Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells' material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter deltax = mid R:x2 - x1mid R: (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves.     

Acoustic radiation force acting on elastic and viscoelastic spherical shells placed in a plane standing wave field

The theory of the acoustic radiation force acting on elastic spherical shells suspended in a plane standing wave field is developed in relation to their thickness and the content of their hollow regions. The theory is modified to include the effect of a hysteresis type of absorption of compressional and shear waves in the material. The fluid-loading effect on the acoustic radiation force function Y(st) is analyzed as well. Results of numerical calculations are presented for a number of elastic and viscoelastic materials, with the hollow region filled with water or air. These results show how the damping due to absorption, the change of the interior fluid inside the shells' hollow regions, and the exterior fluid surrounding their structures, affect the acoustic radiation force.     

Dynamic acoustic radiation force acting on cylindrical shells: theory and simulations

An object placed in an acoustic field is known to experience a force due to the transfer of momentum from the wave to the object itself. This force is known to be steady when the incident field is considered to be continuous with constant amplitude. One may define the dynamic (oscillatory) radiation force for a continuous wave-field whose intensity varies slowly with time. This paper extends the theory of the dynamic acoustic radiation force resulting from an amplitude-modulated progressive plane wave-field incident on solid cylinders to the case of solid cylindrical shells with particular emphasis on their thickness and contents of their hollow regions. A new factor corresponding to the dynamic radiation force is defined as Y(d) and stands for the dynamic radiation force per unit energy density and unit cross sectional surface. The results of numerical calculations are presented, indicating the ways in which the form of the dynamic radiation force function curves are affected by variations in the material mechanical parameters and by changes in the interior fluid inside the shell's hollow region. It was shown that the dynamic radiation force function Y(d) deviates from the static radiation force function for progressive waves Y(p) when the modulation frequency increases. These results indicate that the theory presented here is broader than the existing theory on cylinders.     

Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves

In this paper, analytical equations are derived for the time-averaged radiation force induced by progressive and standing acoustic waves incident on elastic spherical shells covered with a layer of viscoelastic and sound-absorbing material. The fluid surrounding the shells is considered compressible and nonviscous. The incident field is assumed to be moderate so that the scattered field from the shells is taken to linear approximation. The analytical results are illustrated by means of a numerical example in which the radiation force function curves are displayed, with particular emphasis on the coating thickness and the content of the hollow region of the shells. The fluid-loading on the radiation force function curves is analysed as well. This study attempts to generalize the various treatments of radiation force due to both progressive and standing waves on spherically-shaped structures immersed in ideal fluids. The results show that various ways can be effectively used for damping resonance peaks, such as by changing the fluid in the interior hollow region of the shells or by changing the coating thickness.     

通过周期环板和附连流体的两同心圆柱壳体间的振动耦合效应

理论研究了两个同心圆柱壳体间通过周期环饭和附连流体的耦合效应。在环板内只有准纵波存在的假定下,给出环板的反作用力的表达式,并建立外壳体的声辐射解析表达式。无限长双层壳体的数值分析结果和舱段模型的实验结果一致。通过数值结果同时分析了声学流体和周期环板的载荷特征,以及它们对外壳体远场声辐射的影响。      

Axial time-averaged acoustic radiation force on a cylinder in a nonviscous fluid revisited

Objective

The present research examines the acoustic radiation force of axisymmetric waves incident upon a cylinder of circular surface immersed in a nonviscous fluid. The attempt here is to unify the various treatments of radiation force on a cylinder with arbitrary radius and provide a formulation suitable for any axisymmetric incident wave.

Method and results

Analytical equations are derived for the acoustic scattering field and the axial acoustic radiation force. A general formulation for the radiation force function, which is the radiation force per unit energy density per unit cross-sectional surface, is derived. Specialized forms of the radiation force function are provided for several types of incident waves including plane progressive, plane standing, plane quasi-standing, cylindrical progressive diverging, cylindrical progressive converging and cylindrical standing and quasi-standing diverging waves (with an extension to the case of spherical standing and quasi-standing diverging waves incident upon a sphere).

