius of the generated ADV-bubbles by 50%. This increase in elasticity significantly impacted both linear (e.g., fundamental) and nonlinear (e.g., subharmonic) acoustic responses of the ADV-bubbles, by up to 15 dB. These findings open doors to a novel ADV-assisted tissue characterization technique.

Nonlinear Frequency Mixing Ultrasound Imaging of Nanoscale Contrast Agents.

Nanoscale ultrasound contrast agents show promise as alternatives for diagnostics and therapies due to their enhanced stability and ability to traverse blood vessels. Nonetheless, their reduced size limits echogenicity. This study introduces an enhanced nanobubble frequency mixing ultrasound imaging method, by capitalizing on their nonlinear acoustic response to dual-frequency excitation. A single broadband transducer (L12-3v) controlled by a programmable ultrasound system was used to transmit a dual-frequency single-cycle wavefront. The frequency mixing effect enabled simultaneous transducer capture of nanobubble-generated sum and difference frequencies in real time without the need for additional hardware or post-processing, by substituting the single-frequency wavefront in a standard contrast harmonic pulse inversion imaging protocol, with the dual-frequency wavefront. Optimization experiments were conducted in tissue mimicking phantoms. Among the dual-frequency combinations that were tested, the highest contrast was obtained using 4&8 MHz. The nanobubble contrast improved with increased mechanical index, and achieved a maximal contrast improvement of 8.4 ± 0.5 dB compared to 4 MHz pulse inversion imaging. In imaging of a breast cancer tumor mouse model, after a systemic nanobubble injection, the contrast was improved by 3.4 ± 1.7, 4.8 ± 1.8, and 6.3 ± 1.6 dB for mechanical indices of 0.04, 0.08, and 0.1, respectively. Nonlinear frequency mixing significantly improved the nanobubble contrast, which facilitated their imaging in-vivo. This study offers a new avenue to enhance ultrasound imaging utilizing nanobubbles, potentially leading to advancements in other diagnostic applications.

Time-domain simulation of the acoustic nonlinear response of acoustic liners at high sound pressure level

Time-domain simulation of the acoustic nonlinear response of acoustic liners at high sound pressure level

In Situ Fatigue Damage Monitoring by Means of Nonlinear Ultrasonic Measurements

In the present work, the results of acoustic nonlinear response of ultrasonic wave propagation when monitoring the progress of damage induced by fatigue on notched C45 carbon steel specimens have been reported. Two ultrasound probes were fixed to the specimens during the tests. The input signal was sinusoidal type, while the corresponding ultrasound response signal was acquired and recorded at each stage of the test by means of a digital oscilloscope. A nonlinear frequency study was performed on the acquired data to evaluate the change in the second- and third-order nonlinearity coefficients of β1 and β2, respectively, on the tested specimens. Ultrasonic results were correlated to plastic strain at the notch tip in the initial phases of fatigue and stiffness degradation. The results showed a significant increase in second-order nonlinearity β1 in the early stages of fatigue life. Subsequently, starting from about 30–40% of the fatigue life, the nonlinearity of β1 increases. Before final failure, from 80 to 85% of fatigue life, the second-order nonlinearity further increases in the crack propagation stages. The nonlinear parameter of the third-order β2 was less sensitive to damage than the parameter β1, showing a rapid increase only starting from approximately 80 to 85% of the fatigue life. The proposed method proved to be valid for detective damage induced by fatigue and to predict the lifetime of metal materials.

Nonlinear vibroacoustic response and sound transmission loss analysis of functionally graded doubly curved shallow shells

This paper presents the semi-analytical nonlinear vibroacoustic and sound transmission loss behaviors of functionally graded doubly curved shallow. The model is developed by considering the simple power law scheme of material distribution in the thickness direction, under thermal load and incident oblique plane sound wave, as well as Donnell’s nonlinear shallow shell theory. By defining the stress function in terms of the force resultants and applying differential operators to these resultants, the coupled compatibility equation and nonlinear equation of motion are obtained only with regard to the stress function and displacement components. The methods of inverse differential operator and average form approach are then utilized to solve the particular and homogeneous solutions of the stress function associated with different boundary conditions. Based on this solution and the use of the Galerkin method with trigonometric mode shape functions, the nonlinear partial differential equation of motion is turned into the Duffing equation. Next, the method of multiple scales is implemented to capture the frequency of the shell corresponding to transverse motion. Finally, the nonlinear vibration and acoustic responses of shells are studied by considering the variation of important parameters such as aspect ratio, dimensionless amplitude, volume fraction power of functionally graded material, phase portrait, sound transmission loss, velocity, average mean square velocity of drive point, and the sound power level of the shells.

