Non resonant transmission modelling with statistical modal energy distribution analysis

Abstract

Statistical modal Energy distribution Analysis (SmEdA) can be used as an alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of sound transmission through a thin structure, it is well-known that the non resonant response of the structure plays a significant role in transmission below the critical frequency. In this paper, we present an extension of SmEdA that takes into account the contributions of the non resonant modes of a thin structure. The dual modal formulation (DMF) is used to describe the behaviour of two acoustic cavities separated by a thin structure, with prior knowledge of the modal basis of each subsystem. Condensation in the DMF equations is achieved on the amplitudes of the non resonant modes and a new coupling scheme between the resonant modes of the three subsystems is obtained after several simplifications. We show that the contribution of the non resonant panel mode results in coupling the cavity modes of stiffness type, characterised by the mode shapes of both the cavities and the structure. Comparisons with reference results demonstrate that the present approach can take into account the non resonant contributions of the structure in the evaluation of the transmission loss.

A graph theory approach to identify resonant and non-resonant transmission paths in statistical modal energy distribution analysis

“…in vacuo modes) should be used instead. According to the dual modal formulation (see [18] for the case of two coupled mechanical subsystems and [22] for a cavity-structure problem), the acoustic pressure field (stress field in a general case) is the appropriate one to describe subsystem 1, whereas the displacement field is adequate for subsystem 2. Denoting byP andQ the sets of resonant modes in subsystems 1 and 2, respectively containing N p and N q modes, the acoustic pressure at point M in the cavity and the displacement at point N on the structure can be estimated using the modal expansions:…”

“…This will allow one to inspect how non-resonant transmission can be accounted for in SmEdA, a topic that has only been addressed very recently [22]. For the ease of exposition and without loss of generality, suppose that the system is made of two cavities separated by a panel.…”

“…However, it is well known that resonant transmission, as described by the standard SmEdA approach (7), cannot correctly represent the whole acoustic transmission through the panel below the critical frequency, which is governed by the mass law. To tackle with this problem it was proposed in [22] to include the panel nonresonant modes in the analysis. Although the frequencies of these non-resonant panel modes do not coincide with those of the cavity resonant modes, the modes are strongly coupled one to another because of spatial matching.…”

“…Recently, SmEdA has been extended to incorporate the contribution of non-resonant transmission through condensation of the DMF equations. This has resulted in the appearance of indirect coupling between modes in non-physically connected subsystems, standard non-resonant paths in SEA being recovered as a particular case [22].…”

“…For instance, determining which modes play a predominant role in the energy transmission between subsystems for even simple cases, such as two cavities separated by a homogeneous wall, may implicate hundreds of modes at mid-frequencies. A thorough analysis of the interaction of modal works and involved modal coupling loss factors then becomes necessary to find the dominant modal energy transmission paths between the excited cavity and the receiver one [22]. It is the goal of this work to try to lighten this process by resorting to an alternative approach.…”