Rigid Piston Research Articles

Акустические характеристики пористого алюминия, применяемого для изготовления шумопоглощающих устройств промышленного оборудования

Noise-absorbing devices made of porous aluminum have been used as components of units and systems of modern industrial equipment (pressure regulators, compressors, exhaust systems, pneumatic tools, heat engines, etc.). The advantages of products made of the material are high mechanical strength, resistance to chemicals, vibrational and thermal loads, and recyclability. Noise absorption in the structure of porous aluminum is caused by the loss of energy as a result of viscous friction and heat exchange between oscillating air particles and the skeleton of the material. Structural parameters of porous metals significantly affect the efficiency of noise absorption. Experimental studies of sound-absorbing properties of porous aluminum samples of different thicknesses, porosity, and pore sizes have been carried out for the present paper. An acoustic impedance tube, in compliance with the requirements of ISO 10534 and ASTM E1050 on 5–20 mm thick samples, has been used for the study. The porosity of samples was 0.5–0.7, whereas the average pore size was equal to 0.6–2 mm. Two variants of sample installation have been investigated, i.e., without an air gap and with the formation of a 20 mm air gap relative to the surface of the rigid piston of the impedance tube. The impact of structural parameters and thickness of porous aluminum samples on their noise-absorption properties has been assessed based on the results of the study. It has been determined that the increase of average pore size within the range between 0.6 and 2 mm causes the reduction of the noise-absorption coefficient. The effect becomes more pronounced when a sample with the formation of an air gap relative to the piston surface is installed. With identical average pore sizes and thicknesses, the highest values of sound absorption coefficient by the porous aluminum samples have been registered for a porosity of 0.6. The study results can be used for the development and modernization of sound-absorbing devices for industrial equipment made of porous aluminum.

Sound radiation of a vibrating circular plate set in a hemispherical enclosure

This study rigorously addresses the Neumann–Robin problem of sound radiation from a vibrating flexible disk embedded into a hemispherical enclosure. The enclosure is acoustically soft on its inside surface and hard on its outside surface. The method of superimposed solutions, expressed in terms of Dini series and spherical harmonics, has been applied for this purpose. The presented solution is applicable to any vibration velocity profile on the radiator, with an elastically supported thin plate excited asymmetrically used as an example. The results presented here can be valuable for modeling vibroacoustic responses of various speakers, sensors, and microphones with edges either clamped to the enclosure or nearly free. Achieving this involves modifying the values of the boundary stiffness for resisting transverse displacement and the rotation of the plate’s edge. Additionally, when applying these results to model the responses of alarm or signaling transducers, high-amplitude responses are expected for selected resonant frequencies. In such cases, the boundary stiffness values can be set to ensure multiple strong and wide resonant maxima in the frequency characteristics. In addition, the results presented in this study include solving the dynamic equation of motion for the plate or rigid piston with external excitation. This equation is coupled with the wave equation inside and outside the hemispherical enclosure, allowing the inclusion of the enclosure’s effect on the plate-enclosure system’s responses. This approach can be useful for modeling and improving the acoustic responses of spherical speakers. In such cases, the boundary stiffness values should be relatively small to emulate a soft suspension of the plate. The impedance of the enclosure’s internal surface can be arbitrarily selected, ranging from acoustically hard to acoustically soft. In this study, the impedance of mineral wool has been applied. Numerical analysis is presented for frequencies below 4kHz, with errors smaller than 0.2%. The results have been validated using the finite element method.

Nominal Versus Actual Spatial Resolution: Comparison of Directivity and Frequency-Dependent Effective Sensitive Element Size for Membrane, Needle, Capsule, and Fiber-Optic Hydrophones.

