OS-V: 1100 Transmission Loss in a Muffler

Calculates the transmission loss using Finite Element Method in OptiStruct.

New regulations and standards for noise emission compel the industries to make some improvements about decreasing the noise emitted. The muffler attenuates the noise emitted by source (ex: engine). During the transmission of the sound across the length of the muffler, generally there is a loss (desired) which is called as the Transmission Loss. This Transmission Loss gives a value in decibels(dB) that corresponds to the ability of the muffler to dampen the noise. You will verify your results obtained using OptiStruct with an Analytical Method.

Benchmark Model

Mufflers are generally irregular shapes, but for the simplicity of the problem, the muffler modeled here has a single expansion chamber with a constant cross-section area.

Figure 1. Finite Element Model


As mentioned earlier, acoustic characteristics of the muffler can be determined with transmission loss. A simple geometry is considered which consists of an inlet pipe, an expansion chamber and an outlet pipe. Three points are considered on the muffler to tap the pressure at those points. These pressure values are used to calculate the Transmission Loss.

The finite element model, Figure 1 is meshed with tetra elements of 9.5e-3 m size. The model is fully constrained at one end and the other end is anechoic end (for example, free to radiate into space). Density and speed of sound are required as material propertries for the acoustic element.

The material properties are:
1.2 kg/m3
Velocity of Sound in Air
345 m/s


The problem has been solved using Direct Frequency Response Analysis in OptiStruct.

The results are plotted over a range of frequency (0-2500 Hz) to monitor the Transmission Loss over a broad frequency spectrum. Pressure contour can be visualized by importing an .h3d file in HyperView.

Figure 2. Contour Plot of Sound Pressure

Figure 2 shows the cut section of the muffler. Sound Pressure (db) variation across the muffler is shown for the frequency of 2350 Hz.

For both the calculations, you tap the pressure at three different points along the length of the muffler, Figure 1. These pressure values are used to calculate the Transmission Loss in both OptiStruct and the Analytical Method.

You can see that for the first two cycles, OptiStruct agrees with Analytical Method, but there is a small difference between the results in the third cycle that could be due to:
  • Analytical Method, Transmission Loss is based on plane wave (2D) propagation, whereas in OptiStruct, you consider 3D wave propagation. This difference in wave type could be accounted for the small discrepancy in the results.

Verify that for most frequencies, OptiStruct results agree with the Analytical Method results.

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • Transmission_Loss.fem
  • Transmission_Loss.oml