Transmission loss of plates with multiple embedded acoustic black holes using statistical modal energy distribution analysis

Acoustic black holes (ABHs) in beams and plates have been extensively studied as a passive method for vibration attenuation and noise reduction. However, most research to date has focused on analyzing the behavior of a single ABH structural element, using numerical or semi-analytical deterministic approaches. If ABHs are to be exploited for practical industrial applications, there is a need to characterize their performance in complex built-up structures and to describe them with statistical methods in the mid-high frequency range. This paper presents a first step towards this goal by employing statistical modal energy distribution analysis (SmEdA) to evaluate the transmission loss of ABH panels separating two air cavities. SmEdA splits vibroacoustic systems into subsystems and establishes power balance equations between the modes belonging to different subsystems. This avoids the energy equipartition assumption of traditional statistical energy analysis (SEA) and extends it to low modal overlap systems. In this work, the benefits of embedding ABHs on plates for noise reduction between cavities are predicted with SmEdA. The role played by the size, shape and number of ABH indentations on the plate are inspected, as well as the influence of other parameters like the truncation thickness, ABH order and damping. The effects of added mass and stiffness of the damping layer are investigated and it is observed that, with proper design, ABH plates can exhibit substantial transmission loss improvement in the vicinity of the critical frequency of uniform plates. Both resonant and non-resonant transmission are considered in the analysis.