Abstract:
In recent years, metamaterials with artificially designed microstructures have attracted increasing research interests due to their unique properties that cannot be easily realized in natural materials. One of the most important applications of metamaterials is in lowfrequency vibration suppression by utilizing the band gap phenomenon. However, the band gaps of locally resonant metamaterials are relatively narrow, which significantly restricts their applications in the circumstances where the vibrations often spread over a wide spectrum of frequencies. One of the main objectives of this thesis is thus to explore the strategies for widening the band gaps of metamaterials. To realize the band gap enhancement, a novel metamaterial with internal couplings is proposed. Both lumped parameter and distributed parameter models are established. Analytical solutions are derived. It is found that with the introduction of internal couplings, the proposed metamaterial can produce multiple band gaps. Moreover, when the internal couplings are realized by negative stiffness springs, by carefully tuning the system parameters, quasi-static band gaps can be achieved for ultralow frequency vibration suppression. In addition, the shunt capacitance circuit technique is proposed to be employed for realizing the implementation of the internal couplings. The employment of the shunt capacitance circuit technique not only enables the implementation of internal couplings, thus the generation of multiple band gaps, but also provides a mechanism for realizing the tunability. Therefore, the proposed design yields a broadband vibration suppression ability across the frequency spectra. On the other hand, subjected to environmental vibrations, piezoelectric energy harvesters could convert mechanical energy into electrical energy. By integrating the metamaterials with piezoelectric materials, it is expected to obtain systems with dual-functionalities: vibration suppression and energy harvesting. Therefore, another main objective of this thesis is to design dual-functional piezoelectric metamaterial systems. Starting from the most conventional mass-in-mass model, a piezoelectric metamaterial system is proposed and the associated theoretical analysis is presented. Dimensionless parametric studies are conducted to optimize the vibration suppression performance and the energy harvesting performance severally. It turns out that different impedance matching schemes are required to achieve optimal vibration suppression and energy harvesting. To address this problem, compromising solutions are proposed for weakly and strongly coupled systems, respectively. Subsequently, the study is extended to a more practical metamaterial beam system. Analytical and finite element models are developed. Two configurations are proposed and their performances are analytically evaluated and compared. The configuration of placing the metamaterial section from the free end of the beam is recommended to achieve better dual-functionalities. Finally, on the basis of the proposed novel metamaterials with internal couplings, piezoelectric elements are introduced to propose a novel piezoelectric metamaterial system. It is demonstrated that the energy harvesting performance can be significantly improved due to the existence of the internal couplings. Since the majority of work presented in this thesis incorporates both metamaterial beams and piezoelectric materials, based on a derived piezoelectric composite finite element a general framework for modelling the piezoelectric metamaterial systems is developed. The proposed approach enables comprehensive studies of such kind of piezoelectric metamaterial beam systems. Within the proposed framework, a method for calculating the band structures of infinitely long metamaterial beams with piezoelectric transducers under short-circuit and open-circuit conditions, as well as the methods for transmittance and energy harvesting performance analysis of finitely long metamaterial beams, are developed. In summary, this thesis presents a series of studies on metamaterial systems embedded with piezoelectric transducers or designed with innovative micro-structures. Multi-functional piezoelectric metamaterial systems are proposed for both vibration suppression and energy harvesting. Internal couplings have been proposed for generating multiple band gaps to yield a broadband vibration suppression ability. It has been shown that the internal couplings in the novel metamaterial beam system also benefits the energy harvesting performance. Furthermore, to facilitate the modelling of the piezoelectric metamaterial beam systems, a general framework based on a derived piezoelectric composite finite element is proposed. Several case studies have been provided for verifying the soundness of the proposed general framework.