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Kai Ming Li
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ABSTRACT: In the absence of atmospheric effects, the sound fields above a locally reacting ground can be accurately predicted by the Weyl-van der Pol formula. The solution is based on an asymptotic analysis to yield two terms: a direct and a ground reflected wave terms. The reflected wave term can be written as a product of a spherical wave reflection coefficient and the sound reflected from a rigid ground. In the contrary, it is more challenging to derive a similar formula for the sound fields above non-locally reacting grounds. In the past, an approximation in the same form as the Weyl-van der Pol formula has been used which becomes inadequate for layered grounds. In this presentation, a brief review of the asymptotic analysis will be discussed. An overview of the analytical and numerical approaches will be presented for obtaining accurate prediction of sound fields above the non-locally reacting ground. It will be further demonstrated that the reflection coefficient can be split exactly into two terms - a plane wave reflection coefficient and a ground wave term involving the boundary loss factor. The correlation between the numerical distance and the location of the surface wave pole will be examined.
The Journal of the Acoustical Society of America 09/2012; 132(3):1904. · 1.55 Impact Factor
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ABSTRACT: In this article, the propagation of sound from a monopole source above an impedance-backed porous layer is examined. The sound fields can be expressed in an integral form that is amenable to further analysis. A standard method of steepest descents is applied to evaluate the integral where the method of pole subtraction is needed to obtain a uniform asymptotic solution for the sound field above the plane surface. To obtain a numerical solution, the location of the pole was determined numerically by means of the Newton-Raphson method. Based on the pole location, the sound fields can then be calculated numerically. It has been demonstrated that the use of a plane wave reflection coefficient to calculate the sound fields is a special case of the asymptotic formula when the pole is located further away from the saddle point.
The Journal of the Acoustical Society of America 06/2012; 131(6):4376-88. · 1.55 Impact Factor
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ABSTRACT: An efficient computation of sound fields due to a monopole source placed above a porous layer is presented. This paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the Sommerfeld integral. Along the steepest descent path, a standard Gaussian-Hermite quadrature can be used to calculate the sound fields effectively. The suggested numerical scheme is accurate at all frequencies except in the very near field. The proposed method is more numerically efficient than other computational schemes, especially at long ranges and high source frequencies.
The Journal of the Acoustical Society of America 06/2012; 131(6):4389-98. · 1.55 Impact Factor
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Kai Ming Li
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ABSTRACT: The response of a fluid-loaded structure is a subject of considerable interests in many areas of engineering. This includes applications in aerospace industry for composite structures, design of offshore and building structures partially immersed in water, and the design of rectangular micro-plates for bio-sensing devices. For many decades, it has been well recognized that the resonant frequencies of structures in contact with fluid decrease significantly if the fluid-loading on the structure is very heavy. For somewhat lighter fluid-loading, the structural properties are important, and the in vacuo resonant frequencies are usually needed in determining the response due to an external driving force. This paper exploits a simple empirical model to estimate the effect of fluid-loading on the resonant frequency of a rectangular plate. Simple formulas were developed to rapidly compute the natural frequencies of rectangular plates loaded with different fluids on both sides. The rectangular plates with simply supported or clamped edges were considered in the present analysis. Particularly, a square plate with a general boundary condition varying from simply supported to clamped edges was examined. Empirical formulas were derived to calculate the change in the resonant frequencies for baffled plates in all cases.
The Journal of the Acoustical Society of America 10/2011; 130(4):2327. · 1.55 Impact Factor
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ABSTRACT: A numerical model based on a wide-angle parabolic equation (PE) technique has been developed for calculating the sound fields above and below a layered ground. A finite element discretization was applied along the vertical direction instead of the classical finite difference scheme. By using the finite element approach, the boundary conditions, i.e., the continuity of pressure and velocity, can be incorporated directly at the air/ground and ground/ground interfaces. The range-dependent sound fields were obtained by marching the finite-element solutions (above and below the layered ground) in the radial direction. This paper reports a preliminary formulation and presents some initial computational results for the sound fields above and below a porous ground. The numerical results from the PE calculations were compared with the results obtained from analytical solutions for and other benchmark results. A linear and cubic Hermite interpolate function was used in the numerical formulations for the finite element model. It has been shown that use of the cubic Hermite interpolation function generally leads to more accurate numerical solutions with fewer elements. [Work partially funded by Federal Aviation Administration and the China Research Scholarship Council.].