A study on the wave propagation on weld joints by the use of feature-guided wave mixing

The concentration of the wave energy around certain features such as bends, stiffeners, and welds in plate-like structures has been identified as feature-guided waves (FGW). In practice, these features can be useful for assessing defects in or near them. The propagation characteristics of FGW propagating along a feature such as a welded joint have been extensively studied. However, most of them are based on the linear acoustic response of materials that generally results in the amplitude and phase variations of the input signal. Compared to linear methods, nonlinear ultrasonic techniques have shown to be effective in characterizing the microstructural changes in engineering materials. In this paper, a wave mixing method is employed to investigate the nonlinear acoustic response of FGWs propagating in a welded joint. The dispersion characteristics of weldguided modes are first revealed via the eigenfrequency analysis of an unbounded welded plate by using the finite element method. The nonlinear response of FWGs is studied through 3D finite element (FE) simulations. A pair of a weld-guided modes of different frequencies are identified and allowed to mix within the welded joint to generate second-order harmonic waves. The current study reveals that the mixing of FGWs could be effectively used for the evaluation of material nonlinearity in welded joints.

Implications of liquid impurities filled in breaking cracks on nonlinear acoustic modulation response: Mechanisms, phenomena and potential applications

Supervised strategies for ultrasonic-based cracks detection in existing structures has been one of particular concerns in the engineering community. However, current researches mostly focus on the clean microcracks, while ignoring the fact that such cracks will be contaminated with liquid impurities (lubricants, silicone oil, etc.) due to its exposure to the operational environment. Actually, the presence of liquid may lead to a non-negligible change in the acoustic performance and interfere with damage diagnosis. The central contribution of this work is to reveal the nonlinear acoustic mechanisms and phenomena induced by the gas–liquid–solid coupling interfaces in such liquid-filled cracks and investigate their potential applications for such crack detection. Firstly, the state equation for a liquid-filled cavity in beams is established to determine the nonlinear dependences of stress–strain relationship at crack wall on the viscous and capillary pressure in liquid. Secondly, a modified acoustic modulation method, in which swept signal is used as the pumping wave to sufficiently trigger and enhance the nonlinear behaviours at the gas–liquid–solid interfaces without requiring exact reference information, is utilized for detecting sub-millimeter cracks filled with different liquid. The results suggest that the liquid fillers may cause considerable increase of the damage-related acoustic nonlinearities involving hysteresis nonlinearity, nonlinear elastic behavior and dissipative nonlinearity. Additional analysis provides compelling evidence for the following valuable conclusions: 1) the capillary pressure is a key factor that promotes conducive to the nonlinear elastic behavior that is the primary source of the first-order sum-difference frequency; 2) the viscous pressure contributes to hysteresis as well as the nonlinear dissipation, and the latter promotes the second-order sum frequency. Further, such nonlinear performance especially dissipation offer promising prospects for nonlinear acoustic diagnostic of such cracks. All results obtained in this study will aid in understanding the nonlinear wave processes and further improving the reliability of crack detection in engineering.

Theoretical and numerical investigations of acoustic field characteristics of shear-horizontal feature guided waves in a welded joint

This paper investigates acoustic field characteristics of shear-horizontal feature guided waves (SH-FGWs) propagating through topographic waveguides like welds and stiffeners in plate-like structures. It establishes mathematical models of second harmonic and quasi-static component (QSC) generated by SH-FGWs in a welded joint and analyzes their theoretical characteristics. Using two-dimensional semi-analytical finite element and three-dimensional finite element methods, it studies the dispersion characteristics of FGWs and acoustic field distribution at specific frequencies of SH-FGWs, as well as their nonlinear response. This study provides new physical insights into the acoustic field distribution and nonlinear response of SH-FGWs in topographic waveguides.

