This application note dives into the differences between the various available solvers and gives two detailed examples how BEM is being used on the market today. The first example covers a radiated acoustic simulation of a washing machine, where a problem is discovered using contribution displays and a solution is found. The second example shows how CAE simulation loadings are applied to a basic gearbox model for radiated acoustic analysis.
FEM and BEM technology overview
Acoustic Harmonic FEM
Acoustic Harmonic FEM is used to predict acoustic responses in the frequency domain or to evaluate acoustic mode shapes of cavities. The method requires a mesh of the acoustic domain and leads to a system of equations with banded symmetric system matrices, which are solved in a very-efficient manner using iterative solvers. Acoustic harmonic finite element models are excited through a set of sound sources in the domain or by imposed normal surface velocities at the boundary or by defined pressures at selected nodes. The velocities can be imported from vibration tests or from structural FEA codes. Acoustic damping is introduced through porous materials (volume absorbers), trim liners (surface absorbers) and fluid damping. The method yields results at all FE nodes or at any field point in the domain.
Acoustic Harmonic BEM
Acoustic Harmonic BEM allows the user to solve acoustic radiation problems and to predict the acoustic response in both enclosures and unbounded domains. It only requires a mesh of the surface boundary the fluid domain, resulting in a very low number of degrees of freedom.
The user specifies a frequency range and intermediate steps, with no constraints on either: different ranges and steps can be combined. Acoustic boundary element models can be excited by a set of sound sources in the domain or by imposed normal surface velocities or surface pressures on the boundary. These boundary conditions can be imported from vibration tests or from structural FEA codes or using generic values. Acoustic damping is introduced through surface impedance boundary conditions. The method yields results at any field point.
Comparison between BEM and FEM
BEM and FEM methods share a number of features such as the use of element technology to affect a solution and the use of pre- and post-processing to manage the information obtained from each method. In some sense, however, the FEM is the more general of the two methods. The FEM may be used for non-linear problems such as when the sound pressure is extremely high or when the acoustic domain is nonhomogeneous, as for example when there are temperature gradients. In its usual form, the BEM is restricted to linear, homogeneous problems.
However, the multi-domain BEM overcomes this last limitation for many problems of practical interest. For most radiation problems, the BEM is preferred over the FEM. With the FEM, one would need to extend the surface mesh into the acoustic domain using three-dimensional volume elements. This is not recommended as it results in a large number of elements, but more important, yields an error since no matter how far the mesh is extended; it is not possible to represent an infinite domain with a finite model using the FEM. This illustrates the fundamental difference between the BEM and FEM: with the BEM, one discretizes only the surface of the radiating body while with the FEM the entire acoustic domain must be discretized. Because with the BEM all numerical approximations are confined to the surface, a coarser mesh can be used as compared to the FEM for the same accuracy.
A primary advantage of the BEM over the FEM is its simplicity which allows the new user to become proficient in a much shorter time. Because the boundary element mesh is only a surface mesh, it is easy to construct and does not have as many potential variations as one has with the FEM.
The solver
Like the finite element approach the boundary element approach also has variations in its solver. The two main ones are the indirect and direct approach. The indirect approach allows you to have open meshes (meshes that are not closed) and your fluid property is applied to the entire model, both inside and outside. That means you can only have one type of fluid property, therefore limiting the number of applications you can already address.
The direct method is again split into two, the interior direct method and the exterior direct method. As their names suggest with these methods you are either working on the inside or outside of the mesh. This also gives the limitation that you must have a closed mesh, so no holes in the model and like the indirect approach you can only have one fluid property per mesh. But unlike the indirect approach you can create a link between two different direct boundary element methods and therefore have more than one fluid property for your simulation.
Another factor to consider is when the acoustic pressure interacts with the structure and in turn excites the structure to generate more noise. This is called a vibroacoustic or a coupled simulation .Imagine a piece of paper in front of a subwoofer(loudspeaker), the air pressure resulting from the low frequency sound from the subwoofer causes the piece of paper to vibrate. This is a coupled simulation, where the sound can affect the structure. If the structure is so stiff, and heavy, like and engine, then a coupled simulation is not necessary.
Other solver methods are the multi-pole boundary element method and the pade expansion method. The pade expansion method aims to solve the helmholts integral equation for a complete frequency band, using factorization of the matrix at selected frequencies. For large problems, the computation time is dominated by the factorization time of the matrix. Therefore, avoiding multiple factorizations gives large time savings.
Application example – simulating the radiated noise of a washing machine
This first example that will be shown is a washing machine; this can be done using the direct or indirect method, depending on the type of mesh you want to use. For both cases you have to decide if you want to perform a direct acoustic response simulation or a coupled response simulation. Considering that the washing machine walls are thin metal, and the air pressure resulting from the motor and drum of the washing machine could affect the structural walls, which in turn would generate more noise. The disadvantage of the coupled method is only the computation time needed.
It is very important that you generate a good acoustic mesh to keep the computation time to a minimum. The only setup difference as shown below is that the structural generation of the vibration data is all done at the same time in the coupled simulation. Below is the process flow of both methods and I will explain each step in further detail.
When it comes to acoustics and virtual design simulation, there are two primary methods: the Boundary Element Method or BEM and the Finite Element Method or FEM. Both methods are available within Virtual.Lab Acoustics. The reason LMS does this is to cover a broader application range since neither the finite element nor the boundary element method is suitable for every application. The choice of method really depends on the type of acoustic simulation. For example, a radiated exterior acoustic simulation requires a different approach than an interior acoustic simulation.