Frequency-dependent effective sensitive element radius [Formula: see text] is a key parameter for elucidating physical mechanisms of hydrophone operation. In addition, it is essential to know [Formula: see text] to correct for hydrophone output voltage reduction due to spatial averaging across the hydrophone sensitive element surface. At low frequencies, [Formula: see text] is greater than geometrical sensitive element radius ag . Consequently, at low frequencies, investigators can overrate their hydrophone spatial resolution. Empirical models for [Formula: see text] for membrane, needle, and fiber-optic hydrophones have been obtained previously. In this article, an empirical model for [Formula: see text] for capsule hydrophones is presented, so that models are now available for the four most common hydrophone types used in biomedical ultrasound. The [Formula: see text] value was estimated from directivity measurements (over the range from 1 to 20 MHz) for five capsule hydrophones (three with [Formula: see text] and two with [Formula: see text]). The results suggest that capsule hydrophones behave according to a "rigid piston" model for k a g ≥ 0.7 ( k = 2π /wavelength). Comparing the four hydrophone types, the low-frequency discrepancy between [Formula: see text] and ag was found to be greatest for membrane hydrophones, followed by capsule hydrophones, and smallest for needle and fiber-optic hydrophones. Empirical models for [Formula: see text] are helpful for choosing an appropriate hydrophone for an experiment and for correcting for spatial averaging (over the sensitive element surface) in pressure and beamwidth measurements. When reporting hydrophone-based pressure measurements, investigators should specify [Formula: see text] at the center frequency (which may be estimated from the models presented here) in addition to ag .

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.

A New System for the Measurement on Small Samples of the Normal-Incidence Insertion Loss of Acoustic Multilayers

<div class="section abstract"><div class="htmlview paragraph">This article presents a new system for the measurement on small samples of the normal-incidence Insertion Loss (IL) of multilayers used for the manufacturing of automotive sound package parts. The system consists of a rigid piston connected to an electrodynamic shaker and facing a tube positioned just above it. The measurement principle is based on the evaluation of the Transfer Matrix (TM) of the piston-and-sample assembly, from which the desired IL can be calculated. The TM can, in turn, be evaluated from the measurement of the piston velocity and of the acoustic pressure inside the tube, with two different tube termination conditions.</div><div class="htmlview paragraph">The proposed measurement system is first of all aimed at simplifying the assessment of the acoustic insulation of multilayers used for the manufacturing of sound package parts. In the automotive field, this assessment is customarily done by measuring the diffuse-field Insertion Loss (IL) of flat samples having an area of around 1m<sup>2</sup> in two-chambers facilities. A kind of test that, while being well-established, may be quite demanding and resource-consuming, in particular when many different multilayers (different materials, different constructions, different layers’ thickness, etc.) have to be compared. With the proposed system, the amount of material and the time needed for a test is strongly reduced compared to this standard practice. Furthermore, the system intends to overcome the limitations of the 4-microphones test procedure based on the ASTM E2611 standard that cannot provide the actual IL of a package (but only its TL, without any support) and that suffers from the influence that samples’ edge conditions may have on the results.</div><div class="htmlview paragraph">In a first part, the article first discusses the principles on which the measurement system is based. In a second part it focuses on some aspects of the measurement hardware that are particularly delicate (e.g. sample’s edge conditions). Eventually, the article describes how a prototype of the measurement system was built and validated.</div></div>

Rigorous characterization of fiber-optic hydrophone responses using a discretized-domain-based rigid-piston model and a broadband photoacoustic pulse

Fiber-optic hydrophones are one of the most fundamental platforms widely used for measurement and evaluation of ultrasound waves in a non-destructive manner. Therefore, there is the need for rigorous modeling of their output responses which enables their extensive use with exact prediction of measured outputs. We characterize fiber-optic hydrophone responses rigorously by devising a modified rigid piston model that accommodates a discretized-domain analysis. Importantly, optical sensing conditions are taken into account accurately including a cross-sectional geometry of fiber and an optical power distribution. Then, we experimentally validate calculation results by utilizing a broadband photoacoustic pulse that effectively works as a normally incident delta-mimicked pulse. This reveals that an edge wave generated from the rim of fiber predominantly determines an output response. Finally, our verified modeling approach is applied, as an example, to design an improved structure adopting an eccentric core fiber that minimizes the edge wave-induced distortion and achieves a significantly flattened frequency response (variation less than 3 dB) over the range of sub-500 MHz.

