Author: Tang, Liling
Title: Acoustic black hole effect for vibration control
Degree: Ph.D.
Year: 2017
Subject: Hong Kong Polytechnic University -- Dissertations
Vibration -- Control
Structural control (Engineering)
Department: Department of Mechanical Engineering
Pages: xxvii, 179 pages : color illustrations
Language: English
Abstract: Developing highly-damped and light-weighted structures is of great importance for various engineering problems. The Acoustic Black Holes (ABH) effect reduces the phase velocity of flexural waves to zero when the structural thickness approaches zero according to a power-law thickness variation, resulting in zero wave reflections and high energy concentrations at the wedge tip. The ABH effect thus shows promising application potentials for vibration controls since only a very small amount of damping materials is required at the energy focalization region. In this thesis, a flexible wavelet-decomposed and energy-based model is established to study various ABH features by preserving the full coupling between the damping layers and the host 1-D ABH structure. Highly consistent with the FEM and experimental results, numerical simulations demonstrate that the proposed wavelet-based model is particularly suitable to characterize the ABH-induced drastic wavelength fluctuation phenomenon. The ABH feature as well as the effect of the wedge truncation and that of the damping layers on the vibration response of the beam is systematically analyzed. It is shown that the conventionally neglected mass of the damping layers needs particular attention when their thickness is comparable to that of the ABH wedge around the tip area. Meanwhile, this model predicts the loss of the ABH effect in a finite beam around the local resonance frequencies of the beam portion delimited and pinned by the excitation point, which should be avoided in the particular application frequency ranges. Due to its modular and energy-based feature, the developed model offers a general platform allowing the embodiment of other control or energy harvesting elements to guide ABH structural design for various applications. To maximum the ABH effect with a minimum achievable truncation thickness, a modified ABH thickness profile and an extended platform of constant thickness are systematically investigated using the developed model. Compared with conventional ABH profile, numerical results show that the modified thickness profile brings about a systematic increase in the ABH effect at mid-to-high frequencies in terms of system loss factor and energy distribution, especially when the truncation thickness is small and the profile parameter m is large. The use of an extended platform further increases the ABH effect to broaden the frequency band whilst providing rooms for catering particular low frequency applications.
As a further extension of the study, the performances of single ABH and multiple ABHs are compared. Multiple ABHs are shown to be able to enhance the overall low frequency performance of the ABH. Meanwhile, multiple ABHs also bring about broadband attenuation bands and wave suppression phenomena at low frequencies. To better understand the underlying physics, the developed model is expanded to an infinite structure with periodic ABH elements. Numerical results show that the periodic boundary conditions in terms of displacement and rotational slope imposed on a unit cell, based on the finite model, are sufficient to describe the band structures of the corresponding infinite lattice. The analysis reveals that the attenuation bands correspond exactly to the band gaps of the infinite structure with the same ABH elements, resulting from the local resonances of the ABH elements. Therefore, enhancing ABH effect by increasing the taper power index m or reducing the truncation thickness h0 would help to generate broader and lower-frequency band gaps. To simultaneously achieve band gaps at high frequencies whilst maintaining the structural strength, a new type of phononic beams is proposed by carving the uniform beam inside with two double-leaf ABH indentations. By incorporating the ABH-induced locally resonant effect and Bragg scattering effect generated by a strengthening stud connecting the two branches of the indentations, ultra-wide band gaps, covering over 90% of the entire frequency range, are achieved through a proper tuning of the ABH parameters and that of the stud. Both numerical and experimental results show that with only three cells, the proposed phononic beams allow considerable vibration energy attenuation within an ultra-broad frequency range, pointing at promising applications in vibration control and high performance wave filter design.
Access: open access

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