Pressure Release Boundary Research Articles

Vibroacoustic response of a locally resonant coated cylindrical shell semi-submerged or fully submerged at a finite depth near a free sea surface

We study the vibroacoustic response of a coated cylindrical shell semi-immersed or fully submerged close to a free sea surface. Different coating designs corresponding to a uniform coating made of a viscoelastic material and locally resonant coatings composed of the viscoelastic material embedded with cavities or hard inclusions are considered. Analytical models that account for fully coupled fluid-structure interaction between the coated shell, the surrounding fluid domain and the free sea surface are developed. The free surface is treated as a pressure release boundary. For a fully submerged coated shell, the image method is employed. For the semi-immersed coated shell, a partial fluid loading condition is imposed on the wetted coating surface. The combined influence of the different coating designs and free surface on the structural and acoustic responses of the semi- and fully immersed shells are described. The influence of variation in dominant coating parameters that primarily impact the local resonances of the inclusions is also reported.

The 1952 Ph.D. dissertation of T.F.W. Embleton on nonlinear acoustic propagation and reflection

In his doctoral research Tony Embleton studied nonlinear acoustics experimentally using techniques available in the Physics Department of Imperial College, University of London. Originally developed by V. Timbrell, the interferometric equipment was substantially improved by Tony Embleton, enabling his Ph.D. findings. Studying propagation in a tube and reflection by both closed and open ends, Tony Embleton was able to substantially confirm the theory of the time, developed by Stokes, Earnshaw, Rankine, Rayleigh, and Taylor, many pieces confirmed for the first time. He also found discrepancies regarding the attenuation coefficients regarding the first and second half cycle of each pulse as well as a shortening of a pulse at reflection from a closed end. These findings are still worthy of further investigation. The results of reflection of pulses from the open end of a tube, forming a pressure release boundary condition, still are very interesting to the present author. A pulse propagating toward the open end steepens, but the reflected wave “unsteepens” which is a unique nonlinear acoustic phenomenon. [Work supported by the Penn State College of Engineering and its United Technologies Corporation Professorship.]

The effects of bathymetry on estimating the depth of a source in range-dependent environments with a single hydrophone

The effects of varying or range-dependent bathymetry, e.g., such as a sloping bottom, on the depth resolution characteristics of single hydrophone matched field processing (MFP), e.g., width of depth main-lobe as a function of source and receiver nominal positions, is not well understood. A major challenge is that in the case of range-dependent environments there are generally no analytical representations for the pressure field, thus requiring numerical methods for their evaluation. To provide some theoretical insights into how the shape of the bathymetry and locations of the source and receiver influences the MFP depth ambiguity function, we study the case of an ideal wedge with perfectly reflective pressure-release boundaries using the analytical solutions of Buckingham [1]. We derive a simple approximation for the depth ambiguity function main lobe width and compare it against the theoretical result for an ideal range-independent environment [2] and then numerically for a penetrable wedge and more realistic shelf-like environments. M.K. Buckingham, “Acoustic propagation in a wedge-shaped ocean with perfectly reflecting boundaries,” NRL report 8793, March 1984. M. Cheney and I.P. Kirsteins, “Resolution of matched field processing for a single hydrophone in a rigid waveguide,” J. Acoust Soc. Am. 151, pp. 3186–3197, 2022.

Acoustic radiation force and torque on an object near a penetrable interface or impedance boundary

An analytical approach for calculating radiation force and torque on a sphere or spheroid near a rigid or pressure release boundary due to an arbitrary incident acoustic field was developed recently by the authors [Proc. Meet. Acoust. 48, 045004 (2022)]. In that approach, the linear scattering problem is solved using the method of images along with expansions of the acoustic fields in spherical or spheroidal wave functions. The expansion coefficients can then be substituted into an existing expression to obtain the radiation force and torque on the object. In the present work, the aforementioned theory is extended to include penetrable interfaces and impedance boundaries using an approximation of the interfacial boundary conditions. For fluid-fluid interfaces, the object can be placed on either side of the interface with respect to the incident field. This approximate analytical approach is computationally efficient and compares well with the results from an independent finite element model. In addition, an experiment was conducted with a plastic sphere submerged in water and positioned near a boundary. Results from the experiment are discussed in relation to the analytical model. [BES is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Reconstruction of the Acoustic Field Radiated Directly from a Vibrating Structure Located Near a Pressure-Release Boundary

