| Author: | Zhou, Tong |
| Title: | Partition of unity finite element method and acoustic black hole effects : structural modelling and vibration suppression |
| Advisors: | Cheng, Li (ME) |
| Degree: | Ph.D. |
| Year: | 2021 |
| Subject: | Thin-walled structures -- Vibration Acoustical engineering Soundproofing Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Mechanical Engineering |
| Pages: | xxvi, 257 pages : color illustrations |
| Language: | English |
| Abstract: | In this thesis, the Partition of Unity Finite Element Method (PUFEM) is developed and applied to compute the vibrational response of various thin-walled structures in the mid-to-high frequency range. This method allows the incorporation of enrichment functions with good approximation properties for the concerned problems. Investigation is first carried out on a uniform Timoshenko beam. Classical C° finite elements are enriched with propagating and evanescent wave solutions, polynomial functions and a Fourier-type series. It is demonstrated that, the wave enrichment offers highly accurate and fast converging results as compared to other formulations and all the PUFEM formulations outperform classical FEM in terms of data reduction. The PUFEM is then extended to thin plate bending problems. Hermite-type Partition of Unity functions are employed to ensure the C1 inter-element continuity. The enrichment consists of a power series and propagating flexural waves in various directions. Particular attention is devoted to the design and analysis of the hybrid wave-polynomial enrichment for approximating the vibration field of a two-dimensional plate. The applicability of the proposed formulations is verified and their advantages over FEM are shown. The Acoustic Black Hole (ABH) phenomenon shows good prospects for the manipulation and mitigation of bending waves in thin-walled structures. ABH structures feature unique space-dependent wave celerity reduction in tapered ABH area, which poses challenges to the existing modelling methods. This work exploits wave functions with the Wentzel-Kramers-Brillouin (WKB) method and a wavelet series as the enrichment functions in the PUFEM framework to better cope with the ABH oscillating behaviour. It is shown that a single PUFEM beam element can capture multiple wavelengths and the ABH-induced wave modulation effects, thus outperforming FEM. A scheme is proposed to handle coupled mechanical system with ABH components. The second part of this thesis is concerned with the development of add-on vibration control devices by capitalizing on the ABH-specific phenomena. A so-called ABH-featured Resonant Beam Damper (ABH-RBD) is first proposed for suppressing broadband vibrations of a primary structure. The ABH-RBD embraces the principles of both dynamic vibration absorbers and waveguide absorbers. Its design and implementation do not need a tedious parameter tuning, owing to the robust ABH effects. Both numerical simulations and experiments demonstrate that the same ABH-RBD is very effective for different primary structures. Three types of vibration reduction mechanisms are revealed, i.e. structural interaction, damping enhancement and their combination. Comparisons with a uniform beam absorber show that the superiority of ABH-RBD is attributed to its ABH-specific features, exemplified by enriched dynamics and enhanced damping. A planar swirl-shaped ABH absorber is then proposed and investigated. Apart from the bending wave deceleration, the speed of torsional waves in the curved ABH also decreases with the thickness thinning. Alongside the bending-twisting coupling brought by the curvilinear configuration, the proposed design exhibits reduced orientation-dependent mechanical properties and meanwhile generates rich resonant modes with high loss factors. Experiments show that deploying multiple ABH absorbers can ensure effective, robust and broadband vibration reduction for a general primary plate. |
| Rights: | All rights reserved |
| Access: | open access |
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