Circular Piston Research Articles

Comparing the end correction of a spherically baffled piston to infinitely baffled and unbaffled circular radiators (L).

Models of acoustical systems commonly employ end corrections to represent the radiation impedance of a vibrating element. Although several analytic solutions appear in the literature, the end corrections of an infinitely baffled circular piston and an unbaffled semi-infinite circular pipe remain popular in modeling applications. This Letter compares the end correction of these two configurations to that of a radially vibrating cap on a sphere. The results show that the spherically baffled end correction, when expressed as a function of spherical-cap radius, falls between these two extremal boundary conditions.

Incorporating the effect of frequency-independent attenuation within the on-axis spatial impulse response of a circular piston

The spatial impulse response is important for numerical simulations of diagnostic ultrasound. The spatial impulse response, which describes transient diffraction due to an impulsive input, yields closed form analytical expressions for various transducer geometries when the medium is lossless. These analytical expressions are advantageous for simulations that repeatedly evaluate these expressions at hundreds of thousands of points. However, spatial impulse responses evaluated for lossy materials typically require additional numerical calculations that substantially increase the computation time. Thus, analytical or rapidly converging numerical expressions for the lossy spatial impulse response are expected to greatly enhance present simulation methods. This motivates the derivation of on-axis spatial impulse responses for a circular piston that model frequency-independent attenuation. Closed-form analytical expressions for the on-axis spatial impulse response are introduced for two closely related frequency-independent attenuation models. The results show that, as the attenuation constant increases, the peak amplitudes of these lossy on-axis spatial impulse responses decrease. The lossy on-axis impulse response also decreases slightly as time increases beyond the initial arrival time, whereas the lossless on-axis spatial impulse response for a circular piston maintains a constant value after the initial arrival time.

Quantitative assessment of acoustic field characteristics in water by radial extracorporeal shockwave therapy

Radial extracorporeal shockwave therapy (rESWT) is a noninvasive medical technique that treats a range of musculoskeletal conditions. To understand its biological effects and develop personalized treatment plans, it is crucial to fully characterize the acoustic field that rESWT generates. This study presents a quantitative assessment of rESWT's acoustic field, achieved through experiments and simulations. The study measures the acoustic fields using a needle-type hydrophone under different machine settings and establishes and calibrates a computational model based on the experimental measurements. The study also determines the spatial distributions of peak pressure and energy flux density for different driving pressures. High-speed photography is used to visualize cavitation bubbles, which correspond to the negative pressure distribution. The study finds that the axial pressure distribution is similar to the acoustic radiation from an oscillating circular piston, whereas the radial pressure distribution cannot be described by acoustic radiation. Furthermore, the study develops a machine learning model that predicts positive pressure distributions for continuous driving pressure. Overall, this study expands our understanding of the acoustic fields generated by rESWT and provides quantitative information to explore underlying biological mechanisms and determine personalized treatment approaches.

Three-dimensional lattice Boltzmann and finite difference methods for the simulation of ultrasound and thermal convection in a microcavity

This article presents a three-dimensional numerical analysis of the phenomena of ultrasound propagation in air, thermal convection, and their interaction. The simulations are carried out using a hybrid numerical approach based on the lattice Boltzmann and the finite difference techniques. For validation purposes, our numerical model is verified in the case of the study of ultrasound propagation in the air without the presence of thermal convection. This is performed by comparing the numerically calculated acoustic pressure with the analytical results. After this verification, the focus is on the examination of the heat transfer improvement by the ultrasound emitted by the vibration of a circular piston. This acoustic source is mounted in the center of the left cold surface of a microcavity, which is differentially heated and filled with air. The obtained numerical results indicate that the heat transfer is significantly improved by using 10 MHz ultrasound.

Three-dimensional time-domain Green's functions and spatial impulse responses for the van Wijngaarden wave equation

An exact analytical three-dimensional time-domain Green's function is introduced for the van Wijngaarden wave equation when the coefficients of the two loss terms satisfy a specific relationship. This analytical Green's function, which describes frequency-squared attenuation in acoustic media such as water, enables the subsequent derivation of new expressions that describe the lossy spatial impulse response for a circular piston. Initial time-domain assessments, which compare the Green's functions for the van Wijngaarden, Stokes, and power law wave equations using the attenuation and sound speed for water, indicate that these three lossy wave equations yield nearly identical results at distances greater than or equal to 10 μm. Lossy spatial impulse responses are also evaluated with increasing distance in and near the paraxial region of a circular piston radiating in water to reveal some interesting time-domain interactions between frequency-squared attenuation and diffraction. Similar behaviors are also demonstrated for the lossy far-field spatial impulse. In addition, the convergence is demonstrated for two analytically equivalent expressions applied to numerical computations of the lossy spatial impulse response. The results show that these new expressions are ideal for describing and explaining fundamental interactions between frequency-squared attenuation and diffraction in the time-domain.

