A study on the acoustic boundary admittance. Determination, results and consequences

Abstract

The acoustic boundary admittance condition represents the stiffness, the mass and the damping behaviour of the surrounding structure. The harmonic analysis of small interior domains (e.g. vehicle cabin) is often carried out only by applying acoustically rigid boundaries since the admittances are unknown or unreliably determined by commonly applied methods. Determination using an impedance tube (or Kundt's tube) does not consider the real sound field; the calculation from the measured reverberation time provides an average admittance (and no phase information) of the whole boundary only. Beginning with the definition of the complex-valued boundary admittance, a brief review of the techniques to determine boundary admittances is followed by a boundary element based method that is suited to calculate the boundary admittances from a known sound pressure field. In addition to known methods, a formulation is found where the nodal admittance is calculated by the quotient of a nodal particle velocity divided by the nodal sound pressure. The nodal particle velocity can be calculated from a known sound pressure field solving a Dirichlet problem. The methods are applied to three simple examples. Finally, other examples are given to demonstrate how the boundary admittance can represent the fluid–structure interaction and phase angle of admittance influences the complex-valued eigenfrequencies.