Significance and some potential applications

This study may be helpful essentially due to its inherent value as a canonical problem in physical acoustics. Potential applications include particle manipulation of cylindrical shaped structures in biomedicine, micro-gravity environments, fluid dynamics properties of cylindrical capillary bridges, and the micro-fabrication of new cylindrical crystals to better control light beams.     

Negative axial radiation forces on solid spheres and shells in a Bessel beam

Prior computations predict that fluid spheres illuminated by an acoustic Bessel beam can be subjected to a radiation force directed opposite the direction of beam propagation. The prediction of negative acoustic radiation force is extended to the cases of a solid poly(methylmethacrylate) PMMA sphere in water and an empty aluminum spherical shell in water. Compared with the angular scattering patterns for plane wave illumination, the scattering into the back hemisphere is suppressed when the radiation force is negative. This investigation may be helpful in the development of acoustic tweezers and in the development of methods for manipulating objects during space flight.     

Pseudo-Gaussian cylindrical acoustical beam – Axial scattering and radiation force on an elastic cylinder

Making use of the addition theorem for the cylindrical wave functions and the complex-source-point method in cylindrical coordinates, an exact solution to the Helmholtz equation is derived, which corresponds to a tightly focused (or collimated) cylindrical quasi-Gaussian beam with arbitrary waist. The solution is termed “quasi-Gaussian” to make a distinction from the standard Gaussian beam solution obtained in the paraxial approximation. The advantage of introducing this new solution is the efficient and fast computational modeling of tightly focused or quasi-collimated cylindrical wave-fronts depending on the dimensionless waist parameter kw₀, where k is the wavenumber of the acoustical radiation. Moreover, a closed-form partial-wave series expansion is obtained for the incident field, which has the property that the axial scattering (i.e. along the direction of wave propagation) and the axial acoustic radiation force (which is a time-averaged quantity) on a cylinder, can be calculated without any approximations in the limit of linear acoustical waves in a nonviscous fluid. Examples are found where the extinction in the radiation force function plot is found to be correlated with conditions giving reduction of the backscattering from an elastic cylinder. Those results are useful in beam-forming design, particle manipulation in acoustic tweezers operating with focused cylindrical beams, and the prediction of the scattering and radiation forces on a cylindrical particle or liquid bridges.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency.The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.     

Axial acoustic radiation force of progressive cylindrical diverging waves on a rigid and a soft cylinder immersed in an ideal compressible fluid

Background and motivation

Previous works investigating the radiation force of diverging spherical progressive waves incident upon spherical particles have demonstrated the direction of reversal of the force when the particle is subjected to a curved wave-front. In this communication, the analysis is extended to the case of diverging cylindrical progressive waves incident upon a rigid or a soft cylinder in a non-viscous fluid with explicit calculations for the radiation force function (which is the radiation force per unit energy density and unit cross-sectional surface) not shown in [F.G. Mitri, Ultrasonics 50 (2010) 620-627].

Method

A closed-form solution presented previously in [F.G. Mitri, Ultrasonics 50 (2010) 620-627] is used to plot the radiation force function with particular emphasis on the difference from the results of incident plane progressive waves versus the size parameter ka (k is the wave number and a is the cylinder’s radius) and the distance of the cylinder from the acoustic source r₀.

Results

Radiation force function calculations for the rigid cylinder unexpectedly reveal that under specific conditions determined by the frequency of the acoustic field, the radius of the cylinder, as well as the distance to the acoustic source, the force becomes attractive (negative force). In addition, the numerical results show that the radiation force on a rigid cylinder does not generally obey the inverse-distance law with respect to the distance from the source.