The Journal of the Acoustical Society of America 10/2011; 130(4):2563. · 1.55 Impact Factor
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ABSTRACT: The current study simultaneously addresses the problem of reflection and refraction of sound from a rigid porous ground surface. A more rigorous approach is used to derive more accurate asymptotic solutions that can be cast in a convenient form for ease of numerical implementations. The solutions provide means for rapid computations of the sound fields above and below the rigid porous ground. The improved asymptotic formulas for both situations agree well with numerical results obtained by other numerical schemes, which are more accurate but computationally more intensive. More importantly, the asymptotic solutions can be written in the well-known form of the Weyl-van der Pol formula, which provides a direct correlation between the reflected wave term for the sound field above the porous ground and the transmitted (refracted) wave term for the sound field below.
The Journal of the Acoustical Society of America 09/2011; 130(3):1103-14. · 1.55 Impact Factor
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ABSTRACT: Windows are a common path for low-frequency sound transmission from outside to inside due to their light weight and low damping. The use of non-periodic stiffening elements to increase window transmission loss without reducing visibility is considered here. The effect of elastic mounting of the window to the surrounding structure as a possible contributor to low-frequency noise transmission was also examined. A finite element model allowing for panel stiffening, either by clamping or by adding variable-stiffness beams within the panel, was constructed; the model allowed for variable positioning of such elements. Several double-panel configurations, representing double-pane windows typically used in energy-efficient constructions, were also modeled with various clamped-stiffening elements. Scale-model measurements of transmission loss of aluminum panels were performed to verify the character of the predictions with variable edge stiffness as used in the numerical models. The computational results show that low-frequency sound below 150 Hz can be reduced by several dB through careful use of stiffening elements and that resilient mounting can reduce the transmission loss of low-frequency sound through windows.
The Journal of the Acoustical Society of America 03/2010; 127(3):1776. · 1.55 Impact Factor
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ABSTRACT: The sound propagation due to a monopole source near a rigid porous ground is reviewed. Closed form approximation solutions for predicting the sound field above the ground surface were derived analytically by (1) the method of pole subtraction and (2) the use of an effective impedance approach. The locations of the surface wave pole according to both methods were examined. These two approximate solutions were compared with an exact evaluation of the Fourier integral representing the sound field above the rigid porous ground. It is found that the approximate solution using the effective impedance approach offers relatively better agreements with the exact numerical solution. In addition, the effective impedance approach generally leads to a more accurate uniform asymptotic solution for the sound field above the rigid porous ground. In this presentation, the reason for this good agreement is explained. The finding is further supported by experimental data obtained by conducting indoor measurements over a layer of glass beads.
The Journal of the Acoustical Society of America 03/2010; 127(3):2038. · 1.55 Impact Factor
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ABSTRACT: With superior sound insulation properties over a single-panel configuration, a double-panel structure with the presence of a cavity has found a wide range of applications for sound insulation. A classical method for combining a finite element method (FEM) with a boundary element method (BEM) is used to examine the transmission of low-frequency noise through double-pane windows in the present study. The technique of component mode synthesis is applied to adjust the stiffness matrix in the FEM formulation in order to examine the effects of elastic boundary conditions on the sound transmission through these structures. However, the Green function for predicting sound propagation in a rectangular long enclosure is used in favor of the free-field Green function for predicting the pressure inside the cavity of the window panes. The predicted pressure in the cavity is then coupled with the FEM formulation for the window panes and the BEM formulations for the sound fields at the outer surfaces of window panes. A parametric study is conducted systematically to allow a detailed examination for the characteristics of sound insulation of a double-pane window at different frequency bands especially for the low-frequency components.