Transient elastography with focused shear wave beams

Transient elastography (TE) is a clinically available ultrasound elastography technique in which mechanical vibration of a small piston at the tissue surface generates a short shear wave pulse that propagates into the body. The piston doubles as an ultrasonic transducer; thus, the shear wave propagation is measured with pulse-echo ultrasound along the beam axis, yielding the wave speed and tissue stiffness. The long shear wavelength compared to piston diameter used in current devices results in low shear wave signal that decays rapidly on axis as the shear wave spreads in all directions, thus limiting the signal-to-noise ratio and imaging depth in practice. We present an overview of our new technology of focused shear wave beams, which aims to overcome these limitations by concentrating shear wave energy in TE near to the beam axis with vibration of a concave circular piston. Analytical modeling of focused shear wave generation and propagation is validated against measurements in gelatin phantoms. Results indicate that focused shear wave beams have relatively larger amplitudes and penetration depths compared to unfocused shear wave beams. Ongoing modeling and experimental efforts towards the measurement of elastic anisotropy, such as of skeletal muscle, using focused shear wave beams will be discussed.

Numerical calculations with an exact analytical time-domain Green’s function for the van Wijngaarden wave equation

An exact analytical time-domain Green’s function is obtained for the van Wijngaarden wave equation when two of the constant coefficients satisfy a certain equality. This analytical expression enables numerical assessments demonstrating that lossy time-domain Green’s function calculations with the inverse fast Fourier transform (IFFT) produce larger errors than expected for most temporal values, even when the IFFT is evaluated with several million points. This analytical time-domain Green’s function also provides the foundation for efficient numerical calculations of spatial impulse responses, which are demonstrated for a 1 cm radius circular piston radiating in water at axial distances of 1 cm, 10 cm, and 1 m. As the axial distance increases, the difference between the lossy and lossless spatial impulse responses also increases, which is particularly evident in the paraxial region. However, the difference between lossy and lossless spatial impulse responses diminishes as the observation point transitions from an on-axis location to another position with the same axial distance just outside of the paraxial region. The observed differences between the lossy and lossless spatial impulse responses transitioning out of the paraxial region are explained by comparing the relative temporal extents of the lossless spatial impulse response and the lossy time-domain Green’s function.

Investigations into acoustic dipole helical wave generation.

Acoustic waves that transmit phase information spatially have recently been applied to navigation and communications systems. This paper will describe a helical wave, a type of wave that transmits phase information across a section of the plane linearly about the azimuth. The wave will be described from the ground up. First, a circular baffled transducer pressure field will be derived. Next, the field generated using two crossed circular transducers will be derived and approximations given for the far field. The general expression for the acoustic field from this arrangement is derived in the far field utilizing a paraxial ray approximation for ideal sources but applied to the more complex conceptualization of the monopole source being given by the circular piston source. In addition, the work presented was investigated numerically in comparison to a different approximation made in the field dependence on monopole separation of the two sources making up the dipole. Next, numerical examination of two crossed dipoles is examined with visualizations of the pressure and discussion of transients created when the direction of spiral changes. Finally, there is a discussion for the detection and estimation of helical waves and potential uses.

Research on near field sound pressure of circular piston source based on angular spectrum method

The accuracy of ultrasonic nondestructive examination is limited by the limitation of near field diffraction. With the development of nearfield optical, angular spectrum method is introduced into the acoustic field, which provides a significant direction for the ultrasonic diffraction limit resolution detection. The main research of this paper is the transmission of near field ultrasound in thin workpiece and the law of the interaction of tiny flaws. The paper establishes the relationship between the longitudinal wave signal and the structure of the workpiece and the types of flaws. A method is found that whether there are flaws can be determined near field area by analysing the acoustic field characteristics of workpiece surface. Finally, comparing the calculation results with the finite element simulation, they verify each other, the method turns out to be correct in this paper. The model can also be used to improve the ultrasonic noise reduction algorithm and the extraction of minimal defect feature. It has a greatly practical significance.

Influence of sound source directivity on finite element simulation of small-room acoustics

Numerical simulation is a flexible and effective method for room acoustic design. Full-range simulation of room acoustics requires a combination of different numerical methods, in which wave acoustic methods (WAM) and geometric acoustic methods (GAM) are used for the low and high frequency region, respectively. In the general low-frequency WAM simulation, a sound source is often assumed to be a point source or loudspeakers are usually approximated by circular planar pistons. However, compared to a large room, the critical frequency between WAM and GAM should be higher in acoustic simulation of small rooms because of relative size between the wavelength and the room, and thus, the above simplifications of actual sound sources, typically loudspeakers, may lead to errors in terms of directivity in the frequency range that the WAM is applied for. Further errors in the desired room impulse responses or other room acoustic parameters caused by directivity errors needs quantitative analysis, and then evaluation can be made on whether it is necessary to consider a more accurate sound source directivity in the WAM simulation of small room acoustics.

