Equivalent Source Formulation Research Articles

Improved accuracy for radiation damping in coupled finite element/equivalent source computations.

In coupled structural-acoustic computations, radiation damping is due to the resistive component of the surface pressure created by structural vibrations. Equivalent sources using tripole sources as basis functions can be used to compute the surface pressure forces for exterior radiation problems. This technique is similar to the Burton and Miller method for eliminating numerical difficulties due to interior acoustic resonances in boundary element computations and has been proven to yield unique solutions. However, numerical computations presented here will show that for the specific equivalent source formulation under investigation, tripole sources overpredict the resistive component of the surface impedance, especially in the mid-to-high frequency range. It will also be shown that for frequency domain calculations, an accurate representation for the resistive component of the pressure forces can be derived from an analytical representation for the source radiation resistance. Unfortunately, this technique is not applicable to time domain computations. It is also shown that more accurate results can be obtained by allowing both the simple and dipole source amplitudes to be independent variables and enforcing boundary conditions in both the exterior and interior directions simultaneously to reduce the magnitude of the interior acoustic field.

An equivalent source CVIS method and its application in predicting structural vibration and acoustic radiation in ocean acoustic channe

The acoustic wave propagating in ocean is severely distorted due to the sound speed profile of sea water and the reflection and absorption of seabed. The FEM/BEM is a preferable method to solve the fluid-structure interactive vibration and sound radiation problem of underwater structure in ocean acoustic environment, since the Green function can be applied in the integral equation. The simple source integral method is more preferable compared with Helmholtz integral because the calculation of normal derivative of Green function is avoided. In order to remove the irregular frequency problem, Zhou (Zhou et al., 2010) proposed a CVIS theory, which however introduced the normal derivative of Green function on CVIS surface and limited its application into ocean acoustical environment. Therefore, an equivalent source formulation of CVIS is proposed based on the definition of normal derivative so that the normal derivative of Green function on the integration of CVIS is replaced. The radiated SPL of spherical shell is calculated in shallow and deep sea with various sound speed profiles. It is shown that the equivalent source CVIS can be used to eliminate the irregular frequency problem of the far field radiated sound pressure of underwater elastic structure in ocean acoustic environment.

Transient finite element/equivalent sources using direct coupling and treating the acoustic coupling matrix as sparse.

Transient structural-acoustic problems can be solved using time stepping procedures with the structure and fluid modeled using finite elements and equivalent sources, respectively. Limitations on the time step size for stable solutions have led to the current popularity of iterative coupling to enforce the boundary conditions at the fluid-structure interface, which also helps to alleviate difficulties caused by the fully populated acoustic coupling matrix. The research presented here examines a monolithic approach using a stabilized equivalent source formulation where the acoustic coupling matrix is either fully diagonal or treated as sparse. In theory, the matrix should be sparse because it relates nodal velocities to nodal acoustic pressure forces during a single time step, and the pressure waves can only travel a distance equal to the sound speed multiplied by the time step. The numerical results demonstrate that for the chosen example problems accurate results are obtained for either diagonal coupling matrices or with a large percentage of the terms set to zero. It is also demonstrated that the formulation adapts well to parallel processing environments and that the times associated with the equivalent source computations are proportional to the number of processors.

A coupled finite element/equivalent source formulation for transient structural-acoustic problems

Recent research suggests that instability problems that occur in the time domain boundary element formulations are manifestations of nonuniqueness difficulties, and that remedies similar to those used in frequency domain formulations can address the difficulties and improve solution stability. For frequency domain equivalent source formulations, the difficulties can be addressed by combining simple and dipole sources together to form “tripole sources”. The basic goals of the current research are to develop an analogous equivalent source formulation for transient acoustic boundary value problems and to combine it with structural finite element analyses to solve transient coupled structural-acoustic problems. A brief description of the equivalent source formulation is given along with several validation cases for acoustic boundary value problems, including one with a closed boundary surface where nonexistence difficulties should occur. The formulation requires convolution summations, which are independent of each other and a brief discussion is given of how the computations can be parallelized. A brief description is also given of the coupled finite element/equivalent source formulation for transient structural-acoustic boundary value problems. Several examples are given to validate the formulation and to demonstrate that the tripole source formulation for the equivalent sources is more stable than the simple source version.

