| Author: | Sun, Xiang |
| Title: | Geometrically nonlinear features of acoustic black hole (ABH) beams and nonlinearity-enhanced ABH Effects |
| Advisors: | Cheng, Li (ME) |
| Degree: | Ph.D. |
| Year: | 2024 |
| Subject: | Noise control Absorption of sound Vibration -- Control Acoustical engineering Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Mechanical Engineering |
| Pages: | xviii, 160 pages : color illustrations |
| Language: | English |
| Abstract: | Acoustic black hole (ABH) techniques have demonstrated remarkable ability for passive vibration and noise control. As a result of a power-lawed thickness decrease, bending waves are slowed down to produce wave compression and energy concentration, conducive to vibration/sound radiation control and energy harvesting. However, the reduced thickness profile of a long and thin ABH beam poses a challenge for both numerical and experimental investigations. Particularly, a large vibration amplitude is produced around the ABH tip to result in significant geometric nonlinearities. In addition, manufacturing limitations may lead to imperfect geometry, such as initial curvature or a residual platform at the tip end of the beam, which can further affect the vibration responses of the nonlinear system. Besides, existing research shows that the ABH effect suffers from a deficiency at low frequencies, typically below the so-called cut-on frequency. Therefore, how to accurately model the geometric nonlinearity of ABH beams with imperfect geometry and to enhance the low-frequency ABH effect remains a bottleneck problem. In the first part of this thesis, an inextensible condensation model, with the consideration of the initial curvature, is proposed based on a geometrically exact model for an Euler-Bernoulli cantilever beam. The free boundary of the cantilever gives rise to more significant longitudinal motion, which increases the inertia effects in the beam vibration which is in turn enhanced by the initial curvature. Specific techniques are proposed to numerically implement the developed model with increased accuracy and robustness. Numerical simulations are then conducted to validate the proposed model through comparisons with the finite element method (FEM), to examine the assumptions underpinning the model and to explore the salient physical features, in particular the inertia-induced effects in both linear and nonlinear cases. Results show a decrease in the natural frequencies due to the initial curvature effect, a transition of the first mode from hardening to softening caused by enhanced curvature-induced inertia effect, and a pronounced asymmetry of the higher-order modes with respect to frequencies. Then, the nonlinear features arising from these geometric factors in imperfect ABH beams are investigated, both numerically and experimentally. Geometric parameters of the ABH beams are updated according to the linear experimental results, which give a better geometry representation of the beams. Numerical results show that the hardening effect dominates in the first two modes of the perfect ABH beam due to the reduced nonlinear inertia effect by the tapered thickness. Then, geometric imperfections are intentionally introduced to the numerical model. With the consideration of the initial curvature, the hardening effect is enhanced by the locally curved ABH tip, which is different from its uniform counterpart, showing a hardening-to-softening transition for the first mode. With an embedded platform of uniform thickness at the free end of the beam, the linear and nonlinear responses are dependent on the platform length alongside enhanced geometric nonlinearities. As a result, the second mode becomes softening-dominant in the platform-embedded ABH beam. The nonlinear experiments confirm that the embedded platform is the major geometric imperfection in the sample. Both simulations and experiments demonstrate the geometrically nonlinear features of ABH beams. Due to the inefficiency of geometric nonlinearity, mechanical nonlinearity is introduced into a cantilever ABH beam to enhance the low-frequency ABH effect through low-to-high frequency energy transfer. Using a grounded cable with cubic stiffness, the sweeping results (with excitation frequency below the cut-on frequency) show that the displacement of the low order modes of the nonlinear ABH beam decreases while the amplitude of its high-order harmonics increases compared to that of its linear counterpart, indicating a significant energy transfer phenomenon enabled by the cable in the nonlinear system. Due to the inherent ABH effect at high frequencies, the damped nonlinear ABH beam absorbs the transferred energy to result in a reduction of the vibration amplitude. To quantify the ABH effect under nonlinear conditions, the damping loss factor of the system is evaluated from energy viewpoint alongside the harmonic balance method. Below the cut-on frequency, the damping loss factor of some dominant modes in the ABH beam is drastically increased, indicating an enhanced ABH effect. This is also confirmed by the time response in the free decay test. Experiments demonstrate the energy transfer phenomenon and the efficient damping effect achieved in the nonlinear system. As a final remark, the study sheds light on the physics behind the geometric and mechanical nonlinear features of ABH beams, alongside useful analysis and numerical tools in tackling such problems. Meanwhile, some promising solutions based on nonlinear principles to alleviate the low-frequency barrier of conventional ABH structures are examined. This constitutes a useful step forward in the ever-increasing endeavors that researchers are making on ABH technology. |
| Rights: | All rights reserved |
| Access: | open access |
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