Porous materials are effective for the isolation of sound with medium to high frequencies, while periodic structures are promising for low to medium frequencies. In the present work, we study the sound insulation of a periodically rib-stiffened double-panel with porous lining to reveal the effect of combining the two characters above. The theoretical development of the periodic composite structure, which is based on the space harmonic series and Biot theory, is included. The system equations are subsequently solved numerically by employing a precondition method with a truncation procedure. This theoretical and numerical framework is validated with results from both theoretical and finite element methods. The parameter study indicates that the presence of ribs can lower the overall sound insulation, although a direct transfer path is absent. Despite the unexpected model results, the method proposed here, which combines poroelastic modeling and periodic structures semi-analytically, can be promising in broadband sound modulation. IntroductionOwing to their high stiffness-to-weight ratio, multipanel structures are widely used in engineering applications, such as aircrafts, underwater, and architectural structures. Their acoustic performance has been studied for a long time [1,2,3]. Composite multipanel structures without any attachments or fillings are always the simplest to operate. Both theoretical, and experimental and numerical methods are developed with regard to their sound transmission loss (STL); for example, the theoretical models by Xin [4], Sakagami [5] (with experiments) and the semi-empirical models by Sharp [1], Gu [6], Davy [7]. These prediction models were reviewed and compared by Hongisto [3] and Legault [8] contemporarily.However, none of them are appropriate for the case studied herein.Composite multipanel structures with attachments or absorption fillings are emphasized more. However, their absorption fillings are complicated; in most cases, they are or can be considered as porous materials. Therefore, two widely used models for porous media can be used, i.e., the Biot theory [9] and the equivalent fluid model (EFM) [10]. In these absorption filling (cavity) problems, the EFM, owing to its simplicity, is widely used together with numerical [11] or semi-analytical methods [8,12,13]. For elastic frame porous problems, the Biot theory should be used [14,15] as the EFM is invalid. Using the Biot theory, together with the simplifications of Deresiewicz [16] and Allard [17], Bolton [18] studied a two-dimensional (2D) multipanel structure with elastic porous materials, where the closed form expressions for 2D poroelastic field are obtained. The three-dimensional (3D) counterpart, with closed-form poroelastic field expressions, has been revealed by Zhou [19]. The effect of flow on these structures was subsequently studied by Liu [20]. The numerical methods [14] for these structures, based on the Biot theory, were also developed.Meanwhile, multipanel structures with attachments were prominent as well.The ...

To obtain excellent sound reduction performance, in this paper we introduce a novel periodic poroelastic composite structure, which combines poroelastic material and periodic structure and aims at using the remarkable acoustic performance of these two. This periodic composite structure comprises three parts, i.e. the poroelastic domain, the elastic domain (thin plate), and the periodic resonators, which can be simple single-degree-of-freedom resonators (SRs) or composite two-degree-of-freedom resonators (CRs). A theoretical model is established by using Biot theory for the poroelastic domain, and by using the effective medium method for the resonator-plate coupling system, which is considered as an isotropic plate with an equivalent dynamic density. This method is validated with degenerated model in the literature; the results obtained by this method are in excellent consistence with the results in the literature. Parameter analyses are performed to test the influences of poroelastic addition and periodic resonator on the sound transmission loss (STL) of this periodic composite structure under two kinds of boundary conditions. The poroelastic addition is found to increase the STL while the influences of resonators are complicated. The STL increases notably in the frequency range bounded by the characteristic frequencies of these resonators, however, a decrease just follows when it exceeds these frequencies, which can be observed in both SR case and CR case under the two boundary conditions. In the meantime, when multiple SR is placed in a periodic lattice, it is found that different resonators with ascending mass and characteristic frequencies have superior STL to those with ascending characteristic frequencies but have equal mass. The case with CR, which is more complicated as expected, shows less STL decrease than the case with SR, but wider frequency range where the STL increases than a poroelastic composite structure without resonators. This results from the fact that the frequency band of vibration suppression in the CR case is wider than in the SR case. As a result, to achieve the desired STL performance in a frequency range, the proposed composite structure using SR with tuned characteristic frequencies is enough; however, if a wider frequency band is expected even if there is a slight STL tradeoff, the CR case is a better option. Though the method proposed is only valid in the low-to-medium frequency range, the results obtained can benefit theoretical development of low-to-medium sound modulation applications, they are also valuable and illuminating for investigating the broadband sound modulation.

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