Nassif Rayess

Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure

This paper presents experimental validations of the Helmholtz Equation Least Squares (HELS) method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020-2032 (1997); Wu and Wang, U.S. Patent Number 5712805 (1998); Wu, J. Acoust. Soc. Am. 107, 2511-2522 (2000)] on reconstruction of the radiated acoustic pressures from a complex vibrating structure. The structure under consideration has geometry and dimensions similar to those of a real passenger vehicle front end. To simulate noise radiation from a vehicle, a high fidelity loudspeaker installed inside the structure at the location of the engine is employed to generate both random and harmonic acoustic excitations. The radiated acoustic pressures are measured over a finite planar surface above the structure by a microphone. The measured data are taken as input to the HELS formulation to reconstruct the acoustic pressures on the top surface of the structure as well as in the field. The reconstructed acoustic pressures are then compared with measured ones at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the surface. Results show that satisfactory reconstruction can be obtained on the top surface of the structure subject to both random and harmonic excitations. Moreover, the more measurements and the closer their distances to the source surface, the more accurate the reconstruction. The efficiency of the HELS method may decrease with increasing of the excitation frequency. This high frequency difficulty is inherent in all expansion theories.

Visualization of acoustic radiation from a vibrating bowling ball

This paper presents visualization of acoustic radiation from a vibrating bowling ball using the Helmholtz equation least squares (HELS) method. In conducting the experiments, the ball is excited by a vibration shaker using stationary random signals. The radiated acoustic pressures are measured using two microphones and taken as input to the HELS formulations. The reconstructed acoustic pressures on the bowling ball surface are compared with those measured at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the bowling ball surface. Results demonstrate that the accuracy of reconstruction based on measurements over a conformal surface is much higher than that over a finite planar surface. This is because the latter often extends beyond the near-field region, making the accuracy of measurements inconsistent. Nevertheless, satisfactory reconstruction of acoustic pressure fields over the entire bowling ball surface can still be obtained based on the measurements taken over a finite planar surface on one side of the source. In a similar manner, the normal component of the surface velocity is reconstructed. Once these acoustic quantities are determined, the time-averaged acoustic intensity is calculated. Also presented are the formulations for estimating a priori the numbers of expansion functions and measurements required by the HELS method and the guidelines for determining the reconstruction error and optimum measurement locations, given the overall dimensions of the source and the highest frequency of interest in reconstruction.

An outline of a proposed acoustic holography system based on the Helmholtz equation–least‐squares (HELS) method

The Helmholtz equation–least‐squares (HELS) method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); Wu, J. Acoust. Soc. Am. 107, 2511–2522 (2000)] has been proven a reliable acoustic holography method. The main advantages are its simplicity in formulations, flexibility in measurement locations, and uniformity in algorithm for a variety of source geometry and conditions. This paper presents a complete acoustic holography system based on the HELS method that makes full use of these advantages. This system has been under development as part of an ongoing research at the Acoustics, Vibration, and Noise Control Laboratory at Wayne State University. The physical setup will be described which includes the front‐end multichannel data acquisition system and the associated hardware. Experimental results on reconstruction of the radiated acoustic fields from a complex source using this system will be demonstrated. Comparisons of this system with other acoustic holography systems currently available will be m...

Visualization of acoustic pressure fields radiated from a complex vibrating structure

This paper presents visualization of acoustic pressures radiated from a complex vibrating structure using the Helmholtz equation least‐squares (HELS) method [Z. Wang and S. F. Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); 104, 2054–2060, (1998)]. The structure under consideration has the same shape and dimension as those of a full‐size vehicle front end. Random noises are generated by an engine noise simulator that consists of many loudspeakers of different sizes. The radiated acoustic pressures are measured a certain distance away from the vehicle surface, which are then taken as the input to a computer model based on HELS formulations. Experiments are conducted in a 12 ft by 12 ft by 6.5 ft fully anechoic chamber at the Acoustics, Vibration, and Noise Control Laboratory of Wayne State University. The reconstructed acoustic pressures on vehicle surfaces and in the field are compared with the measured data. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various ...