Radiation efficiency of a distribution of baffled pistons with arbitrary phases.

The radiation resistance and efficiency of a collection of circular pistons, randomly placed on a plane and vibrating with arbitrary phases, are expressed as a combination of the self- and mutual-radiation components. We use the first product or bridge theorem to construct the directivity pattern of this type of arrangement and the radiation properties are calculated according to Bouwkamp's impedance theorem. To illustrate the versatility of our approach, we refer to special cases for symmetric arrangements, for example, to compare with the modal radiation efficiency in structures having "regular" modal patterns.

Rigorous analysis of the axial acoustic radiation force on a spherical object for single-beam acoustic tweezing applications.

Acoustic tweezers are increasingly utilized for the contactless manipulation of small particles. This paper provides a theoretical model demonstrating the acoustic manipulation capabilities of single-beam acoustic transducers. Analytical formulas are derived for the acoustic radiation force on an isotropic spherical object of arbitrary size, centered on a circular piston, simply supported and clamped radiator in an inviscid fluid. Using these results, the existence of a negative axial force pulling the object closer to the radiator is revealed and explored. These findings offer further insight into the feasibility of trapping objects in the near-field of a single-beam acoustic transducer. The calculations illustrate the trapping capabilities of the different emitters as a function of radiator size, particle size, and distance from the source and highlight the impact of radiator boundary conditions. Manipulation of a cell-like fluid sphere in water and an expanded polystyrene sphere in air are studied in more detail with results that are validated through finite element analysis. The developed theoretical model allows fast evaluation of acoustic radiation forces which could aid in the development of relatively simple and inexpensive contactless manipulation solutions.

An algebraic correction for the Westervelt equation to account for the local nonlinear effects in parametric acoustic array.

This work presents a simple computational approach for the calculation of parametrically generated low-frequency sound fields. The Westervelt wave equation is employed as a model equation that accounts for the wave diffraction, attenuation, and nonlinearity. As it is known that the Westervelt equation captures the cumulative nonlinear effects correctly and not the local ones, an algebraic correction is proposed, which includes the local nonlinear effects in the solution of the Westervelt equation. This way, existing computational approaches for the Westervelt equation can be used even in situations where the generated acoustic field differs significantly from the plane progressive waves, such as in the near-field, and where the local effects manifest themselves strongly. The proposed approach is demonstrated and validated on an example of the parametric radiation from a baffled circular piston.

Numerical spatial impulse response calculations for a circular piston radiating in a lossy medium.

Exact analytical expressions for the spatial impulse response are available for certain transducer geometries. These exact expressions for the spatial impulse response, which are only available for lossless media, analytically evaluate the Rayleigh integral to describe the effect of diffraction in the time domain. To extend the concept of the spatial impulse response by including the effect of power law attenuation in a lossy medium, time-domain Green's functions for the Power Law Wave Equation, which are expressed in terms of stable probability density functions, are computed numerically and superposed. Numerical validations demonstrate that the lossy spatial impulse for a circular piston converges to the analytical lossless spatial impulse response as the value of the attenuation constant grows small. The lossy spatial impulse response is then evaluated in different spatial locations for four specific values of the power law exponent using several different values for the attenuation constant. As the attenuation constant or the distance from the source increases, the amplitude decreases while an increase in temporal broadening is observed. The sharp edges that appear in the time-limited lossless impulse response are replaced by increasingly smooth curves in the lossy impulse response, which decays slowly as a function of time.

The wave beating produced by circular plane pistons

The physics textbooks presents the fundamental concepts of wave beating from an interference process of two plane waves at the time domain. In this work, we propose a teaching practice, based on computational simulation, at undergraduate level, combining the beating caused by waves transmitted from two plane circular pistons vibrating on thickness mode with the resulting acoustic field. The proposal leads to the perception of the beating at the spatial domain. The results show that the pressure amplitude generated from the beating has periodic variations along the central axis from a boundary location. This boundary is determined by the number of extreme values and the ratio between source radius and wavelength.

