John B. Fahnline

A method for computing acoustic fields based on the principle of wave superposition

A method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition. The superposition integral, which is shown to be equivalent to the Helmholtz integral, is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator. The strengths of the sources that produce this condition can, in turn, be used to compute the corresponding surface pressures. The results of several numerical experiments are presented that demonstrate the simplicity of the method. Also, the advantages that the superposition method has over the more commonly used boundary‐element methods are discussed. These include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed, the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary‐element formulation.

Numerical errors associated with the method of superposition for computing acoustic fields

The method of “wave superposition” is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources. The accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated. The ultimate objective of this study, then, is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and, consequently, the accuracy of the superposition solutions. In general, this is dependent upon the particular surface velocity distribution to be reconstructed, as well as other formulation factors such as the acoustic wave number, the number and locations of the surface nodes, and the number and locations of the point sources. Velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources. Numerical experiments ...

A numerical solution for the general radiation problem based on the combined methods of superposition and singular‐value decomposition

In the method of wave superposition, the acoustic field, due to a complex radiator, is expressed in terms of a Fredholm integral equation of the first kind called the ‘‘superposition integral equation.’’ In general, Fredholm integral equations of the first kind are ill‐posed and therefore difficult to solve numerically. In this paper, it will be shown that a simple collocation procedure, when combined with the singular‐value decomposition, can yield accurate results for the numerical solution of the superposition integral. As an example of the application of the method, the acoustic radiation from a circular cylinder will be analyzed using this numerical procedure and compared to the exact solution. It is shown that, for this problem, the accuracy of the numerical solution can be judged by evaluating how well the superposition solution approximates the specified boundary condition on the surface of the radiator. An example is also given of a problem which has no exact solution. In this situation, it is suggested, without proof, that the accuracy of the numerical solution can be judged in a similar manner by evaluating the error in the superposition solution’s satisfaction of the boundary condition.

A lumped parameter model for the acoustic power output from a vibrating structure

Previous applications of lumped parameter models to acoustic radiation problems assume that the characteristic dimension of the vibrating structure is small in comparison to the acoustic wavelength. In this paper, the frequency range of the lumped parameter model is extended by dividing the surface of the structure into elements and characterizing the amplitude of the radiation from each element by its volume velocity. The model is derived by truncating all but the lowest‐order (monopole) terms of a multipole expansion for the acoustic power output. The multipole expansion differs from those derived previously because it is based on elemental quantities rather than global quantities. By comparing the full multipole expansion for the power output to the lumped parameter model, the error in the lumped parameter model as a function of the acoustic and structural wavelengths (k and K) and the size of the largest surface element (L) is determined. This approach is general and provides a means of determining bo...

Numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure

In a previous paper, a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements, expanding the acoustic field from each of the elements in a multipole expansion, and truncating all but the lowest-order terms in the expansion. Here, the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense. This alleviates the difficulties typically encountered in enforcing the boundary condition, leading to a relatively simple numerical solution with well-defined convergence properties. The basis functions for the numerical analysis are taken as the acoustic fields of discrete simple, dipole, and tripole sources located at the geometrical centers of the surface elements. The different source types are used to represent the radiation from different kinds of surface elements: simple sources for elements in the plane of an infinite b...

Computing fluid‐coupled resonance frequencies, mode‐shapes, and damping loss factors using the singular value decomposition

In many acoustic design problems, it would be useful to be able to compute fluid-coupled resonance frequencies, mode shapes, and their associated damping levels. Unfortunately, conventional eigenvalue solution procedures are either computationally inefficient, unreliable, or have limited applicability. Sophisticated methods for identifying modal parameters using the singular value decomposition have recently emerged in the area of experimental modal analysis, where the available data typically consists of velocity-to-force transfer functions for several drive point locations. In this paper, we show that these techniques can be applied to numerically generated frequency domain data and are even more effective because full matrices of transfer function data are available. This typically allows the modes to be completely separated from each other, such that the modal parameters can be identified using analytical formulas. Several benchmark example problems are solved numerically, including a rectangular cantilever plate, a baffled circular plate, and a baffled circular plate covered by an open-ended rigid-walled pipe.

Influence of blade Solidity on Marine Hydrokinetic Turbines.

