Coupled Finite Element/Boundary Element Method for the Analysis of the Acoustic Scattering From Elastic Structures

1995 ◽  
Author(s):  
Bertrand Dubus ◽  
Antoine Lavie ◽  
Dominique Decultot ◽  
Gérard Maze
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Acoustic Waves ◽  
Acoustic Scattering ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Thin Cylindrical Shell ◽  
Isolation And Identification ◽  
Fluid Medium ◽  
Physical Phenomena

Abstract Considerable interest has been expressed recently in the scattering of acoustic waves from elastic targets. For structures of arbitrary shapes, the numerical method relying upon a finite element description of the solid part and a boundary element description of the waves propagating in the infinite fluid medium is the most commonly used. This paper presents a coupling between the ATILA finite element code and the EQI boundary element code performed using a solid variable methodology. Results are presented for a thin cylindrical shell bounded by hemispherical endcaps which are insonified at axial and normal incidences. Comparisons are made with measurements of backscattered pressure spectra and angular patterns obtained with the quasi-harmonic MIIR (Method of Isolation and Identification of Resonances). Emphasis is put on post-processing techniques contributing to the interpretation of physical phenomena such as the extraction of resonant mode shapes.

FRACTAL TWO-LEVEL FINITE ELEMENT MESH FOR ACOUSTIC SCATTERING PROBLEMS

2003 ◽  
Vol 11 (01) ◽  
pp. 1-9 ◽  
Author(s):  
A. Y. T. LEUNG ◽  
G. R. WU ◽  
W. F. ZHONG
Keyword(s):  
Finite Element ◽  
Infinite Number ◽  
Acoustic Waves ◽  
Mass Matrix ◽  
Acoustic Scattering ◽  
Finite Element Mesh ◽  
Element Mesh ◽  
Exterior Region ◽  
Number Of Layers ◽  
Hankel Functions

The problems of acoustic waves scattered by scatterer immersed in unbounded domain is an essential ingredient in the study of acoustic-structure interaction. In this paper the problems of acoustic scattering in an infinite exterior region are investigated by using a fractal two-level finite element mesh with self-similar layers in the media which encloses the conventional finite element mesh for the cavity. The similarity ratio is bigger than one so that the fractal mesh extends to infinity. Because of the self-similarity, the equivalent stiffness (mass) matrix of one layer is proportional to the others. By means of the Hankel functions automatically satisfying Sommerfeld's radiation conditions at infinity, the different unknown nodal pressures on different layers are transformed to some common unknowns of the Hankel coefficients. The set of infinite number of unknowns of nodal pressure is reduced to the set of finite number of Hankel's coefficients. All layers have the same matrix dimension after the transformation and the respective matrices of each layer are summed. Due to the proportionality, the infinite number of layers can be summed in closed form as the entries of each matrix are in geometric series. That is, processing one layer is enough to virtually represent a set of infinite number of layers covering an infinity domain. No new elements are created. Numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems.

Acoustic Scattering by Two Submerged Spherical Shells

1998 ◽  
Vol 06 (04) ◽  
pp. 421-434 ◽  
Author(s):  
Gordon C. Everstine ◽  
Guillermo C. Gaunaurd ◽  
Hanson Huang
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Boundary Element ◽  
Series Solution ◽  
Spherical Wave ◽  
Acoustic Scattering ◽  
Element Model ◽  
Computer Code ◽  
Structural Acoustics ◽  
Coupling Coefficients

We validate, using a coupled finite element/boundary element computer code, a recently-developed1 series solution for the structural acoustics problem of scattering from two submerged spherical elastic shells. Although the general purpose computational tools for acoustic scattering have never been restricted to single scatterers, the availability of the series solution provides, for the first time, the mutual validation of both exact and numerical approaches for a multiple elastic scatterer problem. The excellent agreement between the two solutions presented thus allows this problem to be added to the short list of existing benchmark structural acoustics problems possessing an analytic solution. For the purposes of this comparison, the direction of incidence is taken as parallel with the axis joining the two shells. The numerical solution uses the NASHUA code, which couples a finite element shell model of the two shells with a boundary element model of the surrounding fluid. The exact solution is found by expanding in terms of classical modal series and uses the addition theorem for the spherical wave functions. The exact solution requires coupling coefficients that are expressed in terms of sums of products of Wigner 3-j symbols (or Clebsch-Gordan coefficients).

Free Vibration Analysis of Elastic Plates in Contact with an Inviscid Fluid Medium

2015 ◽  
Vol 07 (03) ◽  
pp. 1550041 ◽  
Author(s):  
Helnaz Soltani ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Stokes Equations ◽  
Plate Theory ◽  
Mode Shapes ◽  
Element Formulation ◽  
Inviscid Fluid ◽  
Elastic Plates ◽  
Fluid Medium ◽  
Shear Deformation Plate Theory

In the present study, a finite element formulation is presented to investigate vibration response of elastic plates in contact with a fluid medium. The fluid is assumed to be incompressible and inviscid, and the impermeability condition of the plate is taken into account. The classical plate theory (CPT), first-order shear deformation plate theory (FSDT), and Reddy third-order shear deformation plate theory (RSDT) are considered for the kinematic description of the solid medium and the simplified Navier–Stokes equations are used as the governing equations for the fluid medium. For each plate theory, a coupled set of finite element equations is derived. The effect of the fluid pressure is considered as an added mass and its effect on natural frequencies and mode shapes is investigated through several numerical simulations by varying the boundary conditions.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Application of the Boundary Element Method and Modal Analysis to Tire Acoustics Problems

1993 ◽  
Vol 21 (2) ◽  
pp. 66-90 ◽  
Author(s):  
Y. Nakajima ◽  
Y. Inoue ◽  
H. Ogawa
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Traffic Noise ◽  
Noise Prediction ◽  
Prediction System ◽  
Tire Noise ◽  
Acoustic Contribution ◽  
Element Method

Abstract Road traffic noise needs to be reduced, because traffic volume is increasing every year. The noise generated from a tire is becoming one of the dominant sources in the total traffic noise because the engine noise is constantly being reduced by the vehicle manufacturers. Although the acoustic intensity measurement technology has been enhanced by the recent developments in digital measurement techniques, repetitive measurements are necessary to find effective ways for noise control. Hence, a simulation method to predict generated noise is required to replace the time-consuming experiments. The boundary element method (BEM) is applied to predict the acoustic radiation caused by the vibration of a tire sidewall and a tire noise prediction system is developed. The BEM requires the geometry and the modal characteristics of a tire which are provided by an experiment or the finite element method (FEM). Since the finite element procedure is applied to the prediction of modal characteristics in a tire noise prediction system, the acoustic pressure can be predicted without any measurements. Furthermore, the acoustic contribution analysis obtained from the post-processing of the predicted results is very helpful to know where and how the design change affects the acoustic radiation. The predictability of this system is verified by measurements and the acoustic contribution analysis is applied to tire noise control.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

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