Near-field acoustical holography is a powerful tool for reconstructing the three-dimensional acoustic field radiated from a vibrating structure located in free space, but it is not applicable when the source is in a half space bounded by a reflecting boundary. This paper develops a method based on half-space spherical wave function expansion for reconstructing the acoustic field radiated directly from a source located near a pressure-release boundary. First, the series of half-space spherical wave basis functions satisfying the pressure-release boundary condition is formulated. Then the acoustic field in a half space is modeled using an expansion in this basis. The expansion coef?cients are determined by solving an overdetermined linear system of equations, obtained by matching this expansion to the measured half-space acoustic pressures. The pressures radiated directly from the source can finally be reconstructed using the free-space spherical wave function expansion with the obtained expansion coefficients. Numerical simulation examples of a vibrating plate located in water near a pressure-release boundary are demonstrated to validate the proposed method. The effects of various parameters, such as the acoustic frequency, the distance between the source and boundary, and the orientation of the source surface, on the reconstruction accuracy are examined.

Finite difference time domain ray-based modelling of acoustic scattering for target identification and tracking

The Finite Difference Time Domain (FDTD) method has provided a powerful technique for modelling and simulation of solutions of a variety of acoustics problems. The purpose of this investigation is to present work on the development of time-domain models of acoustic scattering from targets near a flat pressure-release boundary for use in identification and tracking from a moving receiving platform. The timing from acoustic source to reception are dependent on the location dependent sound speed profile and the specular scattering points on the target. There can be multiple specular points revealed on the target because of interactions with the flat boundary; each of which are modelled utilizing the FDTD method providing path corrections due to variation in propagation brought on by the sound speed profile of the environment.

Advanced NDIF Method for Eigenvalue Analysis of Arbitrarily Shaped Acoustic Cavities With the Partially Pressure-Release Boundary

Abstract In this paper, an advanced non-dimensional dynamic influence function method (NDIF method) for eigenvalue analysis of arbitrarily shaped two-dimensional acoustic cavities with the mixed boundary consisting of the pressure-release and rigid-wall boundaries is proposed. The existing NDIF method has the weakness of having to calculate the singularity of the final system matrix of an analyzed acoustic cavity in the frequency band of interest to obtain the eigenvalues of the cavity because the final system matrix is dependent on the frequency. The newly proposed NDIF method in this paper provides an efficient way to extract accurate eigenvalues and eigenmodes by successfully overcoming the above weaknesses. Finally, the validity and accuracy of the proposed method are shown through verification examples.

A new solution for vibroacoustic analysis of two-dimensional cylindrical shells partially liquid-filled or partially submerged in fluid

In this study, a semi-analytical method is proposed to study the vibration and acoustic radiation of a two-dimensional cylindrical shell partially coupled with internal fluid. Different from the conventional vibroacoustic model of cylindrical shells, two different coordinates are established to describe the motion of the shell and the internal fluid respectively. One coordinate system is established on the free surface, where the sound pressure release boundary condition is satisfied automatically by constructing a sine series expression of sound pressure. Meanwhile, with the center of the shell’s cross section as the origin, the other is established to describe the motion of the shell. Then the Galerkin method and the coordinate transformation technique are adopted to deal with the velocity continuous condition on the partially coupled interface. Finally, the vibroacoustic response can be solved theoretically. The applicability and reliability of the present method are validated by comparison with the finite element method via the free vibration, forced vibration and sound radiation cases. The present method is also extended to deal with the vibration and sound radiation of shell coupled with external fluid successfully. Generally speaking, this study proposes a new method to the solution of the vibroacoustic behaviours of an elastic cylindrical shell partially coupled with fluids theoretically, with a wide application scope and good accuracy.

Scale model observations of coupled vertical modes in a translationally invariant wedge.