Marine hydrokinetic (MHK) devices are currently being considered for the generation of electrical power in marine tidal regions. Turbulence generated in the boundary layers of these channels interacts with a turbine to excite the blades into low-to mid-frequency vibration. Additionally, the self-generated turbulent boundary layer on the turbine blade excites its trailing edge into vibration. Both of these hydrodynamic sources generate radiated noise. Being installed in a marine ecosystem, the noise generated by these MHK devices may affect the fish and marine mammal well-being. Since this MHK technology is relatively new, much of the design practice follows that from conventional horizontal axis wind turbines. In contrast to other underwater turbomachines like conventional merchant ships that have solid blades, wind turbine blades are made of hollow fiberglass composites. This paper systematically investigates the contrast of this design detail on the blade vibration and radiated noise for a particular MHK turbine design.Copyright

Design of an embedded piezoceramic actuator for active control applications

The design of a piezoceramic actuators which is to be embedded in a composite structure is examined. The actuator device must: (1) include a collocated accelerometer; (2) meet certain actuation authority (force, stroke) requirements; (3) be able to survive the embedding process; and (4) have a minimal effect on structural integrity. The need to accommodate an accelerometer limits the minimum thickness of the device. To ensure that the (brittle) piezoceramic material is not broken during the embedding process, it is encased within a frame which has been designed to protect the piezoceramic from short durations of high temperature and pressure. Additionally, the frame is used to apply a compressive prestress to the piezoceramic, ensuring that the piezoceramic is protected from tensile stresses encountered in the operating environment. The output strain levels of the piezoceramic are maximized by using a co-fired stack (178 layers) oriented such that the piezoceramic is excited in the 3 - 3 direction. Because the layers of the piezoceramic stack are to be driven at high voltages, a special high power amplifier was designed which can source the current required by the actuator. The performance of the actuator alone has been tested by driving it uniaxially into a known impedance and measuring the output force and displacement at low frequency. Results form the tests and associated models are presented, which demonstrate the performance capabilities of the actuator.

Active control of the sound radiated by a vibrating body using only a layer of simple sources

Previous research in the area of active noise control has shown that the sound radiation from a vibrating body can be completely controlled using layers of simple and dipole sources located on a surface which completely surrounds the vibrating body. In this paper, the source layer is assumed to consist of simple sources only. If complete control of the sound radiation can be achieved with simple sources only, the implementation of the control strategy will be considerably simplified because simple sources can be approximated with conventional loudspeakers. It is shown that complete control can be achieved when the simple source layer is just outside the boundary surface of the vibrating body (assuming that the fluid coupling between the vibrating body and the surrounding fluid is negligible). When the simple source layer is not near the surface of the vibrating body, the control strategy fails at the resonance frequencies of the volume of fluid between the surface of the vibrating body and the layer of simple sources. It is also shown that in the limit as the source surface approaches the surface of the vibrating body, the control source amplitudes can be written directly in terms of the normal surface velocity of the vibrating body. An example is given to demonstrate the accuracy of the analytical development.

PARALLEL BOUNDARY ELEMENT SOLUTIONS OF BLOCK CIRCULANT LINEAR SYSTEMS FOR ACOUSTIC RADIATION PROBLEMS WITH ROTATIONALLY SYMMETRIC BOUNDARY SURFACES

We propose a distributed parallel algorithm for the solution of block circulant linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces. When large structural acoustics problems are solved using a coupling finite element/boundary element formulation, the most time consuming part of the analysis is the solution of the linear system of equations for the boundary element computation. In general, the problem is solved frequency by frequency, and the coefficient matrix for the boundary element analysis is fully populated and exhibits no exploitable structure. This typically limits the number of acoustic degrees of freedom to 10–20 thousand. Because acoustic boundary element calculations require approximately six elements per wavelength to produce accurate solutions, the formation is limited to relatively low frequencies. However, when the outer surface of the structure is rotationally symmetric, the system of linear equations becomes block circulant. Building upon a known inversion formula for block circulant matrices, a parallel algorithm for the efficient solution of linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces is developed. We show through a runtime, speedup, and efficiency analysis that the reductions in computation time are significant for an increasing number of processors.Copyright