Simulation of Vehicle Pass-by Noise Radiation

1999 ◽  
Vol 121 (2) ◽  
pp. 197-203 ◽  
Author(s):  
S. F. Wu ◽  
Z. Zhou
Keyword(s):  
Acoustic Pressure ◽  
Numerical Solutions ◽  
Normal Component ◽  
Sound Radiation ◽  
Forward Direction ◽  
Numerical Results ◽  
Surface Velocity ◽  
Pressure Fields ◽  
Vibration Responses ◽  
Element Method

This paper presents an extended Kirchhoff integral formulation for predicting sound radiation from an arbitrarily shaped vibrating structure moving along an infinite baffle. In deriving this formulation, the effect of sound reflection from the baffle is taken into account by using the image source theory. Moreover, the effect of source convection motion and that of motion-induced fluid-structure interaction at the interface on the resulting acoustic pressure field are considered. The formulation thus derived is used to calculate sound radiation from a simplified vehicle model cruising along a solid ground at constant speeds. Since analytical and benchmark numerical solutions for an arbitrarily shaped vibrating object in motion are not available, validations of numerical results are made with respect to those of a point source. Next, sound radiation from a full-size vehicle is simulated. For simplicity, the vehicle is assumed to be made of a shell-type structure and excited by harmonic forces acting on its four tires. Vibration responses subject to these excitations are calculated using finite element method (FEM) with HyperMesh® version 2.0 as pre- and post-processors. Once the normal component of the surface velocity is specified, the radiated acoustic pressure fields are determined using boundary element method (BEM). Numerical results show that the effect of source convection motion enhances sound radiation in the forward direction, but reduces that in the rearward direction. Changes in the resulting sound pressure fields become obvious when the Mach number exceeds 0.1, or equivalently, when a vehicle cruises at 70 mph or higher.

RADIATED ACOUSTIC PRESSURE FROM A MOVING, NONUNIFORMLY VIBRATING CYLINDER WITH TWO SPHERICAL ENDCAPS

1994 ◽  
Vol 02 (01) ◽  
pp. 71-82 ◽  
Author(s):  
ZHAOXI WANG ◽  
SEAN F. WU
Keyword(s):  
Near Field ◽  
Translational Motion ◽  
Normal Component ◽  
Forward Direction ◽  
Numerical Results ◽  
Surface Velocity ◽  
Reverse Direction ◽  
Far Field ◽  
Field Source ◽  
Sound Diffraction

This paper presents numerical results of radiated acoustic pressures from a moving, nonuniformly vibrating cylinder with two spherical endcaps, based on an extended Kirchhoff integral formulation. Specifically, we consider cases in which the normal component of the surface velocity is nonzero on a portion of the surface, and zero elsewhere. Numerical results demonstrate that the radiation patterns depend critically on the frequency and source dimensions. For a noncompact source, the strongest radiation may not necessarily stem from a vibrating surface, but rather from a nonvibrating surface due to the effect of sound diffraction. The more noncompact the source is, the larger the number of side lobes in the near field and the more concentrated these side lobes will be. In the far field, however, the side lobes become smeared and less distinguishable. In other words, the effect of sound diffraction is greatly reduced in the far field. Source translational motion induces sound radiation in the perpendicular direction and enhances the radiated acoustic field in general. Enhancement in the forward direction is much greater than in the reverse direction.

Extended Kirchhoff Integral Formulations for Sound Radiation from Vibrating Cylinders in Motion

1993 ◽  
Vol 115 (3) ◽  
pp. 324-331 ◽  
Author(s):  
S. F. Wu ◽  
Z. Wang
Keyword(s):  
Acoustic Pressure ◽  
Near Field ◽  
Translational Motion ◽  
Sound Radiation ◽  
Forward Direction ◽  
Numerical Results ◽  
Rectilinear Motion ◽  
Dimensionless Frequency ◽  
Translational Speed ◽  
Kirchhoff Integral