Wave-to-wire models of wells and impulse turbines for oscillating water column wave energy converters operating in the Mediterranean Sea

Despite the huge potential, energy harnessing from sea waves is often still at a demonstrative stage. Oscillating water column (OWC) wave energy converters have proven to be one of the few suitable solutions to this end. A wave-to-wire analytical code modelling an entire wave energy converter based on the OWC technology, operating with either a Wells or an impulse turbine, was developed. The hydrodynamics, thermodynamics, and aerodynamics of the caisson were determined with a rigid piston approach. Two original low-order aerodynamic models were created for the two turbines, providing an interesting compromise between accuracy and computational cost. Finally, a control strategy was applied to monitor the instant rotor angular velocity and torque in both design and off-design conditions. The simulation tool was applied to screen the geometry of two typologies of air turbines for a specific chamber under the wave conditions of a selected Mediterranean site located in Sardinia (Italy). In particular, annual and seasonal scatter matrices were utilised to define the wave conditions of the site, providing an overview of the seasonal performance variation. The designed Wells and impulse turbines are capable of converting 47.67 and 41.14 MWh/year and operate with an overall efficiency of 5.77% and 4.98%, respectively.

On the spherical expansion for calculating the sound radiated by a baffled circular piston

An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow and the loss of significant figures. A rigorous and closed form solution of the integral is derived in this paper based on the recurrence method, which is accurate in the whole frequency range and thousands of times faster than the existing methods. It is shown that the proposed method can be extended for the calculation of the sound radiated by a baffled piston and an unbaffled resilient disk with axisymmetric velocity and pressure profiles, respectively, and some baffled rotating sources where the velocity profile is asymmetric.

Stress analysis on the frame holder of generator translation motion on horizontal direction for sea wave power plant using finite element method (fem)

The generator is a machine component that converts mechanical energy into electrical energy. Generators can be found in power generation systems. In this paper, generators are used on the sea wave power plants [1-4]. This generator works by utilizing the effects of ocean waves that rise and fall so as to push the piston to move in the same direction with ocean waves. The performance of the generator is influenced by the magnitude of the force of the piston, rotors and stator. Stable, rigid and smooth piston movements also can increase generator output performance. The design and material of the generator holder is very influential on the generator stiffness. Generator stiffness includes deformation and stress that occur and can be obtained using the finite element method (FEM) [5-13]. In this paper focus on simulating the generator holder shape horizontal direction and the amount of deformation and stresses by varying frame holder generator shape and inclination (750, 800, 900). In previous studies, the translational motion generator frame holder design is less rigid (stable). From the simulation results, the maximum voltage value (σmax) of von mises is 6,427 MPa, the deflection value is 61.29 mm with 900 generator stand design positions.

Wave-to-Wire Model of an Oscillating-Water-Column Wave Energy Converter and Its Application to Mediterranean Energy Hot-Spots

Oscillating water column (OWC) systems are among the most credited solutions for an effective conversion of the notable energy potential conveyed by sea waves. Despite a renewed interest, however, they are often still at a demonstration phase and additional research is required to reach industrial maturity. Within this framework, this study provides a wave-to-wire model for OWC systems based on an impulse air turbine. The model performs a comprehensive simulation of the system to estimate the attendant electric energy production for a specific sea state, based on analytical models of the primary (fixed chamber) and secondary (air turbine) converters coupled with the tertiary converter (electric generator). A rigid piston model is proposed to solve the hydrodynamics, thermodynamics, and hydrodynamics of the chamber, in a coupled fashion with the impulse turbine aerodynamics. This is solved with a novel method by considering the cascades as sets of blades, each one consisting of a finite number of airfoils stacked in the radial direction. The model was applied for two Mediterranean sites located in Tuscany and Sardinia (Italy), which were selected to define the optimal geometry of the turbine for a specified chamber. For each system, the developed analytical wave-to-wire model was applied to calculate the performance parameters and the annual energy production in environmental conditions typical of the Mediterranean Sea. The selected impulse turbines are able to convert 13.69 and 39.36 MWh/year, with an efficiency of 4.95% and 4.76%, respectively, thus proving the interesting prospects of the technology.

