Effect of Periodic Interconnected Piezoelectric Elements on Wave Propagation in 1D and 2D Media

Abstract

Various methods for controlling wave propagation, and their ensuing vibrations have been proposed. This thesis will focus on one such method, whereby periodic piezoelectric inductancecapacitance (LC) shunts will be interconnected following different schemes. The electrical components will then be tuned to tailor the wave propagation properties of one (1D) and two (2D) dimensional materials. The periodicity of the mechanical and electrical domains will be exploited to design these electromechanical materials based on the characteristics of their bandstructure, namely by identifying weak eigenvalue coupling phenomena where the exchange of energy, mechanical to electrical, leads to wave attenuation. Moreover, the bulk of the work presented in this thesis will aim at attenuating transverse mechanical waves, however, another part of the research will delve into utilizing both local and interconnected shunts for controlling longitudinal waves with the purpose of modifying the depth and/or width of Bragg-scattering band-gaps, thus promoting wave propagation. By interconnecting the piezoelectric LC shunts, the design space is vastly expanded, as the latter are no longer individual elements, but rather components of a secondary discrete domain along which energy can propagate parallel to the mechanical medium. Albeit, a myriad of electrical interconnection schemes of increased elegance, and complexity could be envisioned, this work will focus on the interconnection of unit-cells comprised of low-pass, band-pass, high-pass filters, tailored to achieve specific effects on the mechanical domain of 1D and 2D media. Furthermore, this thesis will have a strong focus on the design, fabrication, and testing of improved electrical components to achieve wave propagation control over low frequency ranges, that could otherwise not be attained using passive components. Particular attention will be devoted to the development of programmable floating virtual inductances that satisfy the geometric form factor required to achieve full, and seemless integration of the electrical, and mechanical domains of the unit-cell. As a result of the integration and digitalization of the electrical components, it is the goal of this thesis to engender truly "smart" materials with the potential of bridging the gap between theory and practical applications. Analytical models based on the transfer matrix method will be derived to the extent possible, and validated with numerical results obtained using the multi-physics FEM software. Analytical, and numerical work will be validated using experimental test setups.