Shock Amplitude Research Articles

Building a weak shockwave from linear modes

In shockwave theory, the density, velocity and pressure jumps are derived from the conservation equations. Here, we address the physics of a weak shock the other way around. We first show that the density profile of a weak shockwave in a fluid can be expressed as a sum of linear acoustic modes. The shock so built propagates at the speed of sound and matter is exactly conserved at the front crossing. Yet, momentum and energy are only conserved up to order 0 in powers of the shock amplitude. The density, velocity and pressure jumps are similar to those of a fluid shock, and an equivalent Mach number can be defined. A similar process is possible in magnetohydrodynamics. Yet, such a decomposition is found impossible for collisionless shocks due to the dispersive nature of ion acoustic waves. Weakly nonlinear corrections to their frequency do not solve the problem. Weak collisionless shocks could be inherently nonlinear, non-amenable to any linear superposition. Or they could be non-existent, as hinted by recent works.

Influence of sea wave shock on transient start-up performance of water-lubricated bearing

The water-lubricated bearing in ship propulsion system is easily impacted by sea wave shock, which is a great threat to the smooth start-up of the bearing system. Therefore, in the present research, the Euler equations, average Reynolds equation, and sea wave shock function are combined together to build the start-up model of water-lubricated bearing. The influences of amplitude, direction, and entry time of sea wave shock on the start-up performance of bearing are studied. The result shows that the shaft has a strong instantaneous vibration under the influence of friction force at the initial start-up stage, and the shock load with appropriate direction and amplitude can suppress or even eliminate this vibration phenomenon. The earlier the shock enters the start-up process, the more serious asperity contact gets, and the worse the system’s stability becomes. The increase of the shock load amplitude and the advance of the shock load entry time can help the shaft rapidly lift off. This study can provide a reference for the smooth start-up of ship propulsion system in a sea wave environment.

Absolute instability in shock-containing jets

We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin–Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

Remarks on acoustic propagation in inhomogeneous fluids: Single-phase shock regularization under the Maxwell model

The atmospheric shock problem considered in a recent article by Jordan (2020) is revisited. We show that the amplitude blow-up suffered by upward propagating acoustic shocks in an atmosphere whose ambient temperature is constant can also be eliminated by regarding air as a Maxwell fluid (i.e., a type of viscoelastic fluid), thus obviating the need for the dual-phase model assumed by Jordan (2020). Using an approach based on the Laplace transform, we then establish the existence of a range of values of the Maxwell relaxation time parameter for which the shock amplitude tends to zero and, moreover, that the upper bound of this range can be determined exactly by solving a certain quartic polynomial. And while linear, the equation of motion studied herein is shown to exhibit behaviors remarkably similar to those of certain PDEs that arise in nonlinear acoustics theory.

Dual-Use Transducer for Ultrasound Imaging and Pulsed Focused Ultrasound Therapy.

Pulsed focused ultrasound (pFUS) uses short acoustic pulses delivered at low duty cycle and moderate intensity to noninvasively apply mechanical stress or introduce disruption to tissue. Ultrasound-guided pFUS has primarily been used for inducing cavitation at the focus, with or without contrast agents, to promote drug delivery to tumors. When applied in tandem with contrast agents, pFUS is often administered using an ultrasound imaging probe, which has a small footprint and does not require a large acoustic window. The use of nonlinear pFUS without contrast agents was recently shown to be beneficial for localized tissue disruption, but required higher ultrasound pressure levels than a conventional ultrasound imaging probe could produce. In this work, we present the design of a compact dual-use 1-MHz transducer for ultrasound-guided pFUS without contrast agents. Nonlinear pressure fields that could be generated by the probe, under realistic power input, were simulated using the Westervelt equation. In water, fully developed shocks of 42-MPa amplitude and peak negative pressure of 8 MPa were predicted to form at the focus at 458-W acoustic power or 35% of the maximum reachable power of the transducer. In absorptive soft tissue, fully developed shocks formed at higher power (760 W or 58% of the maximum reachable power) with the shock amplitude of 33 MPa and peak negative pressure of 7.5 MPa. The electronic focus-steering capabilities of the array were evaluated and found to be sufficient to cover a target with dimensions of 19 mm in axial direction and 44 mm in transversal direction.