Multi-material 3D printed hydraulic actuator for medical robots

Purpose This study aims to investigate the potential of using polymer multi-material additive manufacturing (MMAM) to produce miniature hydraulic piston actuators combining rigid structures and flexible seals. Such actuators offer great potential for medical robots in X-ray and magnetic resonance environments, where conventional piston actuators cannot be used because of safety issues caused by metal components. Design/methodology/approach Hydraulic pistons with two different integrated flexible seal shapes are designed and manufactured using MMAM. Design 1 features a ring-shaped seal made from a flexible material that is printed on the surface of the rigid piston shaft. Design 2 appears identical from the outside, yet an axial opening in the piston shaft is added to enable self-reinforced sealing as fluid pressure increases. For both designs, samples with three different outer diameters are fabricated leading to a total of six different piston versions. The pistons are then evaluated regarding leakage, friction and durability. Findings Measurement results show that the friction force for Design 2 is lower than that of Design 1, making Design 2 more suitable for the intended application. None of the versions of Design 2 shows leakage for pressures up to 1.5 MPa. For Design 1, leak-tightness varies with the outer diameter, yet none of the versions is consistently leak-tight at 1.5 MPa. Furthermore, the results show that prolonged exposure to water decreases the durability of the flexible material significantly. The durability the authors observe may, however, be sufficient for short-term or single-use devices. Originality/value The authors investigate a novel design approach for hydraulic piston actuators based on MMAM. These actuators are of particular interest for patient-specific medical devices used in radiological interventions, where metal-free components are required to safely operate in X-ray and magnetic resonance environments. This study may serve as a basis for the development of new actuators, as it shows a feasible solution, yet pointing out critical aspects such as the influence of small geometry changes or material performance changes caused by water absorption.

Motion characteristics of a novel elastic rotating micro-electromechanical power system

This article reports a conceptual study of a new micro-electromechanical power system using elastic leaf piston rotating engine rather than conventional engines as the main component. The proposed innovative elastic rotating micro-electromechanical power system adopts two leaf pistons to substitute the traditional rigid piston for establishing elastic combustors and operates with a novel Humphrey thermodynamic cycle, which brings about high power density and energy conversion efficiency. The motion model of leaf piston is carried out by using the Euler–Bernoulli theory, and a novel calculation method of trial and error is presented to iteratively simulate the motion of elastic piston. The effects of the piston length and installation position on the combustor variation are also investigated. Results indicate that the contact point of piston and cylinder is not the piston end and keeps moving, and the combustor is periodically compressed and expanded by the rotor and piston motion to perform the intake, compression, expansion, and exhaust. Besides, the minimum combustor volume lasts an amount of time, which provides a possible realization of full isovolumetric combustion. A larger installation phase angle of pistons means a longer compression and expansion, larger combustor volume and shorter constant-volume duration.

ВЛИЯНИЕ ИЗГИБА ПЛУНЖЕРА НА ИЗМЕНЕНИЕ ОБЪЕМА В ЦИЛИНДРОВОЙ ПОЛОСТИ АВИАЦИОННОГО АКСИАЛЬНО-ПЛУНЖЕРНОГО НАСОСА

In this article, the task is to consider the effect of the piston bending in an axial- piston pump under the action of hydraulic force on the kinematics of the pump. The change in kinematics due to the elastic deformation of the piston is estimated by the axial displacement of the piston face. The study takes into account the bias of the plunger in the gap, the elastic bending deformation of the plunger, the contact deformation of the plunger and the cylinder block. The task is considered on three models: a rigid piston in a rigid cylinder block; deformable piston in a rigid cylinder block; deformable piston, block, shoe, and disk. The values of the displacement of the piston, caused by elastic forces and misalignment in the gap depending on its position were obtained for the first time as a result of the analysis. The problem is solved both analytically and numerically using the finite element method. In the analytical solution of the problem, the piston is represented as a beam supported by pin and roller at the points of contact of the piston with the walls of the cylinder block. The three-dimensional model of the pump is applied to solve the problem by the finite element method, the contact deformation of the piston and the block is considered. According to the simulation results, the displacement of the piston is obtained depending on the position of the piston. The results of modeling an analytical model are presented in the form of a smooth function, and the results of numerical simulation using the finite-element method obtained for several points are interpolated by a smooth function. The conclusions suggest that the greatest deformations are achieved in the piston located at the bottom dead center, and the gap between the piston and the sleeve and the overall stiffness of the contact parts have the greatest effect. The results of the work can be used to correct the geometrical parameters of a heavily loaded aviation axial-plunger pump to reduce flow and pressure pulsations caused by the kinematics of the pump.