The Journal of the Acoustical Society of America 03/2010; 127(3):1993. · 1.55 Impact Factor
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ABSTRACT: In an earlier study [K. M. Li, J. Acoust. Soc. Am. Soc. 123, 1352-1363 (2008)], an analytical expression has been derived to predict the penetration of sound into a rigid porous ground due to a monopole source. In the present study, this analytical formula has been exploited for a numerical method to characterize the acoustical properties of rigid porous materials. They can be obtained from a pair of excess attenuation spectra measured above and below a thick layer of the material. Specifically, its propagation constant and complex density ratio can be determined from the measured data by a downhill simplex method. A series of preliminary indoor measurements was conducted in an anechoic chamber for measuring the propagation of sound above and below a layer of glass beads of different sizes. Based on the measured excess attenuation spectra, the acoustical characteristics of two different sizes of glass beads were determined numerically. These acoustical parameters were compared with the predictions based on the classical impedance model.
The Journal of the Acoustical Society of America 03/2010; 127(3):2038. · 1.55 Impact Factor
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ABSTRACT: The classical problem of sound scattering by an acoustically hard cylinder due to a point monopole and a line airborne source is extended in the present study. The solution to the homogeneous Helmholtz equation is expressed in a cylindrical coordinate system and represented by an expansion of Fourier integrals. Incorporating the image source method and the Bessel function addition theorem, the analytical solution is derived for the prediction of multiple scattering of sound by a hard cylinder placed above a ground surface of finite impedance. The total sound field can be expressed as a sum of four components: the incident field, the reflected wave, and the scattered fields from the cylinder and its image. The total far-field scattered potential was evaluated asymptotically by the method of stationary phase. Experimental measurements by using a point source were conducted in an anechoic chamber to validate the theoretical formulations. The numerical predictions of using a point source model give good agreements with all the experimental data but there are obvious discrepancies in the spectral magnitudes between the calculation and experimental results when a line source model is used to simulate the scattering problem due to a point source excitation.
The Journal of the Acoustical Society of America 02/2010; 127(2):664-74. · 1.55 Impact Factor
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ABSTRACT: The current study examines the propagation of sound in street canyons with geometrically reflecting surfaces. An image source method is a popular numerical model to estimate the propagation of sound energy in a street canyon. This numerical model calculates the total sound energy received at a field point by summing the contributions from individual image sources incoherently. The discrete image source model is generalized by replacing rows of point sources with their respective line sources. An integral formulation is derived, which can be evaluated exactly to give a simple analytical solution. The expression permits rapid computations of the sound energy due to a point source placed in a street canyon. The transient sound energy at a receiver point is also examined. It has been demonstrated that the transient sound energy can be expressed in terms of a standard exponential integral. The Schroeder integration method is then used to calculate the reverberation times, which allow a straightforward assessment of the acoustic environment in street canyons. Indoor and outdoor experiments were conducted to validate the proposed integral formulation. The analytical formulas were also compared with numerical results based on the standard image source method and with published experimental data.
The Journal of the Acoustical Society of America 09/2009; 126(2):644-55. · 1.55 Impact Factor
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ABSTRACT: An asymptotic solution is derived for the sound fields below an extended reaction ground due to an arbitrarily oriented dipole placed near the airground interface. The derived approximate solutions are compared with accurate numerical schemes based on the fast field formulation and the direct numerical integration of the Fourier integral. It has been shown that the sound field above the ground can be computed accurately by using the concept of effective impedance [K. M. Li et al., J. Acoust. Soc. Am. 104, 679-685 (1998)]. The effective impedance approach is used to derive the asymptotic formula for predicting the penetration of sound into the extended reaction ground. However, there are apparent discrepancies in the predicted sound fields according to the analytical solution and the accurate numerical schemes. A modified analytical formula is then developed that leads to more accurate numerical results. The resulting analytical formula due to an airborne acoustic excitation may be used as a basis for a future study to compute the particle displacements induced by an elastic object buried in a rigid-frame porous medium.
