Energy Scavenging and Wave Manipulation in Linear and Nonlinear Dynamical System

This dissertation presents results in two broad, inter-related areas. The first three chapters deal with modeling and analysis of electro-mechanical vibratory systems and harvesting ambient oscillatory energy. The final three chapters present results for manipulating elastic and sound waves in periodic structures.;Chapter 1 presents a novel result concerning the rattleback which is an ellipsoidal toy with some curious properties. When placed on a surface, the rattleback has a preferred direction of spin. This phenomenon has been termed spin reversal and the effect is attributed to the asymmetry between the inertia and geometry axes of the top. In this work, results are presented demonstrating that the rattleback, when placed on a vibrating platform, will start to spontaneously spin. Based on a simple linearization for small angular velocities, we derive an expression for the resonant frequency. A simple electromagnetic energy harvester is proposed consisting of a magnetized rattleback surrounded by magnetic coils is proposed and the possible transduced electric power is evaluated.;Chapter 2 proposes the use of a piezoelectric curved beam implanted inside the human Carotid artery as a power source for implanted biomedical devices proximate to the head. The curved beam is analytically modeled and based on blood pressure data and arterial distension the displacements and induced bending strain are calculated. Based on Gauss's law, the direct piezoelectric effect is used to calculate the electric power generated across a load resistance. A maximum power of 11.5 microWatts was harvested using PZT-5H in the Carotid artery.;Chapter 3 presents a methodology for the uncertainty analysis of piezoelectric energy harvesters. Extant methods in the literature for uncertainty propagation involve approximation and/or assume the parameter stochasticity to be small and single dimensional. We use the Conjugate Unscented Transform (CUT) method which can accurately estimate moments of output variables under multidimensional uncertainty with minimum computation. The common cantilevered energy harvester consisting of steel substrate with piezoelectric patches and a set of repulsive magnets is considered. The results show that CUT method is accurate, computationally efficient and can propagate 4 dimensional uncertainty. Also, we found that a naive and purely deterministic analysis of energy harvester can grossly overestimate the harvested power. This may have applications in evaluating worst-case scenarios.;Chapter 4 presents an analysis of elastic waves in a novel metamaterial whose stopbands can be tuned by changing the fold angle. The metamaterial consists of repeating units of panels and hinges so that the panels can fold around the hinges. As such, this model can be used to represent solar arrays, hinged folding structures and origami-inspired structures. The Transfer Matrix (TM) method is used for the analysis. A comprehensive COMSOLRTM Finite Element Method (FEM) simulation is conducted for validation. It is shown that the bandgaps in the structure become wider when the fold angle is increased. Bandwidth increases of as much as 250 % were observed in the bandgaps when the fold angle is changed from 0 deg to 90 deg.;Chapter 5 extends the analysis of elastic waves to a nonlinear metamaterial. The linear torsion spring in Chapter 4 is replaced by a hinge with cubic nonlinearity. No closed form solution for nonlinear lattices exists in the literature. A harmonic balance formulation is derived and the Galerkin projection is used to obtain a set of algebraic nonlinear equations that are numerically solved to obtain the dispersion relationship. It is shown that introducing nonlinearity engenders amplitude-dependent dispersion. Another interesting observation is that only the leading bandgap edge is affected. Hardening nonlinearity causes the bandgap edges to shift to higher frequencies and softening nonlinearity engenders the opposite. The trailing bandgap edge is, however, independent of the nonlinearity. It is further shown that the wavemode corresponding to the trailing bandgap edge corresponds to the first modeshape of a simply supported beam. Since the moment at the ends of a simply supported beam are zero, this explains the independence of the trailing bandgap edge with respect to nonlinearity.;Chapter 6 presents an active wave manipulation strategy for building an acoustic diode using a smart fluid. An acoustic diode permits sound traveling in only one way. Thus, transmission reciprocity is broken. A smart fluid like Magnetorheological fluid (MRF) is considered and a time-varying magnetic field is acted upon the fluid. It is well known in the literature that local sound speed in MRF is dependent on the applied magnetic field. This creates a space-time periodic media that has bandgaps for forward and backward traveling waves in different frequencies thereby achieving one-way sound propagation. A dispersion relationship for an unsteady and non-homogenous fluid is developed. (Abstract shortened by ProQuest.).