Modal Element Method for Scattering and Absorbing of Sound by Two-Dimensional Bodies

1993 ◽  
Vol 115 (3) ◽  
pp. 314-323 ◽  
Author(s):  
K. J. Baumeister ◽  
K. L. Kreider
Keyword(s):  
Finite Element ◽  
Pressure Field ◽  
Acoustic Scattering ◽  
Paper Analysis ◽  
The Body ◽  
Two Dimensional ◽  
Incoming Wave ◽  
Computational Region ◽  
Homogeneous Domain ◽  
Element Method

The modal element method for acoustic scattering from a two-dimensional body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains—the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. In this paper, analysis for two-dimensional scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

A Thévenin-Inspired Approach to Multiple Scattering in Acoustics

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Randall P. Williams ◽  
Neal A. Hall
Keyword(s):  
Multiple Scattering ◽  
Pressure Field ◽  
Acoustic Scattering ◽  
The Body ◽  
Progressive Wave ◽  
Incoming Wave ◽  
Acoustic Transducers ◽  
Scattering Effects ◽  
Multiport Network

We have previously shown how Thévenin's theorem may be used to solve problems in linear acoustic scattering from a mobile body, by forming the solution as a superposition of the field scattered from the body when held immobile and the solution for radiation from the body in a quiescent field (Williams, R. P. and Hall, N. A., 2016, “Thévenin Acoustics” J. Acoust. Soc. Am., 140(6), pp. 4449–4455). For problems involving scattering from multiple mobile bodies, the approach can be extended by using multiport network formalism. The use of network formalism allows for the effects of multiple scattering to be treated using analogous circuit models, facilitating the integration of scattering effects into circuit-based models of acoustic transducers. In this paper, we first review Thévenin's theorem for electrical and linear acoustic systems, and discuss the Thévenin-inspired approach to scattering from one rigid, mobile cylinder. Two-port formalism is introduced as a way to address problems involving two scatterers. The method is illustrated using the problem of scattering from a pair of rigid, mobile cylinders in an ideal plane progressive wave. The velocities of the cylinders and the resultant pressure field in response to the incoming wave are found. Unique features of the method compared to more conventional approaches are discussed.

Sign in / Sign up

Export Citation Format

Share Document