Practical vibroacoustic systems involve passive acoustic treatments consisting of highly dissipative media such as poroelastic materials. The numerical modeling of such systems at low to mid frequencies typically relies on substructuring methodologies based on finite element models. Namely, the master subsystems (i.e., structural and acoustic domains) are described by a finite set of uncoupled modes, whereas condensation procedures are typically preferred for the acoustic treatments. However, although accurate, such methodology is computationally expensive when real life applications are considered. A potential reduction of the computational burden could be obtained by approximating the effect of the acoustic treatment on the master subsystems without introducing physical degrees of freedom. To do that, the treatment has to be assumed homogeneous, flat, and of infinite lateral extent. Under these hypotheses, simple analytical tools like the transfer matrix method can be employed. In this paper, a hybrid finite element-transfer matrix methodology is proposed. The impact of the limiting assumptions inherent within the analytical framework are assessed for the case of plate-cavity systems involving flat and homogeneous acoustic treatments. The results prove that the hybrid model can capture the qualitative behavior of the vibroacoustic system while reducing the computational effort.

Modeling complex vibroacoustic systems including poroelastic materials using finite element based methods can be unfeasible for practical applications. For this reason, analytical approaches such as the transfer matrix method are often preferred to obtain a quick estimation of the vibroacoustic parameters. However, the strong assumptions inherent within the transfer matrix method lead to a lack of accuracy in the description of the geometry of the system. As a result, the transfer matrix method is inherently limited to the high frequency range. Nowadays, hybrid substructuring procedures have become quite popular. Indeed, different modeling techniques are typically sought to describe complex vibroacoustic systems over the widest possible frequency range. As a result, the flexibility and accuracy of the finite element method and the efficiency of the transfer matrix method could be coupled in a hybrid technique to obtain a reduction of the computational burden. In this work, a hybrid methodology is proposed. The performances of the method in predicting the vibroacoutic indicators of flat structures with attached homogeneous acoustic treatments are assessed. The results prove that, under certain conditions, the hybrid model allows for a reduction of the computational effort while preserving enough accuracy with respect to the full finite element solution.

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This article presents a novel and advanced finite element formulation of the structural-acoustic problem involving thin and thick multilayered composite plates coupled with a cavity. Exploiting the Carrera's unified formulation, many plate and fluid-structure interface elements based on different kinematic models, including higher-order equivalent single-layer and layerwise theories, are developed within a single mathematical framework. Accordingly, a large number of vibro-acoustic models can be easily obtained and selected according to the accuracy requirements of the application. In particular, it is shown that refined models can be adopted in those cases where models relying on traditional or low-order plate theories fail in providing the correct estimation of the fluid-structure coupling. The proposed formulation is also validated with respect to some reference cases available in the literature

Modeling complex vibroacoustic systems including poroelastic materials using finite element (FE) based methods can be computationally expensive. Several attempts have been made to alleviate this drawback, such as high order hierarchical basis and substructuring approaches. Still, these methods remain computationally expensive or limited to simple configurations. On the other hand, analytical approaches, such as the Transfer Matrix Method (TMM), are often used, thanks to the lower computational burden. However, since the geometrical flexibility of the FE method is always needed in the low/mid-frequency range, attempts have been made to couple the FE model of the master system with a TM model of the sound package. Although these hybrid approaches seem promising, the open literature is not comprehensive. The aim of this work is to present a hybrid FE-TMM approach based on a Green's function formulation. The idea is to account for the sound package by approximating the effects over the treated surface using fundamental solutions (i.e., Green's functions) obtained by the TMM. A benchmark representative of typical applications is used to illustrate the capabilities of the presented methodology in terms of efficiency and accuracy in comparison to other classical methods.