Abstract 
This thesis focuses on the development and implementation of effective methods for acoustic modelling and design of hybrid mufflers for internal combustion engines, through analytical and numerical tools. Due to the increasing concern of society in environmental degradation, increasingly severe environmental laws have been dictated, in which the noise from vehicles has become a major source of pollution. It is then customary to develop rapid, reliable and low cost computer modelling and design techniques of mufflers that can produce accurate results. 
The thesis is organized so that it begins by making a presentation of the principles of traditional methods of acoustic analysis, as plane wave models. It highlights the importance of absorbent materials as noise attenuation elements and their properties and most important features are defined. It then proceeds with the description and development of models by using numerical techniques such as the Finite Element method. Models are then developed by the use of multidimensional modal techniques, which will finally serve as design tools. Finally, tests are performed for the acoustic characterization of absorbent materials and the theoretical models studied are experimentally validated. 
The plane wave models and the associated matrizant representation have been traditionally used. The reliability of their results, however, is limited to low frequency range and the three-dimensional effects of propagation are not taken into account. The Thesis highlights the need for finding alternative modelling methodologies that account of these three-dimensional effects, which are in turn applied to a wide range of frequencies and a variety of more complex geometries. 
Multidimensional methodologies can be classified into two groups: those based on conventional numerical methods such as the Boundary Element method and the Finite Element method and those supported by analytical techniques. The most widely numerical method used is the Finite Element method. In the field of Acoustics, this turns out to be very versatile to allow for the consideration of geometries with arbitrary cross section, while taking into account the convective effects due to the existence of mean flow. The Boundary Element method is also suitable but has disadvantages when dealing with convective effects, absorbent materials and perforated surfaces. The Finite Element method is applied to the resolution of the convective wave equation, presented in this Thesis with a pressure formulation. It is interesting to observe the acoustic performance of mufflers while their main geometric characteristics are modified. It is also pertinent to compare the results provided by the Finite Element method and those achieved by the plane wave models. This former numerical technique (as well as the Boundary Element method) has a high computational cost which increases as the number of degrees of freedom of the model grows. This may cause problems regarding its suitability during certain analysis stages.
Due to the fact that the data processing time is a decisive factor in the acoustic modelling of mufflers, efforts should be focused on reducing the computational cost, providing a sufficiently precise prediction of the acoustic behavior. For this, a possible strategy is the development of multidimensional analytical modal techniques that can be applied to commercially interesting configurations. This is the core of the Thesis, which is based on an analytical modal approach of the wave equation associated with rectangular, circular and annular ducts, including the presence of absorbent material. Among the existing multi-dimensional modal techniques, the Thesis emphasizes the Direct Integration method and Mode Matching technique. Both techniques provide similar results to the Finite Element method with a lower computational cost, the Mode Matching technique providing the faster convergence. 
The performance of experimental measurements complements the theoretical analysis presented throughout the Thesis. Thus the approach of a measurement system, which reproduces the actual characteristics, is essential in obtaining the necessary data for examination and comparison of theoretical predictions. From the extensive literature, assessment is carry out of some of the most widely extended experimental methods used for estimating the acoustic properties of mufflers and other components of the acoustic systems. In the specific case of the hybrid mufflers investigated in this Thesis, the most relevant parameters of the absorbent material, such as the characteristic impedance , and the wavenumber , are determined.
Keywords: acoustics, wave equation, Finite Elements, experimental measurement, analytical models, numerical models, Mode Matching technique, mufflers, hybrids mufflers.