Design of soundproof panels via metamaterial concept

Sammanfattning: The goal of the work is to find a way to improve the sound insulation properties of different types of panels in order to meet different requirements. Inspired by the nontrivial behavior of the locally resonant acoustic metamaterials, this concept is introduced into the design of structures in order to explore the potential ways to improve the sound insulation behavior in the relevant specific frequency regions. At relatively low frequency region when the bending wavelength is much longer than the distance between isolated resonators, which is also the interesting frequency range in the most part of the work, it may be assumed that the effects of the resonators are uniformly distributed over the entire surface. An impedance approach is hence proposed to estimate the sound transmission loss of the metamaterial panels in order to get more insights from physics. This is realized, in general, by integrating the equivalent impedance of the resonators together with the corresponding impedance of the host panel. Valuable theories are derived based on that, laying a solid foundation for effective/efficient design of metamaterial panels. This approach also provides a fast and reliable tool for the designs prior to a time-consuming and computationally expensive numerical simulation. Based on that, a new design for locally resonant metamaterial sandwich plates is proposed to improve the sound transmission loss performance in the coincidence frequency region. A systematic method to tune the resonance frequency of local resonators is developed. This approach also supplies a method to remove the possible side-dips associated with the resonance of the resonators. The influence of the sound radiation from the resonators is further investigated with the Finite Element models. It is proposed to embed the resonators inside the core material in order to eliminate the possible influence, and also to make a smooth surface. The metamaterial sandwich panel designed in this way combines improved acoustic insulation properties with the lightweight nature of the sandwich panel. Besides the coincidence frequency region, the ring frequency area of a cylindrical shell is another important frequency region for bad sound transmission loss. The effectiveness of locally resonant metamaterial is also investigated. Similar to the case of the flat panel, both impedance model and Finite Element model are developed for the problem of the sound transmission loss properties. The influence of the resonators is presented, and compared with the case of the flat panel. Unlike the case of the metamaterial flat panel, two side-dips around the sharp improvement cannot be avoided when applying the resonators near the ring frequency of the curved panel. The reason for that is explored by using the impedance approach. It is noticed that, while the impedance of a flat panel near the critical frequency is shifted from a masstype impedance to stiffness-type impedance, the impedance of a cylindrical shell is shifted from a stiffness-type (tension-type) impedance to mass-type iv impedance. For a traditional mass-spring type resonator, however, the equivalent impedance is always shifted from a mass-type impedance to stiffness-type impedance when the frequency crosses the resonance frequency. Therefore, when the traditional resonators are applied near the ring frequency, there are always frequencies at which the impedances cancel each other, resulting in the worsened sound transmission loss. In order to have better improvement of the sound transmission loss in this frequency region, new types of resonators have to be developed. A locally resonant metamaterial curved double wall is proposed and studied, with the aim of addressing the mass-spring-mass resonance and ring frequency effects of the wall. The sound transmission loss properties of a curved double wall are first investigated by introducing the concept of ‘apparent impedance’, which expresses the properties of the entire structure in terms of the impedances of the constituting panels and air cavity. The apparent impedance derivation is validated against Finite Element models. The curved double wall is then specifically designed by adjusting the two characteristic frequencies to be close to each other in order to narrow the region associated with a poor transmission loss. This enables, subsequently, to improve the transmission loss in this region by effectively inserting tuned local resonators. The design principles are discussed, and applications for double walls consisting the same curved panels or different curved panels are both included.