Scale-model tank experiments offer a controlled environment in which to make underwater acoustic propagation measurements that can provide high-quality data for comparison with numerical models. This paper presents results from a scale model experiment for a translationally invariant wedge with a 10° slope fabricated from closed-cell polyurethane foam to investigate three-dimensional (3-D) propagation effects. A computer controlled positioning system accurately located a receiving hydrophone in 3-D space to create a dense field of synthetic vertical line arrays, which are subsequently used to mode filter the measured pressure field. The resulting mode amplitudes show the modal propagation zone, the modal shadow zone, and the classical intra-mode interference pattern resulting from rays launched up and along the slope. The observed features of the measured data are compared to three different propagation models: an exact, closed-form solution for a point source in wedge with pressure release boundaries, a 3-D ray trace model, and an adiabatic model. Examination of the mode amplitudes produced by the models reveals how the effects of vertical mode coupling can be observed in the measured data.

Finite difference time domain ray-based modelling of acoustic scattering for target identification and tracking

The Finite Difference Time Domain (FDTD) method has provided a powerful technique for modelling and simulation of solutions of a variety of acoustics problems. The purpose of this investigation is to present work on the development of time-domain models of acoustic scattering from targets near a flat pressure-release boundary for use in identification and tracking from a moving receiving platform. The timing from the acoustic source to reception is dependent on the location dependent sound speed profile and the specular scattering points on the target. There can be multiple specular points revealed on the target because of interactions with the flat boundary, each can be modelled with the FDTD method and providing the correct path corrections using the same method to account for the variation in propagation path brought on by the sound speed profile of the propagating environment.

Direct estimation and experimental validation of the acoustic source characteristics of turbocharged diesel engine exhaust system

The present study aims at application of the novel direct method developed by Kumar and Munjal for naturally aspirated engines [Applied Acoustics 135, 70–84 (2018)] to the turbocharged engine’s exhaust system for estimation of acoustic source characteristics. In this paper, transfer matrices of the turbine and compressor of an automotive turbocharger are derived. Mass continuity across the turbine and compressor along with the respective static pressure ratios are used for deriving their transfer matrices. The acoustic source characteristics of each cylinder for the source-load junction downstream of the exhaust valve/s is computed assuming that the cylinder discharges to the ideal pressure release boundary condition with the constant pressure being product of the turbine pressure ratio and mean pressure in the exhaust pipe downstream of the turbine. Source characteristics of each cylinder are used to estimate the source characteristics downstream of the exhaust manifold. Using the derived transfer matrix of the turbine, the source characteristics are further estimated at the source-load junction downstream of the turbine. Finally, the estimated source characteristics of the engine downstream of the turbine are used to predict the unmuffled sound pressure level (SPL) spectrum which is shown to compare reasonably well with the experimentally measured values. Importance of acoustic modelling of the turbine is highlighted by comparing the SPL spectra predicted using the estimated source characteristics with and without the turbine. The estimated source characteristics and unmuffled approximate SPL spectrum of a turbocharged engine being thus known at the engine’s inception stage, the present study can be used for the integration of design and analysis of the engine and muffler.

Modeling acoustic interactions with a dynamic rough sea surface boundary

The acoustic wave scattering properties of a dynamic pressure-release surface boundary are analyzed using a numeric technique based on the finite-difference time-domain (FDTD) method. Of primary interest is to study the impact of assuming a “frozen” sea-surface on long duration sonar transmissions. Although relatively uncommon in ocean acoustics, the FDTD approach is well suited for modeling boundary roughness and motion. This technique has the additional benefit that the pressure fields are resolved over time, which allows for transient analysis of the observed wave scattering effects. The method is adapted from electromagnetic wave scattering and can properly model the physics of the observed system, which shows a frequency modulated reflection that includes a double-Doppler effect. First, a traditional analytic solution for the static smooth surface boundary ocean half-space model, the Lloyd Mirror, is compared to an equivalent simulation using the FDTD method. Then a dynamic smooth surface boundary is investigated using a modified Lloyd-mirror solution and the FDTD method. Finally, surface roughness for both static and dynamic boundary cases will be considered. Agreement is shown between FDTD simulations and the modified Lloyd Mirror model for both one-dimension and two-dimension cases. [Work supported by the Office of Naval Research.]