Numerical study on transient mixed lubrication response for multiple grooves water-lubricated bearings under non-linear shock with 3D thermal effect

The main purpose of this study is to assess the transient mixed lubrication performance of multiple grooves water-lubricated bearings subjected to external shock considering 3D thermal behavior, and design a groove arrangement to reduce the transient contact force under external shock based on the numerical prediction. The effectiveness of the present numerical simulation is verified by the comparisons with the published results. Based on the numerical study, the transient mixed lubrication behaviors under different shock directions and amplitudes are revealed. The results demonstrate that, due to the hydrodynamic loss of the macro groove (depth is 1.5 mm), the transient mixed lubrication performance of the full groove water-lubricated bearing is poor, especially when the shock direction is horizontal. In order to improve transient tribo-dynamic behavior of the full groove water-lubricated bearing, the four-grooved and six-grooved (partial-grooved) water-lubricated bearings are designed, and its effectiveness is proved by numerical results. Subsequently, the effects of the radial clearance, bush thickness and water-lubricated material on the transient contact force of the partial-grooved water-lubricated bearing are evaluated. Numerical results indicate that the transient contact force is weakened with the increasing of radial clearance, and transient contact performance is improved with the increasing of bush thickness for the vertical shock. Additionally, the simulation results demonstrate that the water-lubricated material with lower hardness and elastic modulus has smaller transient contact force under external shock.

Ultrastructural Analysis of Volumetric Histotripsy Bio-effects in Large Human Hematomas

Large-volume soft tissue hematomas are a serious clinical problem, which, if untreated, can have severe consequences. Current treatments are associated with significant pain and discomfort. It has been reported that in an in vitro bovine hematoma model, pulsed high-intensity focused ultrasound (HIFU) ablation, termed histotripsy, can be used to rapidly and non-invasively liquefy the hematoma through localized bubble activity, enabling fine-needle aspiration. The goals of this study were to evaluate the efficiency and speed of volumetric histotripsy liquefaction using a large in vitro human hematoma model. Large human hematoma phantoms (85 cc) were formed by recalcifying blood anticoagulated with citrate phosphate dextrose/saline–adenine–glucose–mannitol solution. Typical boiling histotripsy pulses (10 or 2 ms) or hybrid histotripsy pulses using higher-amplitude and shorter pulses (0.4 ms) were delivered at 1% duty cycle while continuously translating the HIFU focus location. Histotripsy exposures were performed under ultrasound guidance with a 1.5-MHz transducer (8-cm aperture, F# = 0.75). The volume of liquefied lesions was determined by ultrasound imaging and gross inspection. Untreated hematoma samples and samples of the liquefied lesions aspirated using a fine needle were analyzed cytologically and ultrastructurally with scanning electron microscopy. All exposures resulted in uniform liquid-filled voids with sharp edges; liquefaction speed was higher for exposures with shorter pulses and higher shock amplitudes at the focus (up to 0.32, 0.68 and 2.62 mL/min for 10-, 2- and 0.4-ms pulses, respectively). Cytological and ultrastructural observations revealed completely homogenized blood cells and fibrin fragments in the lysate. Most of the fibrin fragments were less than 20 μm in length, but a number of fragments were up to 150 μm. The lysate with residual debris of that size would potentially be amenable to fine-needle aspiration without risk for needle clogging in clinical implementation.

Large eddy simulation of the turbulent mixing at an oblique interface induced by non-classical planar shock waves

The interaction between the shock wave and phase interface is one of the classic problems in aerospace and turbulent combustion engineering. In this paper, the instability of the gas–liquid interface driven by non-classical planar shock waves is studied. Based on the volume of fluid model and large eddy simulation method, the deformation process and the turbulent mixing phenomenon of the oblique interface induced by non-classical planar shock waves in a two-dimensional plane are numerically investigated by using a high-performance computer cluster. The effects of incident shock wave intensity, initial amplitude, initial wavelength, and inclined angle of the gas–liquid two-phase oblique interface are analyzed. The results show that the incident shock intensity has the most significant effect on the interface deformation and the development of turbulent mixing, and the initial amplitude and wavelength of the incident shock and the inclined interface angle also play a certain role in the deformation and development process. Overall, the width of the turbulent mixing zone increases with time under a given condition, and the convex structure will fall off and break up at the phase interface in the later stage of turbulent mixing.