The Journal of the Acoustical Society of America 05/2009; 125(4):2521. · 1.55 Impact Factor
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ABSTRACT: In the present study, the sound transmission of low-frequency noise through a double-pane window is analyzed by a coupled finite elementboundary element method (FEMBEM). Particularly, the response of solid structure due to the acoustic excitations is treated by FEM while the behavior of fluid medium, which includes the fluid loading above and below the windows and the fluid cavity inside the window (between the double panes), is simulated by BEM. The stiffness matrix in the FEM formulation is adjusted by the technique of the component mode synthesis in order to handle the mounting conditions of windows effectively. Using the proposed model, the transmission of sound pressures through double-pane windows is calculated and validated with published experimental data. A set of comprehensive parametric studies is then conducted to explore for characterizing the acoustical properties of the double-pane windows, which may be used in the design stage.
The Journal of the Acoustical Society of America 11/2008; 124(4):2515. · 1.55 Impact Factor
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ABSTRACT: This paper examines the feasibility of using two-dimensional hard rough surfaces to reduce noise levels in traffic tunnels with perfectly reflecting boundaries. First, the Twersky boss model is used to estimate the acoustic impedance of a hard rough surface. Second, an image source model is then used to compute the propagation of sound in a long rectangular enclosure with finite impedance. The total sound fields are calculated by summing the contributions from all image sources coherently. Two model tunnels are built to validate the proposed model experimentally. Finally, a case study for a realistic geometrical configuration is presented to explore the use of hard rough surfaces for reducing traffic noise in a tunnel which is constructed with hard boundaries.
The Journal of the Acoustical Society of America 09/2008; 124(2):961-72. · 1.55 Impact Factor
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Kai Ming Li
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ABSTRACT: An approximate analytical formula has been derived for the prediction of sound fields in a semi-infinite rigid-porous ground due to an airborne source. The method starts by expressing the sound fields in an integral form, which can subsequently be evaluated by the method of steepest descents. The concept of effective impedance has been introduced by using a physically plausible assumption. The integral can then be simplified and evaluated analytically. The analytical solution can be expressed in a closed form analogous to the classical Weyl-Van der Pol formula that has been used for predicting sound fields above a rigid-porous ground. Extensive comparisons with the wave-based numerical solutions according to the fast field formulation and the direct evaluation of the integral have been conducted. It has been demonstrated that the analytical formula is sufficiently accurate to predict the penetration of sound into a wide range of outdoor ground surfaces.
The Journal of the Acoustical Society of America 04/2008; 123(3):1352-63. · 1.55 Impact Factor
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ABSTRACT: A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and façade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the façade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.
The Journal of the Acoustical Society of America 02/2008; 123(1):121-32. · 1.55 Impact Factor
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ABSTRACT: It is known that the sound field in a long space is not diffuse, and that the classic theory of room acoustics is not applicable. A theoretical model is developed for the prediction of reverberation time and speech transmission index in rectangular long enclosures, such as corridors and train stations, where the acoustic quality is important for speech. The model is based on an image-source method, and both acoustically hard and impedance boundaries are investigated. An approximate analytical solution is used to predict the frequency response of the sound field. The reverberation time is determined from the decay curve which is computed by a reverse-time integration of the squared impulse response. The angle-dependence of reflection coefficients of the boundaries and the change of phase upon reflection are incorporated in this model. Due to the relatively long distance of sound propagation, the effect of atmospheric absorption is also considered. Measurements of reverberation time and speech transmission index taken from a real tunnel, a corridor, and a model tunnel are presented. The theoretical predictions are found to agree well with the experimental data. An application of the proposed model has been suggested.
The Journal of the Acoustical Society of America 07/2005; 117(6):3716-26. · 1.55 Impact Factor
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ABSTRACT: The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.
The Journal of the Acoustical Society of America 02/2004; 115(1):42-56. · 1.55 Impact Factor
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ABSTRACT: A ray model is developed and validated for the prediction of the insertion loss of barriers that are placed in front of a tall building in high-rise cities. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the barrier and façade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model, as they play important roles in determining the overall sound pressure levels for receivers located between the façade and barrier. Comparisons of the ray model with indoor experimental data and wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Case studies are also presented that highlight the significance of positioning the barrier relative to the noise-sensitive receivers in order to achieve improved shielding efficiency of the barrier.
The Journal of the Acoustical Society of America 09/2003; 114(2):821-32. · 1.55 Impact Factor