Using nonlinear ultrasonic measurements to estimate parameters of the sedimentation of slurry solid phase in thickener

Purpose. Improvement of the method for estimating sedimentation process parameters of the slurry solid phase particles in thickener on the basis of measurements of the nonlinear characteristics of ultrasonic waves propagating in a controlled medium. Methodology. The following methods were used: analysis of scientific results and practical developments; methods of mathematical statistics for evaluating the results of experiments; methods of analytical synthesis; methods of numerical modeling for the synthesis and analysis of a mathematical model. Findings. It was established that the nonlinearity of the process of propagation of ultrasonic waves in ore slurry, which is determined by the number and size of crushed ore particles in it, can be estimated by determining the amplitudes of several harmonics of the measured acoustic signal. This approach allows maintaining the productivity of the desliming process in accordance with the characteristics of the ore suspension, without allowing the loss of valuable components. Obtaining real-time information about the characteristics of the particle sedimentation process in the ore suspension at the initial stage enables reducing the duration of transitional processes in the control system. Originality. The method for estimating the parameters of the deposition of the solid phase of the pulp in the thickener has been improved, which is based on the fact that the nonlinearity of the process of propagation of a controlled ultrasonic signal in the thickener; this leads to modulation of the generated ultrasonic packet and, consequently, the appearance of higher harmonics. To obtain a more accurate estimate of the nonlinearity of this process, all the values obtained must be normalized to represent only the relative changes in the acoustic nonlinear response. Practical value. A system for automatic control of the thickener operation is proposed, which uses nonlinear ultrasonic measurements to estimate the parameters of the sedimentation of the solid phase of the pulp in the thickener. According to the results of industrial tests of the system of automatic control of the thickener based on ultrasonic control devices, it was established that its use as part of the automated control system for the technological processes of beneficiation of iron ore raw materials at the ore beneficiation factory of the Northern mining works will allow reducing water consumption by 3.5 % and iron-magnetite losses by 0.6–0.7 %.

Broadband Transient Response and Wavelength-Tunable Photoacoustics in Plasmonic Hetero-nanoparticles.

The optically driven acoustic modes and nonlinear response of plasmonic nanoparticles are important in many applications, but are strongly resonant, which restricts their excitation to predefined wavelengths. Here, we demonstrate that multilayered spherical plasmonic hetero-nanoparticles, formed by alternating layers of gold and silica, provide a platform for a broadband nonlinear optical response from visible to near-infrared wavelengths. They also act as a tunable optomechanical system with mechanically decoupled layers in which different acoustic modes can be selectively switched on/off by tuning the excitation wavelength. These observations not only expand the knowledge about the internal structure of composite plasmonic nanoparticles but also allow for an additional degree of freedom for controlling their nonlinear optical and mechanical properties.

Combined harmonic generation of feature guided waves mixing in a welded joint

In our previous research, the second harmonic generation (SHG) of feature guided waves (FGWs) in a welded joint with material nonlinearity was analyzed theoretically and observed numerically. However, some drawbacks including strict generation criteria, inability of distinguishing nonlinearity, and being unable to localize local defects of SHG-based nonlinear ultrasonic technique, limit the practical testing and application. Wave mixing is a promising alternative to overcome these shortcomings. In this paper, we investigated another acoustic nonlinear response of FGWs, so-called combined harmonic generation (CHG) caused by FGWs mixing in a welded joint. Theoretical analysis of second-order combined harmonic waves induced by two FGWs mixing in a welded joint was firstly implemented based on semi-analytical finite element (SAFE) and perfectly matched layer (PML) methods. Based on the theoretical analysis, four FGW mode triplets, which satisfy the internal resonant conditions, were selected for the observation of CHG caused by FGW mixing in a welded joint from a numerical perspective. CHG induced by FGW mixing with the cumulative growth effect was successfully observed within the mixing zone, which is consistent with the theoretical prediction. This study provides a straightforward analysis not previously available of the process of CHG of FGWs propagating and mixing in a welded joint.

Non-linear effects in thin slits for low frequency sound absorption

In recent years, various novel concepts of efficient low-frequency acoustic absorbers have been proposed. The present paper investigates in detail the non-linear acoustic response of resonators coupled to plates with thin slits. A laser-cut thin plate is positioned inside the neck of a Helmholtz resonator. Various shapes of slits are considered, including a cantilever beam. This system produces a strong acoustic response in the vicinity of the resonance frequency of the beam, which can be adjusted to target low frequencies. However, this acoustic response exhibits a significant dependence on the incident sound level. In this paper, these systems are mechanically and acoustically modelled and characterised under normal incidence in order to describe and predict the non-linearities observed. To this end, a generalised expression for the resistance and reactance of such thin structures is proposed and validated against experimental data.