This paper presents numerical results of sound radiation from vibrating cylinders in rectilinear motion at constant subsonic speeds by using the extended Kirchhoff integral formulations recently derived by Wu and Akay (1992). In particular, the effects of the interaction between the turbulent stress field and the vibrating surface in motion are examined. Numerical results demonstrate that this interaction is significant in the near-field when the dimensionless frequency ka > 2 and the dimensionless source translational speed M > 0.1. If this interaction is completely neglected, the predicted acoustic pressure is underestimated by as much as 10 to 20 percent in the near field. The effects of this interaction, however, decrease in the far-field. The effects of surface translational motion on the resulting sound radiation are also examined. It is found that the surface translational motion has a significant effect on the resulting sound generation in both near- and far-fields. The amplitude of the acoustic pressure is approximately doubled in the forward direction when ka > 2 and M > 0.2, which corresponds to at least a 5 dB increase in the SPL value.

Visualization of Sound Transmission Into a Vehicle Passenger Compartment

2001 ◽  
Author(s):  
Manmohan S. Moondra ◽  
Sean F. Wu
Keyword(s):  
Acoustic Pressure ◽  
Normal Component ◽  
Sound Transmission ◽  
Acoustic Energy ◽  
Surface Velocity ◽  
Valuable Insight ◽  
Passenger Compartment ◽  
Vehicle Interior ◽  
Acoustic Image ◽  
Fine Mesh

Abstract The paper examines the effectiveness of the Helmholtz equation least-squares (HELS) method (Wu and Yu, J. Acoust. Soc. Am., Vol. 104, 2054–2060, 1998; Wu, J. Acoust. Soc. Am., Vol. 107, 2511–2522, 2000) in visualizing the areas that are prone to noise transmission into a full-size vehicle passenger compartment due to exterior excitations such as the engine and turbulent flow. To simulate sound transmission, harmonic excitations are assumed to act on arbitrarily selected vehicle interior surfaces. The surface acoustic pressures are calculated using the boundary element method (BEM) based Helmholtz integral equation. A fine mesh for the interior cavity is generated so as to yield as accurate as possible the acoustic pressure distributions as benchmark using the BEM codes. The radiated acoustic pressures inside the vehicle compartment are calculated and taken as the input to the HELS formulation. Once the HELS formulation is established, the acoustic pressure anywhere including the vehicle interior surface is reconstructed. The normal component of the surface velocity can be reconstructed in a similar manner. Consequently, the normal component of the time-averaged acoustic intensity and acoustic energy flow inside a vehicle passenger compartment can be visualized. This three-dimensional acoustic image can provide valuable insight into vehicle interior noise reduction. The reconstructed acoustic pressures are compared with the benchmark values evaluated at the same locations. The effect of the measurement locations on the accuracy of reconstruction is investigated.

Sound Radiation by a Point Source Near a Surface of Aircraft

2020 ◽  
pp. 17-25
Author(s):  
Natalia K. Musatova ◽  
Mezhlum A. Sumbatyan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Physical Theory ◽  
Acoustic Pressure ◽  
Sound Radiation ◽  
Hankel Function ◽  
Ray Theory ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Element Method

The problem of sound radiation by a source located in the tail of an aircraft is considered. Three methods of finding acoustic pressure are compared: the boundary element method, the Kirchhoff’s physical theory of diffraction and the ray theory. The simplest model in the form of two-dimensional problem and some thin long shape with acute angle is considered. The diffraction problem for an acoustically solid obstacle lay in the solving Fredholm’s integral equation of the second kind. Due to the boundary element method application, the equation along the entire region is reduced to the equation along the boundary. Discretization by grid nodes, selected on the boundary curve, using the collocation method is applied for numerical solution. A system of linear algebraic equations with real coefficients is formed, then the total acoustic pressure is found. The Kirchhoff’s physical theory of diffraction is based on the fact that on an arbitrary convex body in case of short-wave diffraction in the vicinity of each boundary point in the zone of light the boundary value of pressure is equal to twice pressures in the incident field. By the ray theory the modulus of the acoustic pressure in the scattering field is described by the Hankel function. Argument of this function is equal to the length of full path of the beam when it is reflected once from the border. In conclusion, the pressure in cases, when in the sharp edge there is a split node and when there isn’t, are compared. Also a scattering field calculated by three theories and scattering field in the far receiving point are built.

