Numerical and analytical study of vibration damping using a curvilinear acoustic black hole

Abstract

Acoustic black hole (ABH), a relatively new vibration damping technique, is attracting attention due to its potential as lightweight and efficient vibration damper. In the past decades, various research related to ABHs have been conducted, but the study on the effect of length of ABH on the damping performance had not been studied in depth due to practical space limitations. In this thesis, the analysis based on geometrical acoustics shows that increase in length improves the reflection characteristics of ABH very efficiently, and therefore, the curvilinear ABH is proposed to increase the space efficiency of ABH and enhance the damping performance at the same time. As the most basic case of curvilinear ABH, the circular arc ABH of constant curvature is investigated through numerical and analytical study. Through a numerical method, the damping performance of an arc ABH is investigated in terms of the influences of curvature, arc length, and the damping material treatment. It is numerically shown that the curvature has less of an influence on the damping performance in the mid- and high- frequency ranges. The damping performance is enhanced as the arc length is increased. Adding the damping material to an ABH can also strongly enhance the damping performance while not significantly increasing the weight. In addition, the effective size of the added damping material is investigated. In the other part of the thesis, we perform a separate analysis of each effect that affects the reflection of the arc ABH to understand the wave behavior of the arc ABH and to potentially design them. Much reflection occurs in the low frequency region when the tip-to-plate thickness ratio increases. It is analytically, and numerically shown that the taper power should be greater or equal to 2 to assure the smooth change of wavelength near the tip of an ABH. When the tip of an ABH is truncated, increasing the loss factor reduced the reflection coefficient of an arc ABH. Furthermore, it is shown that the curvature is influential to the wave behavior only when the frequency range is below a certain critical frequency. Lastly, in order to theoretically analyze the reflection from an arc ABH, the governing equation of the arc ABH is derived based on the classical shell theory as the first step.