The effect of hydrogen enrichment, flame-flame interaction, confinement, and asymmetry on the acoustic response of a model can combustor

To maximise power density practical gas turbine combustion systems have several injectors which can lead to complex interactions between flames. However, our knowledge about the effect of flame-flame interactions on the flame response, the essential element to predict the stability of a combustor, is still limited. The present study investigates the effect of hydrogen enrichment, flame-flame interaction, confinement, and asymmetries on the linear and non-linear acoustic response of three premixed flames in a simple can combustor. A parametric study of the linear response, characterised by the flame transfer function (FTF), is performed for swirling and non-swirling flames. Flame-flame interactions were achieved by changing the injector spacing and the level of hydrogen enrichment by power from 10 to 50%. It was found that the latter had the most significant effect on the flame response. Asymmetry effects were investigated by changing one of the flames by using a different bluff-body to alter both the flame shape and flow field. The global flame response showed that the asymmetric cases can be reconstructed using a superposition of the two symmetric cases where all three bluff-bodies and flames are the same. Overall, the linear response characterised by the flame transfer function (FTF) showed that the effect of increasing the level of hydrogen enrichment is more pronounced than the effect of the injector spacing. Increasing hydrogen enrichment results in more compact flames which minimises flame-flame interactions. More compact flames increase the cut-off frequency which can lead to self-excited modes at higher frequencies. Finally, the non-linear response was characterised by measuring the flame describing function (FDF) at a frequency close to a self-excited mode of the combustor for different injector spacings and levels of hydrogen enrichment. It is shown that increasing the hydrogen enrichment leads to higher saturation amplitude whereas the effect of injector spacing has a comparably smaller effect.

A theoretical and experimental investigation of the nonlinear acoustic response of acoustic insertion elements.

In a previous paper, a model was developed for the nonlinear acoustic resistance for compact insertion elements. Within the model, two loss coefficients are used to tune the model for each type of element, and data were used to empirically determine these coefficients for an area contraction. This paper extends the nonlinear model, developing expressions based on physical principles for the forward and reverse loss coefficients for both an area contraction and orifice. In addition, experimental data for the acoustic resistance of both elements was taken using an impedance tube. Utilizing the expressions developed, the model compares favorably with the experimental data.

An experimental validation of a nonlinear acoustic resistance model for an acoustically compact area contraction with steady mean flow.

In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.

Numerical analyses of nonlinear acoustic wave radiation behaviors of vibrational objects immersed in infinite fluid

This paper is concerned with numerical analyses of radiated sound behaviors of dynamic systems containing nonlinear vibrational objects immersed in a compressible and inviscid fluid of infinite extent. The vibrational solids are modelled by the Lagrangian description of motion, while the fluid surrounding the vibrational objects is formulated by the two-dimensional linearized Euler equations (LEEs). The nonlinear dynamic responses of the vibrational solids are computed by both the harmonic balance method (HBM) and direct time integration method. A fourth-order dispersion-relation-preserving (DRP) scheme is implemented on a fixed Cartesian grid to solve the governing equations of the fluid. A constrained moving least-squares sharp-interface immersed boundary method is adopted to impose the compatibility conditions on the common boundaries of the vibrational objects and the fluid. Selective filters are employed to suppress the spurious short waves appearing in numerical computations. Several numerical tests are carried out to confirm the validity of the developed vibro-acoustic coupling computational model by comparing the present solutions with the exact solutions. Nonlinear acoustic wave responses of vibrational objects with smooth and non-smooth nonlinearities are examined, including rigid cylinder-shaped oscillators resting on nonlinear mounts, ellipse-shaped objects suspended on nonlinear torsional springs, and rigid isolators with frictions and clearances. It is found that for vibrational objects containing nonlinearities, the amplitude-frequency responses of radiated sound pressure exhibit shifting resonance frequencies, secondary resonances and jump phenomenon. The intermittent collisions of the vibrational objects with clearances can result in abrupt fluctuations and distortions of the radiated acoustic waves in fluid. In addition, the radiation efficiency of high-order harmonics of nonlinear acoustic waves induced by stick/slip transitions of friction interfaces can reach to maximum with the friction coefficient.