Resonance and beating phenomenon in a nonlinear rigid cylindrical acoustic waveguide: The axisymmetric mode

A rigid-walled semi-infinite circular cylindrical waveguide enclosing a weakly nonlinear fluid is considered. A quadratic nonlinear interaction is assumed as a model. A flat rigid piston generates an axisymmetric harmonic pressure that is prescribed as the input at the finite end of the waveguide. The objective is to study the modal interactions of waves. A regular perturbation method is used to separate the linear (primary) and the quasilinear (second harmonic) equations. First, linear solutions are established. Their quasilinear interactions then lead to modal interactions. Typically, the linear wavenumbers at the quasilinear order generate homogenous wavenumbers. Intersections of both these wavenumbers in the wavenumber-frequency plane are considered as resonances since the resulting pressure grows in amplitude in the axial propagating direction. The conditions under which the solutions become resonant or non-resonant are presented. In this last case, a beating phenomenon occurs with distance. It is found that the resonances are rare, except for the plane wave. Generally, the forced linear wavenumbers and the quasilinear generated wavenumbers acquire numerical values close to each other and create the beating phenomenon.

Directivity of sound radiated from baffled rectangular plates and plate strips

Rectangular plates are important components in structures such as vehicles and bridges. The noise radiated by vibrating plates is mainly determined by three factors: the mean-square vibration, the radiation efficiency of the plates and the directivity of the sound. Although the first two factors have been widely investigated, much less attention has been paid to the directivity. The aim of this study is to investigate the directivity indices for rectangular plates subjected to either a single point force or multiple incoherent forces. Particular attention is given to plates with a large aspect ratio, referred to as plate strips. New definitions of directivity index are introduced that are more appropriate to such plate strips. The vibration of the plates is calculated from a modal superposition method based on approximate modal solutions of the plates with various boundary conditions. The Rayleigh integral method is used to obtain the sound pressure radiated from the vibrating plates, assuming that they are set in an ideal infinite baffle. Directivity indices of sound are firstly determined for plates with a small aspect ratio, and then for plate strips with a larger aspect ratio. Examples are given to illustrate the effects of the structural boundary conditions, and the effect of the baffle. For distributed incoherent excitation, as often found in practice, it is shown that the sound directivity pattern in the far field corresponding to the width direction varies insignificantly along the length of the strips; this is different from a single point force excitation. It is also found that the noise radiation from different concrete plates is approximately omnidirectional in the plane perpendicular to the longitudinal direction. Plates and plate strips are much less directional at high frequencies than the corresponding rigid piston. Nevertheless, the maximum value of directivity increases at high frequency as the number of modes in a one-third octave band increases. The dominant directions of sound radiation from plates are mainly controlled by the acoustical wavelength and vibrational wavelength, while the structural boundary conditions and the presence of the baffle have only a minor influence on them. Finally it is shown that, for the prediction of sound directivity of plate strips under distributed incoherent excitation, a two-dimensional vibro-acoustic model can be used in place of the three-dimensional one.