Experimental and numerical research on the underwater sound radiation of floating structures with covering layers

2014 ◽  
Vol 229 (3) ◽  
pp. 447-464 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Yu wang ◽  
Feng Xiao ◽  
Hongxing Hua
Keyword(s):  
Low Frequency ◽  
Sound Radiation ◽  
Numerical Results ◽  
Homogenization Theory ◽  
Sound Insulation ◽  
Underwater Sound ◽  
Frequency Range ◽  
Floating Structures ◽  
Covering Layer ◽  
Element Method

This paper presents experimental and numerical investigation into the underwater sound radiation characteristics of a free-floating stiffened metal box covered with three different kinds of covering layers and subjected to mechanical excitation. One box is bare while the other three are, respectively, covered with solid covering layers, chiral covering layers, and chiral covering layers filled with expanded polystyrene (EPS) foams. The equivalent elastic modulus of chiral covering layer is obtained by the homogenization theory. The finite element method and boundary element method are used to calculate the underwater sound pressure. The measured and numerical results are illustrated and the sound insulation mechanisms of three covering layers are discussed. The measured results agree with the numerical results well. The covering layers can obviously reduce the underwater sound radiation of floating structures. Compared with the solid covering layer, the chiral covering layer is less effective in suppressing the sound radiation in the low-frequency range but more effective in the medium- and high-frequency range. The chiral covering layer filled with EPS foams shows the best performance, which is more effective in suppressing the sound radiation both in the low-frequency range and in the medium-frequency range. The EPS foams have a high contribution to the added damping of the chiral covering layer.

The Modified Boundary Element Method for Vibration and Sound Radiation Prediction of Fluid-Loaded Structures

1995 ◽  
Author(s):  
Michael V. Bernblit
Keyword(s):  
Boundary Element Method ◽  
Green’S Function ◽  
Boundary Element ◽  
Green's Function ◽  
Surface Pressure ◽  
Control Point ◽  
Normal Component ◽  
Surface Velocity ◽  
Fluid Loading ◽  
Element Method

Abstract The objective of this study is to modify the conventional Boundary Element Method (BEM) to enable rigorous account of fluid loading. For this purpose the two-level BEM has been developed which allows to split structural and acoustical phases of the problem into two sequential stages. At first step fluid loading is ignored and the in-vacuo normal component of the surface velocity and structural Green’s function are calculated. Then surface pressure distribution is computed from the modified Boundary Integra] Equation with perturbated kernel. Secondly, vibration velocity of fluid-loaded surface is calculated using convolution of the surface pressure and the in-vacuo Green’s function. After that sound pressure is predicted for any control point by Helmholtz formula. The method is applied for volume and planar fluid-loaded radiators as well as to sound scattering by elastic bodies.

Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

2018 ◽  
Vol 15 (05) ◽  
pp. 1850029 ◽  
Author(s):  
Yingbin Chai ◽  
Zhixiong Gong ◽  
Wei Li ◽  
Tianyun Li ◽  
Qifan Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Numerical Solutions ◽  
Acoustic Radiation ◽  
Unbounded Domains ◽  
Numerical Results ◽  
Smoothed Finite Element Method ◽  
Gradient Smoothing ◽  
Element Method

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshfree methods. In the SFEM-Q4, only the values of shape functions (not the derivatives) at the quadrature points are needed and the traditional requirement of coordinate transformation procedure is not necessary to implement the numerical integration. Consequently, no additional degrees of freedom are required as compared with the original FEM. In addition, the original “overly-stiff” FEM model for acoustic problems (governed by the Helmholtz equation) is properly softened due to the gradient smoothing operations implemented over the smoothing domains and the present SFEM-Q4 possesses a relatively appropriate stiffness of the continuous system. Therefore, the well-known numerical dispersion error for Helmholtz equation is decreased significantly and very accurate numerical solutions can be obtained by using relatively coarse meshes. In order to truncate the unbounded domains and employ the domain-based numerical method to tackle the acoustic radiation in unbounded domains, the Dirichlet-to-Neumann (DtN) map is used to ensure that there are no spurious reflections from the far field. The numerical results from several numerical examples demonstrate that the present SFEM-Q4 is quite effective to handle acoustic radiation problems and can produce more accurate numerical results than the standard FEM.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

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