Interface reflection wave of axisymmetric directional spherical-wave

The sound radiation field of a circular piston source in an infinite plane rigid baffle can be approximated as an axisymmetric directional spherical-wave. The interface response expressions of the axisymmetric directional spherical-wave for the piston parallel with the interface has already been obtained in previous studies. On condition that the distance from the piston center to the interface is much greater than the piston radius, we first derive the conical wave expansion of the axisymmetric directional spherical-wave which is obtained by using the conical wave expansion of the homogeneous spherical-wave and the formula of the axisymmetric directional spherical-wave excited by a circular piston in an rigid infinite plane, and then derive the expression of the interface reflection wave of the axisymmetric directional spherical-wave for the piston non-parallel to the interface. The expression of the interface reflection wave is simplified into a simplified expression by saddle point method on condition that the source distance is much larger than the acoustic wavelength. The simplified expression is not only simple in the calculation, but also clear in the physical meaning. The simplified expression shows that the interface reflection wave of the axisymmetric directional spherical-wave can be regarded as the product of the axisymmetric directional spherical-wave excited by the piston mirror image and the reflection coefficient. The calculations show that when the piston radius is smaller than the acoustic wavelength, the reflected wave is less sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is weak. When the piston radius is greater than the acoustic wavelength, the reflected wave is very sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is strong. Increasing the angle included between the piston and the interface, the reflected wave and its directivity both first increase and then decrease. The reflected wave is largest and the directivity of the reflected wave is strongest when the angle included between the piston and the interface is equal to that between the interface normal and the connecting line between the mirror image of the piston center and the receiving point.

Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in the immediate vicinity of a parallel surface. Previous attempts to characterize these so-called ‘squeeze-film’ systems largely relied on simplifications afforded by neglecting either fluid acceleration or viscous forces inside the thin enclosed gas layer. The present viscoacoustic analysis employs the asymptotic limit of small vibration amplitudes to investigate the flow by systematic reduction of the Navier–Stokes equations in two distinct flow regions, namely, the inner gaseous film where streamlines are nearly parallel to the confining walls and the near-edge region of non-slender flow that features gas exchange with the surrounding stagnant atmosphere. The flow in the gaseous film depends on the relevant Stokes number, defined as the ratio of the characteristic viscous time across the film to the characteristic oscillation time, and on a compressibility parameter, defined as the square of the ratio of the acoustic time for radial pressure equilibration to the oscillation time. A Strouhal number based on the local residence time emerges as an additional governing parameter for the near-edge region, which is incompressible at leading order. The method of matched asymptotic expansions is used to describe the solution in both regions, across which the time-averaged pressure exhibits comparable variations that give opposing contributions to the resulting time-averaged force experienced by the disk or piston. A diagram structured with the Stokes number and compressibility parameter as coordinates reveals that this steady squeeze-film force, typically repulsive for small values of the Stokes number, alternates to attraction across a critical separation contour in the parametric domain that exists for all Strouhal numbers. This analysis provides, for the first time, a unifying viscoacoustic theory of axisymmetric squeeze films, which yields a reduced parametric description for the time-averaged repulsion/attraction force that is potentially useful in applications including non-contact fluid bearings and robot locomotion.

Analysis of the effect of radiating surface geometry on the beam pattern of underwater acoustic transducers

Piston-type underwater acoustic transducers are used individually as well as in arrays for various acoustic applications. Circular pistons, in particular, are widely used in arrays. However, the performance of an array with circular pistons is restricted due to the limited edge contact of the circular geometry, which in turn limits the radiating power of the array. In this study, the radiation characteristics of other common piston geometries that can readily overcome the edge contact limitation of the circular piston were theoretically investigated and compared with each other. The pistons considered include those with circular, square, hexagonal, and octagonal radiating surfaces. The analysis results confirmed that, for smaller pistons with an equivalent circular diameter less than a half wavelength, the effect of the radiation surface geometry is insignificant. As such, pistons of the other shapes can be used to overcome the limitation of the circular piston without deteriorating the radiation characteristics of the array, which opens up many possibilities regarding the design of underwater acoustic piston arrays. The validity of the theoretical analysis was verified through the finite element analysis and experimental measurement of the radiation pattern of a prototype Tonpilz transducer with an octagonal head mass.

Numerical evaluations of the lossy spatial impulse response for a circular piston in the far field

Numerical evaluations of the lossy spatial impulse response are achieved by substituting Green's functions from the Power Law Wave Equation into the Rayleigh integral. The addition of loss introduces noticeable attenuation, dispersion, and delay into the impulse response, which become more pronounced in the far field.

Research on Array Structures of Acoustic Directional Transducer

This paper focuses on the directivity design of array structures of acoustic directional transducers. Based on Huygens principles, the directivity formula of transducer arrays under random distribution in xyz space is derived when the circular piston transducers are used as the array element, which is used to analyze the directivity and acoustic pressure of conical transducer arrangements. In addition, a practical approach to analyze the directivity and acoustic pressure of transducer arrays under random arrangements is proposed. Findings. The conical transducer arrays show side lobes at higher frequency. Below the frequency of 2 kHz, array directivity shows rapid changes. Above the frequency of 2 kHz, array directivity varies slowly with frequency. Besides, the beam width is Θ − 3 dB ≤ 29.85 ° .