# 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 a source (for example, an engine). During the transmission of the sound across the length of the muffler, generally there is a loss (desired) which is called the Transmission Loss. This Transmission Loss gives a value in decibels (dB) that corresponds to the ability of the muffler to dampen the noise. 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.

## Material

As mentioned, 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, 図 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 properties for the acoustic element.

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

## Results

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

The results are plotted over a range of frequencies (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.

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

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:
• In the 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 account for the small discrepancy in the results.

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