Parallel Boundary Element Solutions of Block Circulant Linear Systems for Acoustic Radiation Problems With Rotationally Symmetric Boundary Surfaces

2012 ◽  
Author(s):  
Kenneth D. Czuprynski ◽  
John B. Fahnline ◽  
Suzanne M. Shontz
Keyword(s):  
Boundary Element ◽  
Parallel Algorithm ◽  
Linear Systems ◽  
Acoustic Radiation ◽  
Circulant Matrices ◽  
Element Formulation ◽  
Element Analysis ◽  
Low Frequencies ◽  
Rotationally Symmetric ◽  
Boundary Surfaces

We propose a distributed parallel algorithm for the solution of block circulant linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces. When large structural acoustics problems are solved using a coupling finite element/boundary element formulation, the most time consuming part of the analysis is the solution of the linear system of equations for the boundary element computation. In general, the problem is solved frequency by frequency, and the coefficient matrix for the boundary element analysis is fully populated and exhibits no exploitable structure. This typically limits the number of acoustic degrees of freedom to 10–20 thousand. Because acoustic boundary element calculations require approximately six elements per wavelength to produce accurate solutions, the formation is limited to relatively low frequencies. However, when the outer surface of the structure is rotationally symmetric, the system of linear equations becomes block circulant. Building upon a known inversion formula for block circulant matrices, a parallel algorithm for the efficient solution of linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces is developed. We show through a runtime, speedup, and efficiency analysis that the reductions in computation time are significant for an increasing number of processors.

Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach

2017 ◽  
Vol 232 (18) ◽  
pp. 3235-3249 ◽  
Author(s):  
Nitin Sharma ◽  
Trupti Ranjan Mahapatra ◽  
Subrata Kumar Panda
Keyword(s):  
Boundary Element ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Acoustic Radiation ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Element Formulation ◽  
Present Scheme ◽  
Acoustic Responses

In this article, the vibration-induced acoustic responses of laminated composite flat panels subjected to harmonic mechanical excitation under uniform temperature load are investigated numerically. The natural frequencies alongside corresponding modes of the flat panels resting on an infinite rigid baffle are obtained by using finite element method in the framework of the higher-order shear deformation theory. A coupled finite and boundary element formulation is then employed to acquire the acoustic responses. The governing equation for the sound radiaiton from the vibrating structures is derived by solving the Helmholtz wave equation. The vibration and acoustic responses are computed by using the present scheme via an in-house computer code developed in MATLAB environment. In order to avoid any excess thermal loading conditions first, the critical buckling temperature of the panel structure is obtained and authenticated with the benchmark values. Further, the sound power levels for isotropic and laminated composite panels are computed using the present scheme and validated with the existing results in the published literature. Finally, the influence of lamination scheme, support conditions and modular ratio on the acoustic radiation behavior of laminated composite flat panels in an elevated thermal environment is studied through various numerical examples. The thermal load is found to have substantial influence on the stiffness of the panels and the peaks in the free vibration responses tend to shift to lower frequencies for higher temperatures. It is also inferred that the panels radiate less efficiently whereas the overall sound pressure level is found to follow an increasing trend with increasing temperature.

Dual Boundary Element Analysis for Time-Dependent Fracture Problems in Creeping Materials

2008 ◽  
Vol 383 ◽  
pp. 109-121 ◽  
Author(s):  
E. Pineda ◽  
M.H. Aliabadi
Keyword(s):  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Creep Behaviour ◽  
Boundary Integral ◽  
Element Formulation ◽  
Secondary Creep ◽  
Element Analysis ◽  
Power Law Creep ◽  
Element Method

This paper presents the development of a new boundary element formulation for analysis of fracture problems in creeping materials. For the creep crack analysis the Dual Boundary Element Method (DBEM), which contains two independent integral equations, was formulated. The implementation of creep strain in the formulation is achieved through domain integrals in both boundary integral equations. The domain, where the creep phenomena takes place, is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with secondary creep behaviour. This is con…ned to standard power law creep equations. Constant applied loads are used to demonstrate time e¤ects. Numerical results are compared with solutions obtained from the Finite Element Method (FEM) and others reported in the literature.