Equivalent sources method for supersonic intensity of arbitrarily shaped geometries

Supersonic acoustic intensity is utilized to locate radiating regions on a complex vibrating structure. The supersonic intensity is obtained by a special process that removes the evanescent waves from the near-field acoustical holography measurement. The filtering process is well understood for separable geometries, but unfortunately, there are few results for arbitrarily shaped objects. This work proposes a methodology based on a stable invertible representation of the radiated power operator. The power operator is approximated numerically by the equivalent source formulation and the appropriate complete spectral basis is employed to form the stable invertible operator. The operator is formed with the most efficient radiation modes and these modes are utilized to obtain the supersonic solution for the near-field holographic problem. This concept is tested using numerically generated data in a spherical geometry and the results are validated with the spherical harmonic, supersonic filter. Finally, a vibrating ship-hull structure provides a physical example for application and validation of the proposed methodology in a more complex geometry.

Equivalent sources method for supersonic intensity of arbitrarily shaped geometries

Supersonic acoustic intensity is utilized to locate radiating regions on a complex vibrating structure. The supersonic intensity is obtained by a special process that removes the subsonic waves from the near-field acoustical holography measurement. The filtering process is well understood for separable geometries, but unfortunately, there are few results for arbitrarily shaped objects. This work proposes a methodology based on a stable invertible representation of the radiated power operator. The power operator is approximated numerically by the equivalent source formulation and the appropriate complete spectral basis is employed to form the stable invertible operator. The operator is formed with the most efficient radiation modes and these modes are utilized to obtain the supersonic solution for the near-field holographic problem. This concept is tested using numerically generated data in a spherical geometry and the results are validated with the spherical harmonic, supersonic filter. Finally, a vibrating ship-hull structure provides a physical example for application and validation of the proposed methodology in a more complex geometry. [This work was supported by the Office of Naval Research.]

Wave-based sound propagation in large open scenes using an equivalent source formulation

We present a novel approach for wave-based sound propagation suitable for large, open spaces spanning hundreds of meters, with a small memory footprint. The scene is decomposed into disjoint rigid objects. The free-field acoustic behavior of each object is captured by a compact per-object transfer function relating the amplitudes of a set of incoming equivalent sources to outgoing equivalent sources. Pairwise acoustic interactions between objects are computed analytically to yield compact inter-object transfer functions. The global sound field accounting for all orders of interaction is computed using these transfer functions. The runtime system uses fast summation over the outgoing equivalent source amplitudes for all objects to auralize the sound field for a moving listener in real time. We demonstrate realistic acoustic effects such as diffraction, low-passed sound behind obstructions, focusing, scattering, high-order reflections, and echoes on a variety of scenes.

Sound field separation with sound pressure and particle velocity measurements

In conventional near-field acoustic holography (NAH) it is not possible to distinguish between sound from the two sides of the array, thus, it is a requirement that all the sources are confined to only one side and radiate into a free field. When this requirement cannot be fulfilled, sound field separation techniques make it possible to distinguish between outgoing and incoming waves from the two sides, and thus NAH can be applied. In this paper, a separation method based on the measurement of the particle velocity in two layers and another method based on the measurement of the pressure and the velocity in a single layer are proposed. The two methods use an equivalent source formulation with separate transfer matrices for the outgoing and incoming waves, so that the sound from the two sides of the array can be modeled independently. A weighting scheme is proposed to account for the distance between the equivalent sources and measurement surfaces and for the difference in magnitude between pressure and velocity. Experimental and numerical studies have been conducted to examine the methods. The double layer velocity method seems to be more robust to noise and flanking sound than the combined pressure-velocity method, although it requires an additional measurement surface. On the whole, the separation methods can be useful when the disturbance of the incoming field is significant. Otherwise the direct reconstruction is more accurate and straightforward.

