Linda P. Franzoni

An acoustic boundary element method based on energy and intensity variables for prediction of high-frequency broadband sound fields

A boundary element method is formulated in terms of time-averaged energy and intensity variables. The approach is applicable to high modal density fields but is not restricted to the usual low-absorption, diffuse, and quasiuniform assumptions. A broadband acoustic energy/intensity source is the basic building block for the method. A directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately. A distribution of infinitesimal, uncorrelated, directional sources is used to model the boundaries of an enclosure. These sources are discretized in terms of boundary elements. A system of equations results from applying boundary conditions in terms of incident, reflected, and absorbed intensity. The unknown source power for each element is determined from this system of equations. A two-dimensional model problem is used to demonstrate and verify the method. Exact numerical solutions were also obtained for this model problem. The resul...

A discussion of modal uncoupling and an approximate closed-form solution for weakly coupled systems with application to acoustics

Modal analysis is often used to solve problems in acoustics, leading to a system of coupled equations for the modal amplitudes. A common practice in analytical work utilizing modal analysis has been to assume that weak modal coupling is negligible, thereby enabling the modal coefficients to be solved independently in closed form. The validity of this assumption, as well as the order of the error from neglecting modal coupling, is discussed. It is possible to incorporate the principal effects of weak modal coupling in a very simple way without solving the fully coupled system. An approximate closed-form solution for weakly coupled systems of equations is developed. The procedure gives insight into the errors incurred when coupling is neglected, and shows that these errors may be unacceptably large in systems of practical interest. A model problem involving a pipe with an impedance boundary condition is solved when the one-dimensional sound field is harmonically driven, and when it undergoes reverberant dec...

ON THE ACCURACY OF MODAL ANALYSIS IN REVERBERANT ACOUSTICAL SYSTEMS WITH DAMPING

That the modal analysis method works well regardless of the amount of damping in the system, provided that modal coupling is included in the analysis, is shown. The soundfield produced by a vibrating piston in a tube with an absorptive end is calculated. An exact solution is compared to results computed by modal analysis with and without the inclusion of modal coupling. Recent published results, which did not include the effects of modal coupling, incorrectly concluded that discrepancies were due to limitations of modal analysis, rather than the uncoupling assumption.

Transcending the traditional: Using tablet PCs to enhance engineering and computer science instruction

Traditional instructional methods present many obstacles to effective teaching and learning in engineering and computer science courses. These include a reliance on text-based or static mediums to convey equation- and graphics-heavy concepts, a disconnect between theoretical lecture presentations and applied laboratory or homework exercises, and a difficulty in promoting collaborative activities that more accurately reflect an engineering approach to problem solving. Additionally, technical courses can suffer, like any other course, when students are not actively engaged in the learning and when instructors cannot gauge student understanding. This project has explored the utility of Tablet PCs for overcoming these challenges within a sample of courses in engineering and computer science. There were three primary questions: which knowledge domains benefit from the use of Tablet PCs; whether observed benefits are derived from Tablet PC-specific activities; and what problems limit the effectiveness of Tablet PCs in educational settings? The evaluation of assessment data using regression approaches demonstrated that Tablet-PC-specific activities had a consistent, meaningful, and positive impact upon engineering and computer science courses.

An innovative design of a probe-tube attachment for a 12-in. microphone

Nonintrusive devices are needed to measure sound pressure levels in the mid- to high-frequency range. This need arises due to the small acoustic wavelengths which are present at these frequencies, and the interference caused by conventional microphones which are typically of relatively large diameter. Smaller microphones are less sensitive, and may not be small enough to be useful at very high frequencies or when physical size constraints are limiting. Simple probe attachments have been developed by others to address these problems; however, generally the transfer functions of these devices have possessed undesirable peaks due to the presence of standing waves within the transducers. In this paper, several possible options for making a microphone attachment that will convert a standard 12-in.-diam microphone into a probe-tube are discussed. Recommendations are made with regard to the particular use and ease of construction of the attachment. The new concepts eliminate standing waves, within certain freque...

A study of damping effects on spatial distribution and level of reverberant sound in a rectangular acoustic cavity

Based on computer simulations of sound fields in rectangular enclosures, important observations are made regarding sound pressure levels and the spatial variation of the broadband reverberant field. From these observations an empirical formula is deduced that describes the slow spatial variation of the broadband reverberant mean-square pressure in one lengthwise direction. Two room shapes were studied: an elongated rectangular enclosure and an almost cubic enclosure, both with broadband sound source(s) on an endwall. Source position, relative phasing of multiple sources, level, and placement of absorptive material were variables in the study. The numerical results for the spatially averaged mean-square pressure in the reverberant field were often not in very close agreement with values predicted from a traditional Sabine approach. The prediction was improved by accounting for the power absorbed on the first reflection and an approximate formula is given for this correction factor. The reverberant sound fi...

