A Model Theory for the Fibrous Absorber, Part I: Regular Fibre Arrangements

The axial propagation of sound waves in a model consisting of parallel fibres will be calculated. The viscous forces and the thermal conduction are taken into account. This will lead to viscous waves and to thermal waves besides the usual acoustic compressional wave. The potential function for the total field near a fibre will be treated as the superposition of the radiated field from the fibre itself and of the scattered fields from all the other fibres. The explicit field equations for a regular square fibre arrangement will be derived and the influence of the order of symmetry of the arrangement will be discussed. This will lead to simplifications in the field equations and to field equations for the case of a homogeneous fibre distribution.