Acoustic focusing via guided waves in bianisotropic fluid layers

Willis fluids display a complex, effective dynamic response stemming from microstructural asymmetry, long range order, and/or time-varying material properties. These materials are characterized by constitutive relations that couple the pressure and momentum density to both the particle velocity and the volume strain. This coupling has been shown to be analogous to electromagnetic bianisotropic media, which exhibit coupled electric and magnetic fields [Phys. Rev. B 96, 104303 (2017)]. In a recent study, an acoustic lens composed of an array of Willis fluid layers was demonstrated, where the pressure phase imparted by each array element was tuned by varying the direction of Willis polarization and was determined using finite element analysis. In this work, we report on analytical solutions for guided waves in layers of fluid displaying Willis coupling and derive dispersion relations for layers with rigid and pressure-release boundary conditions. Special cases highlighting the effect of Willis polarization direction are presented via numerical examples. The acoustic lens is revisited with array phases obtained from analytical solutions, eliminating the need for finite element methods. Lenses designed for focusing and steering incident pressure waves are demonstrated using fully analytical models. [Work supported by NSF, ONR, and ARL:UT.]

Sensitivity Analysis of Hybrid Split-Step Fourier/Finite Difference Parabolic Equation Models

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air interface.

An Analytical Solution for Free Flexural Vibration of a Thin Cylindrical Shell Submerged in Acoustic Half-Space Bounded by a Free Surface

An analytical solution is proposed for the free flexural vibration of a finite cylindrical shell submerged in half-space bounded by a free surface in the low frequency range. The motion of the shell is described by the Flügge shell theory and the fluid surrounding the shell is assumed to be an acoustic media. The free surface effect is considered by satisfying the pressure release boundary condition. The accuracy of the present method is verified through comparison with the finite element solution. To throw light on the influence mechanism of free surface on the coupled modal frequencies, a modal added mass is introduced and calculated. Numerical results show that when the shell is close to the free surface, the presence of free surface will make a negative contribution to the modal added mass and finally result in the corresponding increase of the coupled modal frequencies. But the free surface effect will decrease when the immersion depth of the cylindrical shell increases. Finally, the free surface effect can be neglected if the immersion depth is higher than four times the shell radius. This conclusion is helpful to select proper test environment for an experiment on the dynamic characteristics of submerged cylindrical shells.

Semi-analytical research on acoustic-structure coupling calculation of partially submerged cylindrical shell

Vibroacoustic analysis of a partially submerged cylindrical shell-liquid coupling system is a typical acoustic-structure interaction problem in an acoustic half-space. Generally, the vibration and acoustic solutions of this problem almost depend on numerical method in previous studies. However, whether from the aspect of verifying the numerical methods or from the aspect of revealing the vibroacoustic mechanism of the acoustic-structure interaction system, the development of an analytical or semi-analytical method is indispensable. In this study, a semi-analytical method is proposed to address the vibroacoustic response of a horizontal cylindrical shell partially immersed in water The acoustic coordinate system is established on the free surface, and the sine series function is introduced to express the sound pressure to meet the pressure release boundary condition on the free surface automatically. Then based on the two-dimensional Flgge shell theory, the motion equation of the shell-liquid coupling system is established with using the center of the shell as the origin of the coordinate system. By using the Galerkin method, the velocity continuous condition on the fluid-structure interface is established. Then the relation matrix between the acoustic pressure amplitude and the shell displacement amplitude is derived after converting the sound pressure from different coordinate systems into that in the same coordinate system by using the geometry relationship of two coordinate systems. Then the vibration and sound radiation of this coupling system are predicted by solving the coupled matrix equations, and the coupled free vibration can also be addressed by solving the characteristic equation after setting the determinant of the coefficient matrix to be zero. To verify the accuracy and reliability of the present method, the coupled natural frequencies, the vibration response and the distribution of the sound pressure obtained from the present method are compared with those obtained from the finite element method, showing that they are in good agreement with each other. Then the shapes of the first four order modes for the coupled system are presented and compared with those of the system submerged in unbounded fluid field, and the couple between different modes, and the couple between the symmetric and antisymmetric modes are observed due to the effect of the free surface. The characteristics of the root mean square velocity of the shell with different immersed depths are discussed, which reveals that the peaks of response curves shift to the lower frequencies with increasing immersed depth. The characteristics of far field sound pressure directivity are presented and explained by the image method in detail. This study provides a novel method to analytically predict the vibroacoustic response of an elastic structure partially coupling with the fluid field when bounded in a sound half space.

