Abstract
In recent years the boundary element method (BEM) has become a well established tool for the
analysis of acoustic problems involving unbounded domains, such as sound radiation or sound
scattering problems. The BEM is based on a boundary integral formulation, which relates the field variables in the solution domain to a set of variables defined on the problem boundary. In this way, only the boundary of the considered problem has to be discretized, which yields relatively small numerical models. However, due to the global nature of the boundary integral formulation, the system matrices are fully populated with complex coefficients and are frequency dependent. Furthermore, since the dynamic boundary variables are expressed in terms of locally defined polynomial shape functions, a large number of elements are required in order to get reasonably prediction accuracy, especially for 3-dimensional problems at higher frequencies. As a result, the use of the BEM is restricted to low-frequency applications.
As an alternative to the element based methods, recently a wave based prediction technique (WBT)
has been developed. It is based on an indirect Trefftz approach in that it uses exact solutions of the
governing differential equation to approximate the dynamic field variables, instead of simple
polynomial functions. As a result, a less fine element discretization is sufficient. This results in smaller
numerical models which exhibit an enhanced computational efficiency as compared with the element
based methods. The capability of WBT to solve 2D radiation problems has been shown successfully
by B. Pluymers in 2006.
This paper discusses the extensions of the WBT for the analysis of sound radiation problems in 3
dimensions. For a class of problems with restricted boundary domains the necessary shape functions to
cover the radiation domain outside a spherical envelope of the boundaries are derived. Furthermore,
necessary extensions of the numerical integration involved in building the system matrices are
investigated. The performance of the method is demonstrated with a numerical example in the
frequency range up to 1kHz
analysis of acoustic problems involving unbounded domains, such as sound radiation or sound
scattering problems. The BEM is based on a boundary integral formulation, which relates the field variables in the solution domain to a set of variables defined on the problem boundary. In this way, only the boundary of the considered problem has to be discretized, which yields relatively small numerical models. However, due to the global nature of the boundary integral formulation, the system matrices are fully populated with complex coefficients and are frequency dependent. Furthermore, since the dynamic boundary variables are expressed in terms of locally defined polynomial shape functions, a large number of elements are required in order to get reasonably prediction accuracy, especially for 3-dimensional problems at higher frequencies. As a result, the use of the BEM is restricted to low-frequency applications.
As an alternative to the element based methods, recently a wave based prediction technique (WBT)
has been developed. It is based on an indirect Trefftz approach in that it uses exact solutions of the
governing differential equation to approximate the dynamic field variables, instead of simple
polynomial functions. As a result, a less fine element discretization is sufficient. This results in smaller
numerical models which exhibit an enhanced computational efficiency as compared with the element
based methods. The capability of WBT to solve 2D radiation problems has been shown successfully
by B. Pluymers in 2006.
This paper discusses the extensions of the WBT for the analysis of sound radiation problems in 3
dimensions. For a class of problems with restricted boundary domains the necessary shape functions to
cover the radiation domain outside a spherical envelope of the boundaries are derived. Furthermore,
necessary extensions of the numerical integration involved in building the system matrices are
investigated. The performance of the method is demonstrated with a numerical example in the
frequency range up to 1kHz
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 5th Int. Workshop on the Trefftz Method |
| Pages | 157-172 |
| Publication status | Published - 2008 |
| Event | 2008 International Workshop on the Trefftz Method - Leuven, Belgium Duration: 31 Mar 2008 → … |
Publication series
| Name | Computer Assisted Mechanics and Engineering Sciences |
|---|---|
| Volume | 15.2008,3/4 |
Conference
| Conference | 2008 International Workshop on the Trefftz Method |
|---|---|
| Country/Territory | Belgium |
| City | Leuven |
| Period | 31/03/08 → … |