Flexural wave mitigation and utilization through electro-mechanical coupling in an acoustic black hole beam

Abstract

Acoustic black hole (ABH) exhibits unique and appealing features of wave retarding and energy focusing when bending waves propagate along a structure with a tailored power-law thickness profile. However, existing ABH structures are mostly effective only above the so-called cut-on frequency. In this thesis, electromechanical coupling is explored to tackle the problem. Nonlinear electrical circuits are tactically introduced to an ABH structure to generate effective low-to-high frequency transfer while achieving low-frequency vibration mitigations through dynamic absorber effects. As such, intentionally added electrical nonlinearity alleviates the limitations of existing linear ABH structures, extends and broadens the effective ABH range, which are conducive to applications like vibration control and energy harvesting (EH) etc. Using a PZT-coated ABH beam as a benchmark, an improved electromechanical semi-analytical model is first established based on Timoshenko theory. The model considers the high-frequency shear and rotational effects of the beam, as well as its coupling with PZT coating and other additional elements like damping layers. External electrical modules including both linear and nonlinear circuits can also be easily integrated into the system, thus forming a complete set of fully coupled electromechanical model. Comparisons with FEM and experimental results validate the propose model and confirm its higher accuracy and improved efficiency compared with the existing Euler-Bernoulli counterpart. The model allows for flexible design and optimization of the PZT layout and electrical circuits to maximize the EH efficiency or to tactically alter ABH effects in the host structure in views of achieving tactic energy manipulation and vibration control. The proposed model is then used to analyze typical ABH-specific features in an ABH beam such as energy focusing and wave compression. Numerical results demonstrate that installing PZT in the vicinity of the ABH tip area warrants better EH performance than the common practice of harvesting at the clamped end of a uniform beam. Studies on the PZT layout and the effects of parameters of external circuit illustrate their impact on the electro-mechanical coupling strength and the ultimate EH efficiency. Design guidelines on PZT layout in relation to the targeted wavelength and frequency range are developed. To cope with the low frequency deficiency of existing linear ABH structures, electrical nonlinearities are intentionally imposed via PZT patches over an ABH beam to tactically influence its dynamics through electromechanical coupling. Results show the beneficial effects arising from the intentional electrical nonlinearity in terms of generating energy transfer (ET) from low to high frequencies inside the beam, before being dissipated by the ABH covered by a small amount of damping materials around the energy concentration area. As a result, the effective frequency range of the ABH is broadened, which is also beneficial to low frequency vibration control. In addition to the energy transfer across the frequency barrier in the mechanical part, electro-mechanical energy transfer and dissipation also take place, similar to a NES. Typical electro-mechanical energy transfer process is also enlightened. In addition to the aforementioned nonlinear energy transfer, simultaneous low-frequency vibration mitigation is also considered. It is noted that increased nonlinear strength, albeit beneficial to energy transfer, jeopardizes the expected dynamic absorber (DA) effects. Meanwhile, enhanced nonlinear effects need to be upheld. To tackle the problem, different solutions are exploited, exemplified by the use of negative capacitance in the nonlinear shunts with the embodiment of parallel linear branches for low-frequency vibration mitigation. Studies offer a comprehensive design methodology to realize multi-modal vibration control and enhanced ET in different frequency bands. Finally, the proposed linear and nonlinear digital vibration absorbers are implemented in experiments. Experimental results not only validate the basic beam model, but also confirm typical phenomena which are predicted numerically such as typical ABH features, electromechanical coupling characteristics and the expected energy transfer using intentional nonlinear electrical shunts. As a whole, this work constitutes the very first attempt to use nonlinear electromechanical coupling to deliver controllable and tunable nonlinearities in an ABH structure. In addition to the proposition of the semi-analytical model, the study reveals rich nonlinear phenomena specific to ABH structures, sheds lights on the underlying mechanisms and finally shows the potential of achieving simultaneous vibration reduction and energy transfer to selectively break down the frequency barrier existing in conventional linear ABH structures. The accomplished work paves the way forward to further explore ABH-based technology and its practical applications.