Nonlocal Acoustic Black Hole Metastructures: Achieving Ultralow Frequency and Broadband Vibration Attenuation

2019-11-21T13:16:46Z (GMT) by Siddharth Nair
The development of novel passive techniques for vibration attenuation and control of broadband energy propagation through structural systems have been a major challenge in various complex engineering applications. These passive attenuation and control methodologies are necessary for the efficient performance of advanced lightweight aerospace and mechanical systems operating under extreme working conditions.

Acoustic Black Holes (ABH) have rapidly emerged as an effective approach to either dissipate or harvest mechanical energy in vibrating thin-walled structures. The characteristic dimension of an ABH, typically its diameter, is strictly connected to the occurrence of a cut-on frequency value below which the ABH is ineffective in absorbing the incoming wave. From a general perspective, lower the cut-on frequency, larger the ABH diameter needed to absorb the incoming wave. Design and manufacturing constraints of the host structure impose stringent limitations on the maximum ABH diameter and hence, limiting the lowest achievable cut-on frequency. The combination of these factors typically result in the poor energy extraction performance at low frequencies.

This thesis proposes the concept and explores the performance of an intentional nonlocal design for periodic grids of ABHs embedded in thin plates (referred to as ABH metastructures). The nonlocal design is conceived with the twofold objective of lowering the cut-on frequency of the ABH grids and extending the operating frequency range so as to achieve broadband performance. Different nonlocal designs are presented and their dynamic performances are investigated using numerical models. As opposed to the traditional material nonlocality, this thesis introduces nonlocal effects using an intentionally tailored geometric approach. A secondary layer is connected to the load-bearing ABH metastructure base, whose dynamic properties are sought to be controlled.

A semi-analytical model is also presented in order to characterize the role of nonlocality on the dispersion behavior and its effect on the broadband dynamic response. In linear elasticity, material nonlocality is mathematically represented by a spatially varying attenuation function. As the nonlocal model developed in this thesis follows geometric nonlocality approach, the required nonlocal attenuation factor is found to have a spatial as well as a temporal dependence. The analytical nonlocal constitutive relations in conjunction with the numerically obtained stress-strain parameters are used to identify the dynamic attenuation factor for the nonlocal ABH metastructure. The results provide substantial theoretical and numerical evidence of the potential of engineered nonlocal ABH design as an efficient ultra-low frequency passive attenuation technique for lightweight structures.