Enhanced sound absorption of aluminum foam by the diffuse addition of elastomeric rubbers

The sound absorption properties of open cell aluminum foams are understood to be significant (Ashby et al. Metal Foams: A Design Guide, 2000) with theoretical models presented in the literature [J. Acoust. Soc. Am. 108, 1697–1709 (2000)]. The pores that exist in metal foams, as artifacts of the manufacturing process, are left unfilled in the vast majority of cases. Work done by the US Navy (US patent 5895726 A) involved filling the voids with phthalonitrile prepolymer, resulting in a marked increase in sound absorption and vibration damping. The work presented here involves adding small amounts of elastomeric rubbers to the metal foam, thereby coating the ligaments of the foam with a thin layer of rubber. The goal is to achieve an increase in sound absorption without the addition of cost and weight. The work involves testing aluminum foam samples of various thicknesses and pore sizes in an impedance tube, with and without the added rubber. A design of experiment model was employed to gauge the effect of t...

Vibration damping of metal foam‐polymer interpenetrating phase composite.

The damping and basic dynamic properties for a novel type of multifunctional hybrid material known as metal foam‐polymer composite are investigated. This material is obtained by injection molding a thermoplastic polymer through an open cell aluminum foam, in essence creating two contiguous morphologies, an aluminum foam interconnected “skeleton” with the open pores filled with a similarly interconnected polymer substructure. This coexistence of both materials allows each to contribute its salient properties (e.g., the plastics contributing surface toughness and the metal foams contributing thermal stability). Basic damping testing results are presented for various aluminum foam porosities and pore sizes as well as for three types of polymers. A basic mathematical model of the damping is also presented. The integrity of the interface between the aluminum foam and the polymer is discussed in terms of its effect on the overall material damping.

An expanded spherical wave expansion for arbitrary sound fields

Spherical wave function expansions as means of describing the acoustic field radiated by arbitrarily shaped objects are very convenient and gaining popularity. The HELS method for acoustic holography is one methodology advocating the use of spherical wave functions as a basis for the solution of the inverse acoustic problem. Such methodologies only provide an approximation to the actual sound field and as such suffer from errors, albeit understood to be bounded and manageable in a large number of cases. Based on the sound radiation model of a volume distribution of monopole sources, these approximation errors are found to be due to the presence of monopole sources outside the largest inscribed virtual sphere. Monopole sources outside that virtual sphere are not accounted for in the expansion and thus come out as errors. These errors are greatly reduced if the spherical wave function expansion is modified to account for the largest number of monopole sources in the model. This is accomplished by employing ...

Application of multisource discrimination to the HELS method

In most engineering applications, the acoustic fields are usually generated by multiple incoherent sources. When such acoustic fields are sampled and taken as input data to the Helmholtz equation least‐squares (HELS) formulations directly, the reconstruction might not be accurate. Hence there is a need to discriminate the contributions from individual sources and separate the composite sound field into a set of spatially coherent subfields that are also mutually incoherent. In this paper, we apply the principal component decomposition technique to the HELS method to reconstruct acoustic radiation from multiple incoherent sources in a free field. The key ingredients of this technique include a diagonalization by singular value decomposition (SVD) of the cross‐spectral matrices generated by a number of reference microphones. Each diagonal term corresponds to a subfield that results from a so‐called virtual sound source. Even though such virtual sources are not always representative of the actual sources, th...

Spherical wave approximation to arbitrary sound fields

The ability to expand the acoustic field radiated from arbitrarily shaped objects in the form of a series of spherical wave functions has always been a point of interest. Despite the paucity of theoretical understanding, experimental and numerical work has repeatedly shown that such expansions can lead to relatively accurate approximations of the radiated sound fields. A general understanding of the problem as well as a quantitative approximation of the resulting errors are deduced from the sound radiation model based on a volume distribution of monopole sources. The errors involved in the approximation are a direct result of the presence of monopole sources outside the largest inscribed sphere. It is shown that under many circumstances, such errors are relatively small and can be mitigated further by the proper choice of the method used to determine the coefficients of the expansion. The collocation method with an appropriate sampling scheme has been used with a great deal of success to determine the exp...

Analysis of reconstruction of radiated acoustic pressure fields by using the HELS method

This paper presents a detailed analysis of reconstruction of the acoustic pressure fields radiated from a partially vibrating sphere by using the Helmholtz equation‐least squares (HELS) method [Z. Wang and S. F. Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); 104, 2054–2060 (1998)]. The objectives of this study are to gain insight into an acoustic inverse problem and to develop guidelines that may be helpful in the future reconstruction work. Because of the complexities involved, many questions such as where and how many measurements should be taken, how many expansion terms are necessary for a given number of measurements, etc., remain unanswered. These questions will be tackled here. The reasons for selecting a partially vibrating sphere are twofold: (1) the resulting acoustic pressure field contains a very pronounced near‐field effect; and (2) analytic results are known so the reconstructed acoustic pressures can be checked rigorously. The impact of a loss of the near‐field effect on reconstruction will...