Phase-Aberration Correction for HIFU Therapy Using a Multielement Array and Backscattering of Nonlinear Pulses.

Phase aberrations induced by heterogeneities in body wall tissues introduce a shift and broadening of the high-intensity focused ultrasound (HIFU) focus, associated with decreased focal intensity. This effect is particularly detrimental for HIFU therapies that rely on shock front formation at the focus, such as boiling histotripsy (BH). In this article, an aberration correction method based on the backscattering of nonlinear ultrasound pulses from the focus is proposed and evaluated in tissue-mimicking phantoms. A custom BH system comprising a 1.5-MHz 256-element array connected to a Verasonics V1 engine was used as a pulse/echo probe. Pulse inversion imaging was implemented to visualize the second harmonic of the backscattered signal from the focus inside a phantom when propagating through an aberrating layer. Phase correction for each array element was derived from an aberration-correction method for ultrasound imaging that combines both the beamsum and the nearest neighbor correlation method and adapted it to the unique configuration of the array. The results were confirmed by replacing the target tissue with a fiber-optic hydrophone. Comparing the shock amplitude before and after phase-aberration correction showed that the majority of losses due to tissue heterogeneity were compensated, enabling fully developed shocks to be generated while focusing through aberrating layers. The feasibility of using a HIFU phased-array transducer as a pulse-echo probe in harmonic imaging mode to correct for phase aberrations was demonstrated.

Performance Analysis of Absolute Acceleration Shock Response Spectrum

The Absolute Acceleration Shock Response Spectrum (AASRS), which is most commonly used in engineering is analyzed in detail, and the effects of shock duration, shock amplitude and shock waveform on AASRS are discussed respectively. Shock duration has the greatest influence on the shape and change trend of AASRS, followed by shock amplitude. However, shock amplitude only affects the amplitude of AASRS and does not change the overall change trend. Shock waveform has the smallest influence on AASRS and mainly affects the frequency point of peak acceleration.

Defibrillation threshold modeling to refine implant recommendations for an extravascular ICD system

Abstract Background The extravascular ICD (EV ICD) is a novel defibrillator that couples a substernal lead to a device under the left axilla. The electrode locations for best defibrillation performance are unknown. In this study we use data from a 21 patient pilot study to address this question. Objective To create computational torso models to study the effect of device and lead position on defibrillation threshold (DFT). Methods Finite element models were developed from CT and intraoperative imaging of the 21 patients enrolled in the EV ICD Pilot Study. Between 150 and 200 combinations of electrode locations were created for each patient, including the actual implant locations as determined from post-implant CT. The shock amplitudes from DFT testing and multiple vector impedance measurements from a large subset of patients and their as-implanted models were used to calibrate global model parameters. In total, 3330 implant models were automatically meshed, simulated and analyzed to compute predicted DFT values. For each patient an acceptable implant zone was calculated in which it is predicted that they would pass implant DFT testing. The zones for all patients were aligned and combined using common anatomical landmarks so that a common zone for acceptable DFT performance could be calculated for the cohort. Results Two patients were omitted due to incomplete CT data and 16 models were used during the calibration phase. Final analysis was performed using 19 patient models. The model results recommend positioning the lead slightly left of the sternal midline with the most proximal electrode 10 mm above the xiphisternal junction. Similarly, the device should be positioned so that its upper margin is at the height of the leftmost projection of the heart as seen in the AP view, and its posterior margin aligned with the posterior margin of the ventricles. The figure illustrates these positions. The model predicts that using these locations will result in acceptable DFT performance for all 19 patients - including one who failed testing at implant. Conclusion Modeling showed that DFT is dependent on both lead and device location. Furthermore, the predicted DFT and impedance values are consistent with clinical measurements. Specific lead and device locations were determined that are both clinically identifiable and provide acceptable DFTs in all patients. Implant positioning Funding Acknowledgement Type of funding source: Private company. Main funding source(s): Medtronic PLC

Analysis of the Failure and Performance Variation Mechanism of MEMS Suspended Inductors with Auxiliary Pillars under High-g Shock.

