The main issue in the present paper is to comment and
illustrate on new acoustic examples the method of analysis of modal series,
termed “method of orthocomplement”, that has been recently proposed by the
authors to improve the convergence of such series. The general
method consists in a direct analysis and transformation of the remainders of
ordinary series. It results in a family of “hybrid” modal representations
involving an ordinary modal sum of order N, a “quasi-static” term based on
the N first modes, and an “accelerated” modal series. Using the transformed
modal formulae eliminates the Gibbs oscillations – that are attached in
infinite dimensional models to modal boundary discontinuities – and also
the consequences of such phenomena on finite element approximations. The
method is applied in the present paper to plane waves in acoustic tubes and
to 3D acoustic fields inside a car compartment, in view of the synthesis of
acoustic receptances or impedances to be used in practical acoustic
design. The main technical difficulty being the treatment of
singular linear boundary problems or systems of linear equations that arise
during the study of closed rigid cavities or tubes, a whole section of the
paper had thus to be devoted to pseudo-inversion.