MS23.3 - Vibro-Acoustics

The study introduced in this work focuses on the possible use of a hanging chain as an Acoustic Black Hole (ABH) for a passive vibration control solution. An acoustic black hole is effectively a waveguide in which a wave propagates away from the source and does not return. It can be achieved by exploiting the effect of inhomogeneity obtained by a variation in the structure geometry or material. One way of achieving the ABH effect in waveguide is by a local stiffness reduction combined with a local increase in damping. This can be achieved, for instance, by reducing the thickness of a waveguide, such as in a beam accompanied by a gradual increase in damping along the beam. This results in a significant reduction in the speed of a damped propagating wave. Hence there is very little reflection of the wave at the end of the beam. An alternative to using a beam is to use a hanging chain. This is a system that has a decreasing the wave speed naturally without having to change its geometry and thus it overcomes the constructive challenges inherent to an ABH realized by using a beam. The reduction of the local stiffness is obtained by the effect of gravity. This effect decreases linearly from the top, where the chain is fixed, to the bottom, where the wave speed tends to zero. The study of transverse vibration on hanging chains is a classical problem in structural dynamics that can be analysed as a string-like structure in which the tension is a function of gravity, and hence reduces from the top to the bottom of the chain. The motion of the chain can be described in terms of Bessel or Hankel functions, which are needed to account for the variation of tension along the position in the chain. However, both Bessel and Hankel functions have numerical singularities that generally affect the solutions at the boundary’s conditions, which must be handled carefully. In this work, the hanging chain problem has been revisited in terms of free and forced vibration. Using the wave approach, infinite and finite chains are investigated. The receptance and dynamic stiffness matrices are obtained, which facilitate the understanding of the asymptotic behaviour at low and high frequencies. The formulation presented allows other mechanical elements to be attached to the chain using the dynamic stiffness approach. Some experimental results are presented to support the theoretical analysis.

Periodic systems exhibit frequency bands (pass-bands and stop-bands or bandgaps) which can manipulate propagating waves in certain frequency ranges. Phononic crystals (PCs) can create bandgaps by virtue of Bragg’s scattering, at wavelengths of the order of their unit cell size. However, this poses a restriction on their application in low-frequency ranges, for which a very large unit cell size will be required. On the other hand, acoustic metamaterials (AMMs) can create bandgaps at much lower frequencies than those possible by PCs, by utilizing the concept of local resonance (LR). Many design strategies and architectures have been explored to achieve wide low-frequency bandgaps in AMMs for several applications, which include noise/vibration insulation, energy absorption and harvesting, protection of sensitive machinery and components, and earthquake shielding. There are always some imperfections and uncertainties associated with the manufacturing process of any material or structure. Periodic systems like most AMMs, are sensitive to such manufacturing variabilities, which may considerably affect their performance. There may also be issues like vibration mode localization that arise due to the presence of such imperfections. Very limited literature has explored the role of aperiodicity in the performance of AMMs. Further, the introduction of aperiodicity in the design methodology of AMMs within a probabilistic framework has not been adequately addressed. Systems such as spring-mass models or vibrating beam structures provide a simple framework to explore complex AMM design methodologies. In this study, we try to incorporate aperiodicity in a LR metamaterial beam design to address two issues: (i) increase the width of low-frequency LR bandgap, and (ii) reduce the effect of manufacturing variabilities on the bandgap and make the system more robust. The metamaterial beam comprises a homogeneous host beam with free-free boundary conditions. Fifteen equally spaced double-cantilever-like beams are installed on this host beam, acting as resonators. These resonators create a LR bandgap in the 750-1000 Hz frequency range. A genetic algorithm-based optimization technique is utilized to achieve a novel design of the resonators. This algorithm maximizes the bandgap width (in the same frequency range) and allows for introducing aperiodicity in the system by assigning different properties to some resonators. This design is numerically shown to have a much-enhanced LR bandgap width vis-à-vis the periodic system. Furthermore, manufacturing variabilities in the system parameters (dimensions, Young’s modulus, density) and their effect on bandgap width is considered. Uncertainty quantification using Monte Carlo simulations shows that aperiodicity in design contributes toward robustness with respect to such imperfections or variabilities. Thus, adopting this design philosophy of introducing aperiodicity can improve the overall functionality of AMMs.