A hybrid finite element – statistical energy analysis approach to robust sound transmission modeling

Abstract

When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a computationally efficient modeling strategy is adopted that accounts for this uncertainty. The partitioning wall is modeled deterministically, e.g. with finite elements. The rooms are modeled in a very efficient, nonparametric stochastic way, as in statistical energy analysis. All components are coupled by means of a rigorous power balance. This hybrid strategy is extended so that the mean and variance of the sound transmission loss can be computed as well as the transition frequency that loosely marks the boundary between low-and high-frequency behavior of a vibro-acoustic component. The method is first validated in a simulation study, and then applied for predicting the airborne sound insulation of a series of partition walls of increasing complexity: a thin plastic plate, a wall consisting of gypsum blocks, a thicker masonry wall and a double glazing. It is found that the uncertainty caused by random scattering is important except at very high frequencies, where the modal overlap of the rooms is very high. The results are compared with laboratory measurements, and both are found to agree to within the prediction uncertainty in the considered frequency range.

A review of mid-frequency vibro-acoustic modelling for high-speed train extruded aluminium panels as well as the most recent developments in hybrid modelling techniques

“…in Refs. [46][47][48][49], direct applications of these approaches to vibro-acoustic modelling of extruded aluminium panel structures are still quite problematic because of the complex dynamic nature of extruded panel structures [50,51]. It is true to say that mature and adequate prediction techniques are still very much needed for solving sound transmission through, and radiation from, extruded aluminium panels used for high-speed train structures.…”

Semi-Discrete Coincidence in the Mid-Frequency Sound Transmission Through Rib-Stiffened Panels

“…For the sound insulation predictions, a hybrid finite element -statistical energy analysis (FE-SEA) approach [10,15,16] is adopted. This approach allows coupling diffuse field (or SEA subsystem) models of modally dense components to deterministic models of modally sparse components in a rigorous way.…”

“…Measured values are used for the damping loss factor of the wall as reported in Table 3. Full details on sound transmission modeling with the hybrid method can be found in [15]. For completeness, it is mentioned that the acoustic direct field dynamic stiffness matrices of the rooms (SEA subsystems) were evaluated by means of a wavelet approach [8], using a square interpolation grid covering the flat plate surface and a distance between the grid points of 2.08 cm.…”

“…One should keep in mind that this uncertainty is due to the assumption of a harmonic diffuse field model for the rooms. This assumption can be justified when the acoustic pressure field in the rooms is sensitive to small wave scattering elements, and for the transmission rooms at KU Leuven this is the case from about 140 Hz onwards [15]. At lower frequencies, the uncertainty due to the presence of small wave scattering elements will be overestimated with a diffuse field model.…”

“…This is the frequency range in which the sound fields in the rooms can already be considered as diffuse (in contrast to the low-frequency range), while the modal behavior of the wall is still important (in contrast to the high-frequency range). A detailed finite element model of the rib-stiffened plate is constructed and coupled to a reverberant model of the adjoining rooms within the recently developed hybrid finite element -statistical energy (FE-SEA) analysis framework [16,10,15]. This framework is substantially more flexible and general than conventional statistical energy analysis as it allows, for example, (i) incorporating diffuse and non-diffuse vibro-acoustic system components within a single model in a computationally efficient way, (ii) assessing the uncertainty inherent in the assumption of diffuse sound fields in the rooms, and (iii) computing coupling loss factors in a rigorous and straightforward way, accounting automatically for both resonant and non-resonant transmission [9].…”