Microelectromechanical systems (MEMS) suspended inductors have excellent radio frequency (RF) performance and they are compatible with integrated circuit (IC). They will be shocked during manufacturing, transportation, and operation; in some applications, the shock amplitude can be as high as tens of thousands of gravitational acceleration (g, 9.8 m/s2). High-g shock will lead to the inductor deformation which affects its performance or even failure of the inductor structure. However, few studies have been carried out on the inductors under high-g shock. In this study, a kind of MEMS suspended inductor with excellent RF and mechanical performance is designed and fabricated. The failure and performance variation mechanism of the inductor under high-g shock is analyzed by measuring and comparing the performance measurement results and the π model parameters extraction results of the inductors before and after air cannon shock test. The results show that the increase of energy loss caused by substrate parasitic effect and the properties variation of the coil material affected by high-g shock are the main reasons for the decrease of RF performance parameters, and the critical stress exceeding the interlayer adhesion is the main reason for the failure of the inductor.

Shock wave in one-dimensional dusty plasma crystal with charge gradient

In this paper, the effect of charge gradient in a one-dimensional dusty plasma crystal is considered to investigate shock structure. Under the continuum limit, the nonlinear Korteweg–de Vries (KdV)–Burgers equation with a charge gradient effect is derived using the reductive perturbation method. Then, the shock solution based on the KdV–Burgers equation is obtained. The influence of the parameter ε, which measures the effect of charge gradient on the dynamic of the shock wave, is discussed in detail. It is found that the shock amplitude and strength increase with the increase in the parameter ε. Furthermore, it is also found that charge gradient effect makes oscillatory shock more easily converted to monotonic shock.

Scalability of increase in spall threshold in the presence of cylindrical protrusions on metals surface

The article analyzes the extent to which the previously detected effect of increase in spall threshold due to nanorelief on the surface can be scaled to large dimensions of the target, the impactor and the relief elements. Earlier, it was shown on the basis of molecular dynamics simulation that the presence of a relief can significantly increase the spall threshold due to plastic deformation in the surface layer of metal and energy dissipation of the reflected shock wave. To study the scalability of this effect on the case of macroscopic targets, and not only on nanoscale systems, an analytical estimation is constructed for decrease in the shock amplitude wave due to plastic dissipation during flattening of cylindrical protrusions on the surface. On the basis of this estimation, it is shown that an increase in the splitting threshold of the rear surface of metals with relief is scalable.

Collapse characterization and shock mitigation by elastomeric metastructures

Viscoelastic metastructures made with elastomeric polymers are recently suggested as solutions for shock mitigation and crash absorption. In these investigations, the mechanical properties are used as proxy indicators of capabilities to suppress energy transfer under such dynamic load conditions. Yet, recent high speed video studies revealed a startling disconnect between quasi-static and dynamic behavior in metastructures having internal beam networks due to the coupled local–global dynamics that are not triggered during quasi-static load cycles. This research undertakes an extensive high speed video data collection synchronized with force measurements to reveal the influences that govern transient shock mitigation properties in elastomeric metastructures. Despite an intuitive advantage of prolonging the collapse behavior through material design, it is conclusively found that unimodal collapse of the metastructure cross-section is the most effective mechanism to mitigate shock amplitude, prolong the duration of the transmitted force, and to reduce the impulse passed through the media. This research may specifically inspire the next generation of elastomeric, reusable shock damping materials.

Partial amorphization of experimentally shocked plagioclase: A spectroscopic study

AbstractShock amorphization of plagioclase, from partial to complete, has been used to evaluate the degree of shock in meteorites. Important information on the shock amplitude can be derived from the measurement of the refractive index in plagioclase, either from mineral separates or in petrographic thin sections. However, this technique is time‐consuming, and associated sample preparations are considered destructive and are not always possible for precious and rare meteorite samples. In addition, plagioclase amorphization is commonly inhomogeneous at the sample scale and a statistically meaningful number of grains must be considered. Here, we apply several nondestructive spectroscopic techniques, such as Raman spectroscopy, photoluminescence, and cathodoluminescence, to plagioclase experimentally shocked at 28 GPa, and thus in the transition regime between crystalline plagioclase and fully amorphous material. Most of the plagioclase was transformed into diaplectic glass at 28 GPa, yet some grains exhibit heterogeneously distributed crystalline domains. This confirms that intrinsic and extrinsic factors lead to local variations in the intensity of the shock pressure within individual plagioclase crystals of homogeneous composition. The amorphization of plagioclase can qualitatively (and potentially also quantitatively) be investigated by spectroscopic techniques, highlighting such local variations in the shock efficiency.