Conclusion and potential applications

These results suggest that it may be possible, under specific conditions, to pull a cylindrical structure back toward the acoustic source using progressive cylindrical diverging waves. They may also provide a means to predict the radiation force required to manipulate non-destructively a single cylindrical structure. Potential applications include the design of a new generation of acoustic tweezers operating using a single beam of progressive waves (in contrast to the traditional version of acoustical tweezers in which an acoustic standing wave field is produced using two counter-propagating acoustic fields) for investigations in the field of flow cytometry, particle manipulation and entrapment.     

Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves’ amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.     

Transition from progressive to quasi-standing waves behavior of the radiation force of acoustic waves—Example of a high-order Bessel beam on a rigid sphere

Prior computations have predicted the time-averaged acoustic radiation force on fluid spheres in water when illuminated by an acoustic high-order Bessel beam (HOBB) of quasi-standing waves. These computations are extended to the case of a rigid sphere in water which perfectly mimics a fluid sphere in air. Numerical results for the radiation force function of a HOBB quasi-standing wave tweezers are obtained for beams of zero, first and second order, and discussed with particular emphasis on the amplitude ratio describing the transition from progressive waves to quasi-standing waves behavior. This investigation may be helpful in the development of acoustic tweezers and methods for manipulating objects in reduced gravity environments and space related applications.     

Acoustic radiation of cylindrical elastic shells subjected to a point source: investigation in terms of helical acoustic rays.

The paper deals with the acoustic radiation of a cylindrical elastic shell with no internal loading surrounded by a fluid medium when its external surface is subjected to a point source. The problem is addressed via the use of the spatial Fourier transform. An expression is obtained for the radiated pressure that is evaluated for the far field using both the stationary phase method and the fast Fourier transform (FFT). The acoustic field calculated from the FFT is much more complicated than that obtained by using only the stationary phase method. In agreement with the geometrical theory of diffraction (GTD), alternative interpretations of the radiated field in terms of helical acoustic rays allows one to understand the reason for this result. The outstanding phenomenon underlined by the use of the FFT is the emergence of an infinite number of spatial dispersion curves associated with each leaky wave propagating in shells when excited by a point source.     

驻波声场中圆柱形管道周围颗粒的运动特性

针对圆柱形管道外部的流体与颗粒介质运动问题,提出了结合圆柱周围声辐射力和声流Stokes力的研究方法。从柱体外部声流方程出发,得到影响涡流结构的无量纲参数Rem≥325.27时,外涡最大流速大于内涡最大流速。在此基础上,采用Nyborg的边界滑移速度理论,获得管道外部声流的极限滑移速度,推导得出圆柱附近的声辐射力公式。基于此公式,在理论上推导出颗粒速度为0、声辐射力和声流Stokes力平衡时,颗粒临界直径的表达式。通过对圆柱位于不同位置时,圆柱外部的颗粒运动进行仿真模拟,得到与理论公式相一致的结论:颗粒的临界直径的大小与声波频率有关,当颗粒直径小于临界直径时,声流Stokes力为主导,颗粒随声流运动,颗粒直径大于等于临界直径时,声辐射力为主导,颗粒在声辐射力作用下逐渐向声辐射力的节点聚集。理论与仿真结果表明该方法可用于分析管道外颗粒的分布状态,其研究结果有助于解决电站中换热器的管道结垢、热交换率降低等问题。     

Structure-borne noise reduction for an infinite, elastic cylindrical shell

A theoretical model was developed to evaluate the reduction of structure-borne noise generated by an axially symmetric ring force which is applied on the interior of the cylindrical shell. The vibrating cylindrical shell is coated with a microvoided elastomer that is acoustically soft material designed for the reduction of the generated noise. The analytical model is a two-layer shell structure comprised of a cylindrical shell and an outer layer (coating) that is perfectly bonded to the cylindrical shell. The outer and inner surfaces of the coated shell are in contact with water and air, respectively. The analysis for this problem is based on the theory of elasticity, acoustic wave equations, and pertinent boundary conditions. Effects of various parameters such as coating thickness and material properties on the noise reductions are presented.     

