A Modified Helmholtz Equation Least Squares Method for Reconstructing Vibroacoustic Quantities on an Arbitrarily Shaped Vibrating Structure

2021 ◽  
pp. 2150006
Author(s):  
Lingguang Chen ◽  
Sean F. Wu
Keyword(s):  
Helmholtz Equation ◽  
Numerical Simulations ◽  
Least Square ◽  
Surface Velocity ◽  
Source Surface ◽  
Target Structure ◽  
Normal Surface ◽  
Reconstruction Process ◽  
Modified Helmholtz Equation ◽  
Accurate Reconstruction

A modified Helmholtz equation least-square (HELS) method is developed to reconstruct vibroacoustic quantities on an arbitrarily shaped vibrating structure. Unlike the traditional nearfield acoustical holography that relies on the acoustic pressures collected on a hologram surface at a short stand-off distance to a target structure, this modified HELS method takes the partial normal surface velocities and partial acoustic pressures as the input data. The advantages of this approach include but not limited to: (1) The normal surface velocities that represent the nearfield effects are collected directly, which lead to a more accurate reconstruction of the normal surface velocity distribution; (2) The field acoustic pressures are also measured, which leads to a more accurate reconstruction of the acoustic pressure on the source surface as well as in the field; and (3) There is no need to measure the normal surface velocities over the entire surface, which makes this approach quite appealing in practice because most vibrating structures do not allow for measuring the normal surface velocities over the entire source surface as there are always obstacles or constrains around a target structure. Needless to say, regularization is necessary in reconstruction process since all inverse problems are mathematically ill-posed. To validate this approach, both numerical simulations and experimental results are presented. An optimal reconstruction scheme is developed via numerical simulations to achieve the most cost-effective reconstruction results for practical applications.

Reconstruction of Normal Surface Velocities of a Simply-Supported Baffled Plate Using Helmholtz Equation Least Square Method

2008 ◽  
Author(s):  
Huancai Lu ◽  
Sean F. Wu
Keyword(s):  
Helmholtz Equation ◽  
Least Square Method ◽  
Analytic Solutions ◽  
Least Square ◽  
Source Surface ◽  
Normal Surface ◽  
Spherical Object ◽  
Simply Supported ◽  
Hankel Functions ◽  
Acoustic Responses

The normal surface velocities of highly a non-spherical object are reconstructed based on the measurement of field acoustic pressures using Helmholtz equation least-squares (HELS) method. The objectives of this study are to numerically examine the feasibility and accuracy of reconstruction and the impacts of various parameters involved in reconstruction of vibro-acoustic responses using HELS. The vibrating object is a simply-supported and baffled thin plate. The reasons for selecting this object are that plate is the most challenging source geometry for HELS method, and it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are primarily embedded in the HELS formulation, yet the analytic solutions to vibro-acoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked in detail. The Rayleigh integral is used to generate the input field acoustic pressures for reconstruction. The Euler’s equation is employed to establish the system model of reconstruction of vector velocities. Regularization associated with the truncated singular value decomposition is utilized to compromise the resultant accuracy and stability of the vector velocity reconstruction. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply-supported plate. The impacts of various parameters such as the measurement points, measurement distance, the location of origin of coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

2020 ◽  
Author(s):  
Sterling McBride ◽  
Ricardo Burdisso ◽  
Corina Sandu
Keyword(s):  
Sound Intensity ◽  
Element Model ◽  
Dominant Frequency ◽  
Contact Forces ◽  
Surface Velocity ◽  
New Wave ◽  
Normal Surface ◽  
Radiated Noise ◽  
Physical Effects ◽  
Effects Of Rotation

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

scholarly journals Two view NURBS reconstruction based on GACO model

2021 ◽  
Author(s):  
Deepika Saini ◽  
Sanoj Kumar ◽  
Manoj K. Singh ◽  
Musrrat Ali
Keyword(s):  
Optimization Algorithms ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Least Square ◽  
Ant Colony ◽  
Free Form ◽  
Reconstruction Process ◽  
Nurbs Curve ◽  
Data Points ◽  
Ant Colony Optimization Algorithms

AbstractThe key job here in the presented work is to investigate the performance of Generalized Ant Colony Optimizer (GACO) model in order to evolve the shape of three dimensional free-form Non Uniform Rational B-Spline (NURBS) curve using stereo (two) views. GACO model is a blend of two well known meta-heuristic optimization algorithms known as Simple Ant Colony and Global Ant Colony Optimization algorithms. Basically, the work talks about the solution of NURBS-fitting based reconstruction process. Therefore, GACO model is used to optimize the NURBS parameters (control points and weights) by minimizing the weighted least-square errors between the data points and the fitted NURBS curve. The algorithm is applied by first assuming some pre-fixed values of NURBS parameters. The experiments clearly show that the optimization procedure is a better option in a case where good initial locations of parameters are selected. A detailed experimental analysis is given in support of our algorithm. The implemented error analysis shows that the proposed methodology perform better as compared to the conventional methods.

scholarly journals A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jinghuai Gao ◽  
Dehua Wang ◽  
Jigen Peng
Keyword(s):  
Helmholtz Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Inverse Source Problem ◽  
A Posteriori ◽  
Modified Helmholtz Equation ◽  
Numerical Tests ◽  
Theoretical Frame ◽  
Set Up

An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical tests are presented to illustrate the effectiveness and stability of our proposed method.

scholarly journals Moving Heat Source Reconstruction from Cauchy Boundary Data: The Cartesian Coordinates Case

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilson C. Roberty ◽  
Denis M. de Sousa ◽  
Marcelo L. S. Rainha
Keyword(s):  
Helmholtz Equation ◽  
Boundary Data ◽  
Representation Formula ◽  
Transient Heat Conduction ◽  
Thermal Source ◽  
Source Reconstruction ◽  
Modified Helmholtz Equation ◽  
Time Space ◽  
Definition Of ◽  
Characteristic Interval

We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a), we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem. Further, the finite differenceθ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data. Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support. Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations. The problem of centroid determination is addressed and questions are discussed from an computational points of view.

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