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Scattering Cross Section of Sound Waves by the Modal Element Method
| Content Provider | Semantic Scholar |
|---|---|
| Author | Baumeister, Kenneth J. Kreider, Kevin L. |
| Copyright Year | 1994 |
| Abstract | The modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustic scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the radar cross section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 < ka < I00. Results show excellent agreement with the analytic solution. electromagnetics, the method has been applied to scattering from dielectric cylinders (Chang & Mei (1976), Lee & Cendes (1987), Baumeister & Kreider (1992)) and propagation in ducts (B aumeister (1991 )). In acoustics, the method has also been applied to scattering from cylinders (Baumeister & Kreider (1993)) and propagation in ducts (Astley & Eversman (1981)). In all of these applications, an eigenfunction expansion is used to represent the acoustic pressure field in the far field. An asymptotic approximation of this expansion presents a simple means of determining the scattering cross section. This paper presents the numerical algorithm for evaluating the acoustic scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the radar cross section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, asymptotic approximations are used in conjunction with the standard modal element method. For validation, the method is applied to scattering from rigid circular cylinders, for which the analytic solution is known. INTRODUCTION The modal element method, which couples finite element algorithms to eigenfunction expansions, has been employed in calculating the scattered field from an acoustical plane wave impinging on a two dimensional body. The primary reasons for employing the modal element method are (1) to accurately describe the radiation boundary condition at the computational boundary and (2) to reduce the size of the numerical grid. In fact, for hard scatterers, the modal element method can effectively reduce a two dimensional scattering problem to a one dimensional problem by employing a single line of elements circumscribing the scattering body. The modal element method has been given various titles, such as the unimoment method and the transfinite element method. In NOMENCLATURE A* modal amplitude of wave moving radially outwards a dimensionless circular cylinder radius H c1_ Hankel function of the first kind k wave number m mode number M f number of modal coefficients used in eigenfunction expansion p dimensionless perturbation acoustic pressure r dimensionless radial coordinate dimensionless property constant O angle between radius vector and positive x axis p. dimensionless property constant oc acoustic scattering cross section to dimensionless frequency Superscript * complex conjugate |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19940032800.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