Vibration of piezoelectric elements surrounded by fluid media

In this paper we analyse vibrational characteristics of piezoceramic shells surrounded by acoustic media. Main results are presented for radially polarized piezoceramic PZT5 elements of hollow cylindrical shapes. The coupling in the radial direction between the solid and the acoustic media is accounted for indirectly, via impedance boundary conditions. The model based on such impedance boundary condition approximations offers a robust simplified alternative to a full scale fluid-solid interaction modelling. By using this model, we analyse numerically the influence of the boundary conditions imposed in the axial direction for long, medium, and short (disk-like) piezoceramic elements.     

Axial radiation force of a bessel beam on a sphere and direction reversal of the force

An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid. The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid. The Bessel beam is characterized by the cone angle beta of its plane wave components where beta=0 gives the limiting case of an ordinary plane wave. Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation. Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam. This condition may also be helpful in the design of acoustic tweezers for biophysical applications. Other potential applications include the manipulation of objects in microgravity. Islands in the (ka, beta) parameter plane having a negative radiation force are calculated for the case of a hexane drop in water. Here k is the wave number and a is the drop radius. Low frequency approximations to the radiation force are noted for rigid, fluid, and elastic solid spheres in an inviscid fluid.     

Fiber-optic, cantilever-type acoustic motion velocity hydrophone

The interaction between fluid loaded fiber-optic cantilevers and a low frequency acoustic wave is investigated as the basis for an acoustic vector sensor. The displacements of the prototype cantilevers are measured with an integrated fiber laser strain sensor. A theoretical model predicting the frequency dependent shape of acoustically driven planar and cylindrical fiber-optic cantilevers incorporating effects of fluid viscosity is presented. The model demonstrates good agreement with the measured response of two prototype cantilevers, characterized with a vibrating water column, in the regime of Re ≥ 1. The performance of each cantilever geometry is also analyzed. Factors affecting the sensor performance such as fluid viscosity, laser mode profile, and support motion are considered. The planar cantilever is shown to experience the largest acoustically induced force and hence the highest acoustic responsivity. However, the cylindrical cantilever exhibits the smoothest response in water, due to the influence of viscous fluid damping, and is capable of two axis particle velocity measurement. These cantilevers are shown to be capable of achieving acoustic resolutions approaching the lowest sea-state ocean noise.     

Influence of circumferential partial coating on the acoustic radiation from a fluid-loaded shell

Acoustic compliant coatings are a common approach to mitigate the radiation and scattering of sound from fluid-loaded submerged structures. An acoustic compliant coating is a coating that decouples an acoustic source from the surrounding acoustic medium; that is, it provides an acoustic impedance mismatch (different density and speed of sound product). Such a coating is distinct from an ordinary compliant coating in that it may not be resilient in the sense of low stiffness, but still provides an acoustic impedance mismatch. Ideally, the acoustic coating is applied uniformly over the entire surface of the fluid-loaded structure to minimize the acoustic radiation and scattering. However, in certain instances, because of appendages, it may not be practically possible to completely cover the surface of a fluid-loaded structure to decouple it from the adjacent acoustic medium. Furthermore, there may be some inherent advantages to optimizing the distribution of the coating around areas from which the acoustic radiation appears to be dominant. This would be analogous to the application of damping treatment to a vibrating structure in areas where the vibration levels are highest. In the case of the acoustic radiation the problem is more complex because of the coupling between the acoustic fluid and the structure. In this paper, the influence of a partial coating on the acoustic radiation from a fluid-loaded, cylindrical shell of infinite extent and excited by either a line force or an incident plane acoustic wave is examined. The solution to the response and scattered pressure is developed following the procedure used by the authors in previous work on the scattering from fluid-loaded plates and shells. The coating is assumed to be normally reacting providing a decoupling layer between the acoustic medium and the structure; that is, it does not add mass or stiffness to the base structure. The influence of added mass or stiffness of the coating can be included as an added inhomogeneity and treated separately in the solution.