Real-time sound propagation and noise modeling in outdoor environments using Equivalent Source Formulation

We address the problem of wave-based sound propagation in outdoor and urban environments. The goal is to accurately simulate acoustic effects, including interference, diffraction, scattering, and higher-order wave effects in large outdoor scenes. We give an overview of a precomputed wave-based solver that is based on equivalent source method and is mainly applicable to large, open scenes [Mehra et al. 2012]. As part of a preprocessing step, it computes a per-object transfer function that models the scattering behavior of each object, and handles pair-wise acoustic coupling between objects using inter-object transfer functions. The runtime component involves fast summation over all outgoing equivalent sources for all objects at the listener location. We highlight its runtime performance and memory efficiency and use it for noise modeling and prediction in outdoor scenes spanning a few hundreds of meters. The sound field is computed in three dimensions, modeling frequency-dependent propagation above ceilings, around buildings and corners, and high-order interactions.

An Interactive 3D Anisotropic Cellular Automata Model of the Heart

A 3D cellular anisotropic automata model with modifiable geometry is described. The modeling parameters include grain size, fiber orientation, and free-wall and septal thickness. From this modifiable model, three specific models corresponding to normal heart, left ventricular hypertrophy, and ventricular dilatation were generated. Each model is a conduction and propagation model in which the atria, the major atrial vessel bases, the ventricles, and the specialized conduction system are represented. Muscle tissues are modeled as bundles of fibers with anisotropic conduction speed of the activation wavefronts. Regional variations of conduction, refractory gradients, and regional potential gradients can also be specified before each simulation. Each element has adaptive properties with respect to cycle length and to the prematurity of incoming impulses. Action potentials can be specified for each cell and an equivalent source formulation is carried out to simulate the vectorcardiogram and the corresponding 12-standard-lead electrocardiogram.

A Cellular Automata Model of the Heart and Its Coupling with a Qualitative Model

Cellular Automata (CA) models offer a good compromise between computational complexity and biological plausibility while qualitative models have expressive power for explicitly describing dynamic processes. In this paper we present a 2DCAmodel and its coupling with a qualitative model. TheCAmodel includes elements characterizing muscle, nodal tissue, and bypass conduction. Each element exhibits adaptive properties to cycle length and to the prematurity of incoming impulses. A crude electrocardiogram is also simulated via an equivalent source formulation. Arrhythmias such as the Wenckebach phenomenon, atrial flutter, or extrasystole-triggered tachyarrhythmias can be simulated using relatively simple models when they incorporate the fast conduction system with muscle tissue and when the model elements exhibit adaptive properties. We then illustrate how aCAmodel can be coupled to a qualitative model to produce a system that combines the fine grained description ofCAmodels with the high level interpretative role of qualitative models.

A novel design and analysis of low loss abrupt bends of dielectric slab waveguides

On the basis of the well-known laws of reflection and refraction of the plane electromagnetic waves, a concept for designing very low loss nonadiabatic junctions between tilted straight sections of dielectric waveguides is investigated. Combining the ray representation of the propagating modes with the equivalent source formulation of the dielectric waveguide excitation problem, a simple and accurate 2-D theory for treating such bends in slab waveguides is developed. Numerical results for typical cases are explained along with some new junctions for achieving large angle redirection of guided waves with very low bending loss.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Blowout limits of turbulent jet diffusion flames for arbitrary source conditions

We present a formulation for the blowout limits of turbulent jet diffusion flames issuing from sources with arbitrary geometries and exit conditions into otherwise quiescent environments. It is argued that, while the liftoff characteristics of turbulent diffusion flames appear likely to be controlled by the straining out of flame sheets, the molecular mixing rate at the flame tip controls their blowout characteristics. The concept of a equivalent is introduced, and the local molecular mixing rate in the flow is expressed in terms of the associated far-field scaling laws. Blowout is expected when a resulting algebraic expression reaches a critical value. Results of a flip experiment verify the far-field equivalent source formulation. Measurements of the blowout limits over a range of geometries, fuels, and diluents show good agreement with the predictions from this formulation.