Sensitivity Analysis of Hybrid Split-Step Fourier/Finite Difference Parabolic Equation Models

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air inter...

Acoustic wave propagation in a sensor port: Experimental measurements and analytical model predictions

In this paper, results from an experimental study on pressure fluctuations in a sensor port are presented. The sensor ports are attached to a large flat plate over which plane acoustic waves propagate. In addition, an analytical model is developed by solving the acoustic wave equation subject to rigid and pressure release boundary conditions. The experimental data is used as input to the model from one end of the sensor port in order to predict the pressure fluctuations at the other end of the sensor port. Two sensor ports are used; a short and a long one. The short sensor port resonates at 1000Hz, whereas the long sensor port resonates at 245Hz. The acoustic source generates harmonic and random plane acoustic waves, which can be modeled easily. Pressure fluctuation measurements are made both on the plate surface and inside the sensor ports for various plane wave inputs; harmonic and random. Power spectra, sound pressure levels and transfer functions are then obtained at the various microphone locations. The experimental results for the short sensor port show an amplification factor of 45 between the inlet and the rigid end of the sensor port at a frequency of 1000Hz. For the long sensor port, the amplification is nearly 50 at a frequency of 245Hz, with lower amplifications at higher frequencies. Using the measured power spectrum at the rigid end of the sensor port for a random plane wave input, the absorption coefficient is calculated using the half-power law. Using this absorption coefficient in our analytical model, predictions were made at both ends of the sensor port using experimental data as input. The model predictions for both sensor ports are in good agreement with experimental data.

Model validation of rough surface scattering at a water/air interface using a hybrid parabolic equation model

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models. For propagation models based on the parabolic equation that utilize split-step Fourier (SSF) algorithms, previous work has involved field transformational techniques to treat the rough surface displacements. Such techniques assume small angle scattering at the interface, which may not produce adequate numerical accuracy. An alternative approach is to model the physical water/air interface, and allow the higher order propagator functions of the parabolic approximation to more accurately model the rough surface scatter. However, the introduction of such large interface discontinuities have been known to introduce phase errors in SSF-based models. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches, as well as the pressure release field transformational technique, for simple rough surfaces. A finite element model is utilized to provide a benchmark solution and comparisons are made for both standard Dirichlet and explicit mixed media treatments of the air-water interface. Tradeoffs between accuracy and stability are discussed, as well as transmission across the water/air interface.

Examination of rough surface scattering from water/air interface using hybrid parabolic equation model

Many ocean acoustic propagation models assume an idealized pressure-release boundary at the ocean surface. This is easily accomplished numerically using finite element, finite difference, and split-step Fourier techniques. For models based on the split-step Fourier algorithm, rough surfaces can also be treated, but require additional complexity in the definitions of the field and propagator functions through a field transformation technique. For this reason, it may be advantageous to model a rough water/air interface in a manner analogous to the bottom treatment by extending the calculation into the air medium, thereby simplifying the definitions of the propagator functions. However, standard approaches to treat density discontinuities in split-step Fourier algorithms invoke smoothing functions, which have been shown to introduce phase errors in range. In this work, the hybrid split-step/finite-difference approach introduced by Yevick and Thomson (1996) is implemented in the Monterey-Miami Parabolic Equation (MMPE) model for both the water/sediment and water/air interfaces. Particular attention is paid to comparisons between the rough surface scattering results from the field transformation technique (applied to a pressure release surface) and the hybrid split-step/finite-difference approach (applied to the water/air interface).Many ocean acoustic propagation models assume an idealized pressure-release boundary at the ocean surface. This is easily accomplished numerically using finite element, finite difference, and split-step Fourier techniques. For models based on the split-step Fourier algorithm, rough surfaces can also be treated, but require additional complexity in the definitions of the field and propagator functions through a field transformation technique. For this reason, it may be advantageous to model a rough water/air interface in a manner analogous to the bottom treatment by extending the calculation into the air medium, thereby simplifying the definitions of the propagator functions. However, standard approaches to treat density discontinuities in split-step Fourier algorithms invoke smoothing functions, which have been shown to introduce phase errors in range. In this work, the hybrid split-step/finite-difference approach introduced by Yevick and Thomson (1996) is implemented in the Monterey-Miami Parabolic Equat...