An Extrapolation Method to Compute Far-Field Pressures From Near-Field Pressures Obtained by Finite Element Method

1995 ◽  
Author(s):  
Jamal Assaad ◽  
Christian Bruneel ◽  
Jean-Michel Rouvaen ◽  
Régis Bossut
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Near Field ◽  
Radiation Condition ◽  
Directivity Pattern ◽  
Extrapolation Method ◽  
External Boundary ◽  
Finite Width ◽  
Far Field ◽  
Element Method

Abstract The finite element method is widely used for the modeling of piezoelectric transducers. With respect to the radiation loading, the fluid is meshed and terminated by an external nonreflecting surface. This reflecting surface can be made up with dipolar damping elements that absorb approximately the outgoing acoustic wave. In fact, with dipolar dampers the fluid mesh can be quite limited. This method can provides a direct computation of the near-field pressure inside the selected external boundary. This paper describes an original extrapolation method to compute far-field pressures from near-field pressures in the two-dimensional (2-D) case. In fact, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition, the far-field directivity pattern can be expressed in terms of the near-field directivity pattern. These developments are valid for any radiation problem in 2D. One test example is described which consists of a finite width planar source mounted in a rigid or a soft baffle. Experimental results concerning the far-field directivity pattern of lithium niobate bars (Y-cut) are also presented.

Determination of Far-Field Pattern of Rigid Scatterers Using Independent Finite Element Method and Eigenfunction Expansion, Part 1: Axisymmetric Scattering

1996 ◽  
Vol 118 (4) ◽  
pp. 575-582 ◽  
Author(s):  
C. P. Vendhan ◽  
C. Prabavathi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenfunction Expansion ◽  
Near Field ◽  
Prolate Spheroid ◽  
Field Pattern ◽  
Far Field ◽  
Outer Domain ◽  
Far Field Pattern ◽  
Element Method

The near-field steady state scattered potential around a rigid scatterer subjected to plane incident wave is computed using the finite element method with radiation boundary dampers on a finite truncation boundary. Then the solution in the outer domain is sought in the form of an eigenfunction expansion and the expansion coefficients are obtained using the finite element solution on the truncation boundary as Dirichlet boundary condition. The scattered far-field pattern is derived from this solution for prolate spheroid and hemispherically capped cylinder problems.

A Combined Finite Element Method with Normal Mode for the Elastic Structural Acoustic Radiation in Shallow Water

2020 ◽  
Vol 28 (04) ◽  
pp. 2050004
Author(s):  
Buchao An ◽  
Chao Zhang ◽  
Dejiang Shang ◽  
Yan Xiao ◽  
Imran Ullah Khan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Normal Mode ◽  
Acoustic Field ◽  
Acoustic Radiation ◽  
Three Dimensional ◽  
Far Field ◽  
Azimuthal Direction ◽  
Element Method

A combined Finite Element Method with Normal Mode (FEM-NM) is proposed for calculation of the acoustic field radiated by a three-dimensional structural source in shallow water. The FEM is used to calculate the near range acoustic field, then the modes expansion at the vertical and azimuthal direction is performed at a certain coupling range. Hence, the true three-dimensional acoustic field at any range is obtained rapidly by the NM theory. The numerical examples show the efficiency and accuracy of this method. The coupling range and the truncation of the vertical modes hardly affect the far field results.

Determination of the Load Capacity of a Finite Width Journal Bearing by a Finite-Element Method in the Case of a Non-Newtonian Lubricant

1984 ◽  
Vol 106 (2) ◽  
pp. 285-290 ◽  
Author(s):  
P. Bourgin ◽  
B. Gay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Journal Bearing ◽  
Load Capacity ◽  
Nonlinear Partial Differential Equation ◽  
Strain Tensor ◽  
Finite Width ◽  
Gradient Technique ◽  
Element Method

Additives are commonly used to improve the performance of lubricating oils. Correlatively, the lubricant viscosity depends on the rate of shear: the fluid becomes non-Newtonian. Assuming that the nonlinear relationship between the rate of strain tensor and the stress tensor is cubic, the film equations are derived within the approximations of lubrication theory. The governing equation, which generalizes the Reynolds’ equation, is a nonlinear partial differential equation, subject to two nonlinear constraints. The particular case of a finite width journal bearing is considered here; this problem is solved by the finite-element method, using a gradient technique. The numerical results are compared with established results for newtonian lubricants. The influence of the non-Newtonian parameter on the pressure field and on the bearing capacity is predicted.

Elastostatic Far-Field Behavior in a Layered Half Space Under Surface Pressure

1980 ◽  
Vol 47 (3) ◽  
pp. 504-512 ◽  
Author(s):  
R. Muki ◽  
S. B. Dong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Asymptotic Expansions ◽  
Power Series Expansion ◽  
Surface Region ◽  
Far Field ◽  
Concentrated Force ◽  
Layered Half Space ◽  
Element Method

Elastostatic problem of a half space with a layer of possibly distinct mechanical properties under arbitrary normal tractions on the surface is reconsidered to establish far-field asymptotic expansions of the displacements. This work was motivated by application of such far field solutions to problems of the layered half space by Global-Local Finite-Element Method (GLFEM). When the traction is a unit concentrated force, the asymptotic expansion is found to coincide, up to the second term of its inverse power series expansion with respect to the distance from the point at interface below the point of load application, with that of the classical Boussinesq solution with a suitably chosen coordinate system. This agreement between the two solutions is also observed for normal tractions on a bounded surface region. Comparative numerical results are given to demonstrate the modeling capabilities of the far-field asymptotic expansions in a GLFEM example. It’s effectiveness is shown in terms of greater accuracy and computational efficiency over the conventional finite-element method.

Modeling recent experiments of apertureless near-field optical microscopy using 2D finite element method

2003 ◽  
Vol 221 (1-3) ◽  
pp. 13-22 ◽  
Author(s):  
R. Fikri ◽  
D. Barchiesi ◽  
F. H’Dhili ◽  
R. Bachelot ◽  
A. Vial ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optical Microscopy ◽  
Near Field ◽  
Element Method
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