PRACTICAL APPLICATION OF INVERSE BOUNDARY ELEMENT METHOD TO SOUND FIELD STUDIES OF TYRES

The acoustic near field caused by tyre/road interaction has traditionally been studied with the aid of Near-field Acoustical Holography (NAH), allowing for a representation of the sound field on e.g. planar surfaces. This technique can be used to visualise the spatial character of the sound field radiated by a tyre. A typical setup for Near-field Acoustical Holography consists of measuring the sound pressure on a plain surface close to the tyre sidewall and transforming this hologram into a picture of the sound field at the actual tyre surface. Assuming stationary conditions, the measurement can be done using a scanning technique. The entire procedure may be sufficient if the goal is to study tyrewall vibration or planar surfaces in general. On the other hand, a complete description of the vibrating tyre surface would be quite informative so that sources of vibration could be studied on the tread pattern. An approach based on boundary element modelling of sound sources and regularisation techniques was compared with Near-field Acoustical Holography in a study of vibration patterns on a rolling tyre. In the present paper, a further investigation of this Inverse Boundary Element Method (IBEM) is done. Emphasis is put on the regularisation process and how to choose an appropriate regularisation parameter in conjunction with the Tikhonov regularisaton. This choice is of vital importance when solving a discrete ill-posed problem and a useful solution is sought. Another aspect of the reconstruction process is to feed our model of the problem with as much a priori knowledge as possible, e.g. in the sense of known velocity data on some surfaces. In the modelling of the tyre this can be done by imposing a boundary condition to the nodes belonging to the rim structure, where the normal surface velocity is expected to be zero. For the covering abstract see IRRD E104312.