“Design and Perfomance Analysis of MR Twin Tube Shock Absorber Damper of Semi-Active Suspension System”

A shock absorber suspension system of vehicle and bicycle in automobile during travelling on a road surface leads jerky, bound and rebound motion a bicycle or vehicle due to this problem by shock and vibration creates discomfort and unsafely to driver and passenger. The vibration coming from vehicle leads to pain, discomfort and dissipated heat and energy which impact on reduction in efficiency shock absorber on semi active suspension system. Comparison method of actual and design Shock absorber by reductions spring stiffness, use falling tube viscometer method for finding efficient fluid mixture for reducing shock and vibration amplitude of theoretical and experimental method. In this research more shock absorbent and energy efficient Shock Absorber Damper is developed for Splendor two wheeler to controlled the vibration of semi active suspension system of vehicle. The fluid greatly increases its viscosity and result in large damping force, less power consummation, fast and smooth response, and cost effective design and environmentally friendly. The damping force increase and decrease in leads to bounce and renounces.

Acoustic propagation in inhomogeneous fluids: regularization via the introduction of fine particles

It is shown, using analytical methodologies, that the velocity field blow-up suffered by vertically ascending acoustic waves in an isothermal atmosphere can be eliminated via the introduction of fine particles. Assuming the inhomogeneous generalization of the particle-laden flow model known as the (linearized) Marble–Thompson model-1, it is established that bounded, exponentially decreasing, shock amplitudes can be obtained provided the mass fraction of particles exceeds a critical value, for which an exact expression is derived. Lastly, supporting numerical results are presented, special cases are discussed, and possible follow-on studies are noted.

Shock Wave Generation and Radiation from a Turbofan Engine Under Flow Distortion

This paper presents aeroacoustic investigations on a full-scale ultrahigh-bypass-ratio engine with inflow distortion at transonic conditions. Computational fluid dynamics (CFD) simulations are first realized to compute the shocks in the vicinity of the fan. These shocks are then radiated in the near field thanks to computational aeroacoustics (CAA) simulations. The chaining between CFD and CAA simulations is done by injecting the shocks in terms of usual conservative variables using a nonreflecting boundary condition. The CAA solver is based on the nonlinearized Euler equations, which allows definition of the CFD/CAA interface close to the fan where the propagation of shocks is highly nonlinear. Both shock generation and propagation mechanisms are investigated, and the effects of inflow distortion are highlighted by comparison with a baseline case without distortion. The flow distortion is shown to be responsible for a modification of shock amplitudes along the circumferential direction. Thus, azimuthal modes appear in addition to the rotor-locked mode present without distortion. A particular feature of the studied configuration is the presence of a supersonic flow region in the bottom part of the nacelle. This supersonic pocket blocks the shocks in the lower half of the nacelle and modifies the angle at which they leave the nacelle in its upper half. Consequently, the far-field radiation (obtained using Kirchhoff’s integral method) is mainly oriented skyward and toward the side of descending blades. Acoustic power estimates are provided to quantify these effects.

Poroacoustic solitary waves under the unidirectional Darcy–Jordan model

Working in the context of poroacoustics, we present new, physically relevant, explicit solutions to the Cauchy problem for the model we term the (1D) damped Riemann equation. The solitary waveforms that evolve from both Lorentzian (C∞-smooth) and symmetric-exponential (C0-smooth) initial conditions are analyzed, the focus being on wave overturning and the evolution/structure of the shocks which develop thereafter. In addition to those for both the multi- and single-valued forms of each solution, expressions for the shock amplitude, velocity, and critical values of the physical parameters are derived/compared. Lastly, links to other areas of continuum physics, and possible follow-on investigations, are noted.