Development and validation of a wave based technique for forward and inverse simulation of vibro-acoustic problems with trim material damping.

In recent years, the vibro-acoustic performance of products has become a key design feature. This evolution has been instigated by growing customer expectations, who associate the sound of a product with a certain quality, and by ever tightening regulations on the noise emission levels of products and the human exposure to noise and vibrations. Another important is the trend towards lightweight materials, fuelled by an increasing ecological awareness and high direct and indirect material costs. These lightweight materials, however, have less favourable vibro-acoustic properties because of their lower weight, while retaining the component's stiffness. Often multilayered damping treatments are added, but almost always a posteriori. Bringing these damping treatments into an integrated design procedure with often conflicting design requirements, including the NVH behaviour (Noise, Vibration and Harshness), thus puts design engineers worldwide to the challenge.

A modern design environment requires a lot of prototyping. Nevertheless, in order to decrease the time-to-market, the use of physical prototypes is strongly decreasing in favour of virtual prototypes, based on Computer Aided Engineering (CAE) tools. Unfortunately, none of the existing tools allows for simulation of the vibro-acoustic behaviour over the full audible frequency range. Whereas dedicated techniques exist for the low and high frequency ranges, this is not the case for the mid frequency range, which is in many applications also the region where the human hearing is most sensitive. Element based methods are limited to the low frequency range characterised by long wavelengths relative to the problem geometry due to more than linearly increasing model sizes and calculation times. Statistical methods rely on a number of underlying assumptions which only hold in the high frequency range where the wavelengths are short. The introduction of lightweight materials and complex damping treatments even further limits the applicability of classical CAE techniques because of their large model sizes and short wavelengths. 

The Wave Based Method, which is at the core of this dissertation, is developed to alleviate the efficiency problems of the low frequency techniques and as such to bridge the mid frequency range. By approximating the dynamic field variables by a set of wave functions which are exact solutions to the governing equation(s), a much more efficient technique can be obtained. The method has already shown its computational efficiency and modelling effectiveness for acoustic and structural problems separately and for the combined vibro-acoustic problem.

In light of the recent emergence of lightweight materials and complex damping treatments, the presented work focuses on the introduction of accurate models for these materials into a highly efficient wave based model of the vibro-acoustic environment. Two separate tracks are followed in order to serve a double purpose. A first, computationally efficient approach, based on a coupling between the Wave Based Method and the Transfer Matrix Method, allows for quick predictions at hardly an increased cost with relation to the vibro-acoustic system model without the damping treatment. A second technique is based on a hybrid coupling between the Wave Based Method and the Finite Element Method and allows for detailed predictions of the dynamic behaviour of complex damping materials and their impact on the vibro-acoustic environment.

Both contributions enhance the applicability of the Wave Based Method to vibro-acoustic problems with localised complex damping treatments. The theoretical developments are supported by a number of validation cases, illustrating the applicability and efficiency of the proposed techniques.