Assessment of the Contribution of Panel Vibration to Airframe Noise

Aerodynamic noise sources not associated with propulsion are termed “airframe noise.” As well-known sources such as flow separation, landing gear vortex shedding, and flap-edge noise are further reduced, the noise sources from the clean airframe will need to be better understood. Although direct radiation from boundary layers is generally agreed to be an insignificant source, the boundary-layer surface pressures can drive the panels to excitation levels that may produce significant airframe noise. An estimate of airframe noise due to structural vibration is presented. This analysis shows that panel vibration driven by turbulent boundary-layer fluctuations can produce airframe noise levels comparable to those measured on aerodynamically clean airframe configurations. The analysis contains a number of engineering approximations, which are discussed along with their implications for either over- or underestimating the acoustic radiation results. Because the analysis shows levels comparable to measured data rather than dramatically lower levels, it is concluded that structural vibration may be a potentially important source of airframe noise and deserves further study.

An angle-by-angle approach to predicting broadband high-frequency sound fields in rectangular enclosures with experimental comparison.

Experiments were performed on an elongated rectangular acoustic enclosure with different levels of absorptive material placed on side walls and an end wall. The acoustic source was a broadband high-frequency sound from a loudspeaker flush-mounted to an end wall of the enclosure. Measurements of sound-pressure levels were averaged in cross sections of the enclosure and then compared to theoretical results. Discrepancies between the experimental results and theoretical predictions that treated all incidence angles as equally probable led to the development of an angle-by-angle approach. The new approach agrees well with the experimentally obtained values. In addition, treating the absorptive material as bulk reacting rather than point reacting was found to significantly change the theoretical value for the absorption coefficient and to improve agreement with experiment. The new theory refines an earlier theory based on power conservation and locally diffuse assumptions. Furthermore, the new theory includes both the angle of incidence effects on the resistive and reactive properties of the absorptive material, and the effects of angle filtering, i.e., that reflecting waves associated with shallow angles become relatively stronger than those associated with steep angles as a function of distance from the source.

IMPROVEMENT OF A HIGH-FREQUENCY BROADBAND ENERGY-INTENSITY BOUNDARY ELEMENT METHOD TO INCLUDE HIGH RESOLUTION SPECULAR REFLECTION

The prediction of the spatial mean-square pressure distribution within enclosed high-frequency broadband sound fields is computationally intensive if determined on a frequency-by-frequency basis. Recently an energy-intensity boundary element method (EIBEM) has been formally developed. This method employs uncorrelated broadband directional energy sources to expeditiously predict such pressure distributions. The source directivity accounts for local correlation effects and specular reflection. The method is applicable to high modal density fields, but not restricted to the usual low-absorption, diffuse, and quasi-uniform assumptions. The approach can accommodate fully specular reflection, or any combination of diffuse and specular reflection. This boundary element method differs from the classical version in that element size is large compared to an acoustic wavelength and equations are not solved on a frequency-by-frequency basis. In the earlier EIBEM, the source strength and directivity associated with the energy sources, distributed over enclosure boundaries, were determined in an iterative manner and the directivity was limited to three terms of a Fourier expansion. Here, the original method is improved by eliminating the iteration and allowing for an unlimited number of terms in the Fourier expansion of the directivity function. For verification, the improved EIBEM is compared to experimental measurements and exact analytical solutions; excellent agreement is obtained.

A power conservation approach to predict the spatial variation of the cross-sectionally averaged mean-square pressure in reverberant enclosures

Although it is commonly assumed that broadband mean-square pressure levels are spatially uniform in reverberant enclosures, there is a gradual spatial variation, especially if the room is long in one direction, and/or the acoustic absorption is not applied uniformly to the enclosure boundaries. An equation for predicting the average cross-sectional sound pressure levels in a lightly damped enclosure with absorption is derived based on conservation of acoustic power. The derivation involves a one-dimensional boundary value problem, the solution of which is an estimate of the average sound pressure level at cross-sections in the interior. In its simplicity, the resulting formula is reminiscent of the classical Sabine formulation; however, this prediction contains a spatially varying function that depends upon the distribution of absorption (side-wall versus end-wall). The formula is demonstrated on a model problem consisting of a rectangular acoustic enclosure with a source on one end-wall, absorption on th...