Study on the Conditions of Near-Field Acoustic Levitation

2010 ◽  
Vol 97-101 ◽  
pp. 4135-4140 ◽  
Author(s):  
Yan De Liang ◽  
Hong Ling ◽  
Yuan Zhang
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Radiation Pressure ◽  
Acoustic Radiation ◽  
Near Field ◽  
Acoustic Levitation ◽  
Element Analysis ◽  
Boundary Element Analysis ◽  
Acoustic Radiation Pressure

This paper establishes a near-field acoustic radiation pressure solving model applying with acoustics theory and derives an initial acoustic levitation calculating formula of rotundity objects. Combining with finite element and boundary element analysis, levitate conditions of levitated objects are calculated. This paper takes rectangular ultrasonic oscillator for example, testing and analyzing conditions of near-field acoustic levitation by using self-designed test equipments, the results are proved to be better.

Boundary Element Analysis of Thermoelastic Effects in Size-Dependent Mechanics

2015 ◽  
Author(s):  
A. Hajesfandiari ◽  
A. R. Hadjesfandiari ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Characteristic Parameter ◽  
Boundary Integral ◽  
Element Formulation ◽  
Length Scale ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Size Dependent

A new boundary element formulation is developed to analyze two-dimensional size-dependent thermoelastic response in linear isotropic couple stress materials. The model is based on the recently developed consistent couple stress theory, in which the couple-stress tensor is skew-symmetric. The size-dependency effect is specified by one characteristic parameter length scale l, while the thermal effect is quantified by the classical thermal expansion coefficient α and conductivity k. We discuss the boundary integral formulation and numerical implementation of this size-dependent thermoelasticity boundary element method (BEM). Then, we apply the resulting BEM formulation to a computational example to validate the numerical implementation and to explore thermoelastic couplings as the non-dimensional characteristic scale of the problem is varied. Interestingly, for a cantilever beam with a transverse temperature gradient, we find significantly reduced non-dimensional tip deflections as the beam depth h approaches the material characteristic length scale l. On the other hand, when l/h < 0.01, the classical size-independent deflections are recovered.

scholarly journals Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems

1992 ◽  
Vol 114 (3) ◽  
pp. 374-380 ◽  
Author(s):  
S. M. Kirkup ◽  
D. J. Henwood
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Linear Systems ◽  
Acoustic Radiation ◽  
Integral Operators ◽  
Test Problems ◽  
Element Solution ◽  
Integral Equation Formulation

Methods for speeding up the boundary element solution of acoustic radiation problems are considered. The methods are based on solving the integral equation formulation of Burton and Miller for the exterior Helmholtz equation over a range of frequencies simultaneously. Methods for speeding up the computation of the discrete forms of the integral operators and the solution of the linear systems that arise in the boundary element method are considered. A particular implementation of speedup methods is described. Results from the application of this to test problems are given.

A Parameter Study of the Burton–Miller Formulation in the BEM Analysis of Acoustic Resonances in Exterior Configurations

2020 ◽  
pp. 2050023
Author(s):  
Xin Chen ◽  
Qiang He ◽  
Chang-Jun Zheng ◽  
Cheng Wan ◽  
Chuan-Xing Bi ◽  
...  
Keyword(s):  
Boundary Element ◽  
Acoustic Radiation ◽  
Coupling Parameter ◽  
Acoustic Resonance ◽  
Integral Approach ◽  
Parameter Study ◽  
Scattering Problems ◽  
Element Analysis ◽  
Boundary Element Analysis ◽  
Acoustic Resonances

The application of a boundary element technique in combination with a contour integral approach to the numerical analysis of acoustic resonances in exterior configurations is investigated in this paper. Similar to the boundary element analysis of exterior acoustic radiation or scattering problems, spurious eigenfrequencies also turn up in the boundary element solution to exterior acoustic resonance problems. To filter out the spurious eigenfrequencies, the Burton–Miller-type combined formulation is employed to shift them from the real axis to the complex domain. The shifting effect brought by the combined formulation with different types of coupling parameters is investigated. Unlike in acoustic radiation and scattering analyses for which [Formula: see text] is suggested as the coupling parameter, it will be shown that the coupling parameter specified as [Formula: see text] with [Formula: see text] (the time-dependent term herein is [Formula: see text]) is more desirable in distinguishing the spurious eigenfrequencies in the boundary element analysis of exterior acoustic resonances.

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