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Title: Dynamic behavior and stability analysis of electrostatic mems resonators and electromagnetic-triboelectric energy harvesting systems
Authors: Yang, Xin
Degree: Ph.D.
Issue Date: 2020
Abstract: Stemming from rapid urbanization leads to smarter cities that can improve the quality of life through advanced micro-electronic technologies. To realize the concept of Internet of Things (IoT) for smart cities, different types of sensors and devices (e.g., micro-electro-mechanical systems (MEMS)) are used to gain data to manage urban services and resources in a smart manner. With the continuous development of wireless sensor networks, the need for sustainable mobile power supplies is of paramount importance. These wireless sensors and devices can be powered by electrochemical batteries that are limited in lifespan and required periodic charging. To enable the vast deployment of sensors everywhere, one promising and feasible alternative is to directly harness energy from our environment (e.g., omnipresent vibration energy from ambient sources) that can allow a better self-autonomy. From the perspective of mechanics, in MEMS devices and vibration-based energy harvesting technologies, nonlinear dynamic oscillations have been a topic to intensive research for recent years. In this research, the following four major topics are investigated to offer a better understanding of nonlinear dynamical behavior in MEMS resonators and energy harvesting systems. They are: (i) the nonlinear free and forced vibration of electrostatically actuated MEMS resonators; (ii) the nonlocal dynamic effect of micro-/nano-scale structures; (iii) the quantitative and qualitative analysis of a tri-stable nonlinear non-natural system; and (iv) the theoretical and experimental studies of a magnetic levitation-based electromagnetic-triboelectric energy harvesting technique governed by a tri-stable nonlinear mechanism. In general, fully-clamped microbeams are one of the major structural components in most MEMS devices. This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated MEMS resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. First, the free vibration of a doubly-clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler-Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly-clamped microbeam driven by two symmetric electrodes is also investigated, where the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a non-autonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated and they are in good agreement with those obtained by the standard Runge-Kutta method.
Micro-/nano-scale structures are widely used in the design of MEMS/NEMS resonators. Nonlocal elasticity theory is one of the most popular theoretical approaches to investigate the intrinsic scale effect of micro-/nano-structures, it incorporates long range interactions between points in a continuum model. From the point of view of physics, the coupling of an internal characteristic length and a material parameter can be regarded as a nonlocal scale parameter. The range of this non-dimensional scale parameter is from zero up to different values previously. The zero nonlocal scale parameter refers to a situation without any nonlocal effect. However, the determination of a peak value for the nonlocal scale parameter is still uncertain. In this research, the nano-structural dependence of nonlocal dynamical behavior is investigated to present the existence of an upper limit for the nonlocal scale parameter through a dynamical analysis of nanorods, nanobeams and nanoplates. It is not only beneficial to the refinement of the nonlocal theory of elasticity, and also useful for the exploration of similar theories in nano-mechanics. In nonlinear energy harvesting technologies, multi-stable oscillating mechanisms are an effective approach to achieve a lower excitation threshold for inter-well motions. The intrinsic behavior of triple-well nonlinear oscillators can be illustrated by Duffing-type equations. To study such nonlinear problems, the large-amplitude oscillation of a triple-well non-natural system is investigated, covering both qualitative and quantitative analysis. By varying the governing parameters, the system is changed from a mono-stable behavior to a tri-stable one (having three stable states). In terms of qualitative analysis, various classifications for the equilibrium points and its trajectories of the system are provided. As exact solutions for this problem expressed in terms of an implicit integral form must be solved numerically, an analytical approximation method based on the NHB method is used to construct lower-order accurate solutions to the oscillation around the stable equilibrium points of this system. Making use of the tri-stable nonlinearity, a magnetic levitation-based electromagnetic-triboelectric energy harvester is designed and investigated. The hybrid generator not only enhances the power output through resonant inter-well oscillation behavior, and also offers a wide and highly efficient operating bandwidth under low-frequency (<10 Hz) and broadband sources. Although many vibration-based energy harvesters are resonant in nature, they have difficulty going into high-energy orbits under random low-level excitations to limit their output power density. To overcome this deficiency, the integration of a slider-driven electromagnetic generator and a sliding-mode triboelectric nanogenerator allows more energy to be harvested from a single motion, which can further improve the power density. Besides, the implementation of magnetic levitation can reduce the possibility of mechanical contact and impact damage to enhance a long-term durability in practical uses. In this study, both theoretical and experimental investigations are presented to verify this new design, in which only four outer magnets are required on a plane to establish a triple-well nonlinear behavior. In the theoretical analysis, the magnetic force of this harvester is calculated by the magnetizing current method and the formation mechanism of this tri-stability is verified by a bifurcation analysis. While for the experimental work, a battery-shaped prototype is fabricated and tested by an electrodynamic shaker to evaluate its working performance. The research findings are expected to be useful for designing MEMS-driven devices and vibration-based energy harvesting systems that can advance the development of current cutting-edge IoT technology.
Subjects: Microelectromechanical systems
Electric resonators
Energy harvesting
Hong Kong Polytechnic University -- Dissertations
Pages: xvii, 199 pages : color illustrations
Appears in Collections:Thesis

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