Engineering Nonlinearity in Low-Dimensional Systems for Energy Conversion

Abstract

Energy converting devices are limited by the properties of available constituent materials. For example, the working fluid in a thermal engine determines its range of operational temperatures, or the choice of semiconductor material constrains a photovoltaic panel’s efficiency. A recent trend in materials’ science seeks to overcome these limitations by developing structured materials that achieve properties exceeding those of conventional materials. This approach has led to the invention of metamaterials, and resulted in devices capable of surpassing fundamental limits, for example focusing waves in a sub-wavelength region. Until now, most of the work in metamaterials has focused on exploiting linear phenomena, for example to open band-gaps, focus or cloak waves. This thesis pursues a fundamental understanding of nonlinear energy conversion processes in artificial lattices. The first part of the work investigates the effect of driven, localized modes on the quasi-static mechanical properties of a material. It demonstrates that an external energy input can be used to tune a material’s differential stiffness over an extreme range including negative and infinite values. The thesis proceeds with the investigation of lattices containing multiple interacting modes. These lattices are shown to act as purely mechanical analogs of optomechanical systems. They are capable of converting mechanical energy into a harmonic motion with a tunable frequency and phase. Phase tunability is a particularly relevant for technological applications because it enables devices that combine energy from multiple sources and avoid destructive interference effects. This thesis continues by investigating energy-converting systems under stochastic excitation. In this regime, mechanical quantities have thermodynamic interpretation, and the system under study behaves as a stochastic heat engine i.e. a low-dimensional equivalent of a conventional thermal machine. The engine presents exotic phenomena such as negative thermal conductivity and nonpassive states of motion. The last part of the thesis introduces an algorithm to generate metamaterial geometries from discrete mass-spring systems. While this algorithm is currently limited to linear systems, overcoming this limitation will enable the fabrication of energy converting metamaterials such as stochastic heat engines.