Modal approach application and significance analysis inside bounded space in a steady state acoustic field condition

Abstract

In the paper there is a problem of investigated bounded space with vibroacoustical source inside generating acoustic field. The first aspect of this work relates to the semi-analytical modelling of an acoustic field which is alternative to finite element method (FEM) or boundary element method (BEM). The second aspect is connected with minimization of significant factors number required to control of acoustic pressure level inside bounded space. Therefore it is assumed that room’s pressure distribution can be described by using modal analysis assumptions. Moreover, acoustic pressure represents the sum over a set of room’s eigenfunctions and time components, i.e. the modal amplitudes. Additional assumption of the highest values of impedance is made. As a result the modal coupling can be neglected. This approach results in the acoustic field model faster than alternative FEM or BEM models. Additionally, the influence of boundaries on the acoustic field is mathematically described. When the shape of bounded space is complicated and the boundaries vary in properties, huge number of experiments (simulations) should be conducted in order to estimate whether the boundaries significantly influence the acoustic filed or the influence can be neglected. By applying the Plackett–Burman or fractional factorial design the number of experiments can be reduced. In addition the statistical interpretation which uses $t$-test is applied. This statistical approach is required when full factorial design is not feasible.