Nonlinear dynamic response of reciprocating compressor system with rub-impact fault caused by subsidence

In this paper, a nonlinear dynamic model of the single-stage reciprocating compressor system with a rub-impact fault caused by subsidence is developed, considering the piston rod flexibility. Meanwhile, different rub-impact scenarios of the crosshead including no corner, a single corner, two opposite corners, and two adjacent corners of the crosshead impacting on the slide, are considered in this model. Numerical simulation results show that the subsidence, time-varying load, and piston rod flexibility have significant effects on the vibration response of the reciprocating compressor system with rub-impact, where the larger the subsidence and time-varying load, the more intense the vibration response. Moreover, compared to the rigid piston rod, the flexible piston rod causes the system to generate stronger shock. In the rub-impact, the crosshead appeared in three different motion modes: noncontact; permanent contact; and collision – and most of the collisions occur in the form of two adjacent corners impacting on the slide. In addition, strange attractors are observed in the phase space trajectories, and the existence of chaotic behavior is verified using the Poincaré section method and maximum Lyapunov exponent method.

Dependence of Rayleigh integral predictions on the ground motion model for acoustic signals produced by underground explosions

Seismoacoustic signatures are produced by above- and below-ground explosions and are often observed at local, regional, and global distances. In the case of an underground explosion, seismic waves propagate to the surface and produce acoustic signatures via pumping of the atmosphere by the ground motion that can be predicted using a Rayleigh integral analysis. Acoustic signature predictions will be discussed and compared with observations from the Source Physics Experiment (SPE) in two scenarios. First, a rigid piston model of the ground motion will be highlighted as a first order model. Second, a more realistic model treating the ground as an elastic medium with finite compressional wave speed will be developed and discussed to demonstrate how such a model changes predicted acoustic signals at local distances. Acoustic signals predicted using each methodology will be compared with observations from SPE to identify how characteristics of the acoustic signal can be leveraged to improve characterization of the underground explosive source.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones—Part I: Spatiotemporal Transfer Function and Graphical Guide

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent "effective" sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Directivity and Frequency-Dependent Effective Sensitive Element Size of a Reflectance-Based Fiber-Optic Hydrophone: Predictions From Theoretical Models Compared With Measurements.

The goal of this work was to measure the directivity of a reflectance-based fiber-optic hydrophone at multiple frequencies and to compare it to four theoretical models: rigid baffle (RB), rigid piston (RP), unbaffled (UB), and soft baffle (SB). The fiber had a nominal 105- [Formula: see text] diameter core and a 125- [Formula: see text] overall diameter (core + cladding). Directivity measurements were performed at 2.25, 3.5, 5, 7.5, 10, and 15 MHz from ±90° in two orthogonal planes. Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to the directivity measurements using the sensitive element radius as an adjustable parameter. Over the range from 2.25 to 15 MHz, the average magnitudes of differences between the effective and nominal sensitive element radii were 59% ± 49% (RB), 10% ± 5% (RP), 46% ± 38% (UB), and 71% ± 19% (SB). Therefore, the directivity of a reflectance-based fiber-optic hydrophone may be best estimated by the RP model.

Needle hydrophone transfer function model for characterizing therapeutic transducers

A rigid piston model has been developed to predict needle hydrophone transfer functions. The model predicts that “effective” sensitive element diameter depends on the frequency and can exceed geometrical sensitive element diameter by a factor of up to 2.25. The model predicts harmonic distortion for hydrophone measurements of focused pressure waves, which were modeled using nonlinear plane wave theory for spectral characteristics and Gaussian radial pressure distributions. The pressure wave model was validated by comparing to hydrophone (sensitive element diameter: 85 microns) measurements performed in focal planes of source transducers (3.5 MHz, 64 mm diameter, 89 mm focus and 5 MHz, 19 mm diameter, 38 mm focus). Root mean squared difference (RMSD) between the model fit and measured relative strengths of the first four harmonics was 9% (3.5 MHz transducer) and 11% (5 MHz transducer) where Blackstock’s sigma parameter (JASA, 39, 1019–1026, 1966), which measures extent of nonlinearity, was optimized to fit the data. RMSD between model and measured half width half maxima was 10 ± 5%. Tone bursts from each transducer were measured using needle hydrophones (sensitive element diameters: 200, 400, 600, and 1000 microns). RMSD between model and measured harmonic distortion was 12 ± 4% for the first four harmonics.