Application of nonlinear system frequency analysis and design to vibration isolation and energy harvesting

Vibration is naturally present in the environment including engineering systems and structures. The presence of vibration can be beneficial or destructive, depending on the nature of the affected system and also the level of vibration. Vibrations at dangerously high levels can be reduced by the addition of some energy dissipation elements (dampers) or/and energy storage elements (springs). Energy dissipation elements, such as dampers, dissipate some of these destructive mechanical vibrations as heat. However, mechanical spring systems absorb and store this mechanical vibration energy as potential energy. Nonlinear analysis is primarily applied in system analysis and design of engineering systems. Many methods are available to perform this purpose including averaging method, perturbation method, harmonic balance and the recently developed Output frequency response function (OFRF). The studies presented in this thesis focus on the application of nonlinear system frequency domain analysis and design to vibration isolation and energy harvesting systems. The OFRF method is the analytical and design tool adopted for all studies presented in this thesis. This method is chosen due to its advantage over other methods. This is because the OFRF reveals a significant relationship between the system output spectrum and the parameters that define the system nonlinearities. Therefore, it can facilitate a systematic analysis, design and optimisation process which other approaches are unable to realize. The first study considered in this thesis is a frequency domain analysis, design and optimisation of a vehicle suspension system which is illustrative of a vibration isolation system. In this study, the suspension system is analysed and designed based on a performance criterion. The main aim of the study is to minimise the transmitted vibration force to a tolerable level. At the specified level, some of the vibration energy is dissipated as heat by the damping system. However, this energy can be harvested into electricity, a process known as energy harvesting. This leads to subsequent studies in this thesis. The next study considers a vibration energy harvester system with nonlinear cubic damping characteristic. In this study, a concept is investigated, using the OFRF method, which increases the average power harvested by the harvesting device compared to an equivalent linear harvester. An extension of this study is further considered with the addition of a nonlinear hardening stiffness element to primarily broaden the operational bandwidth of the harvesting device. A final study is then considered where a dual-function system is investigated. The primary function of the system is vibration isolation while its secondary function is energy harvesting. The system is therefore called a dual-function vibration isolation and energy harvester system. This system is optimised for the best dual-function performance subject to existing constraints. For all the systems considered in this thesis, nonlinearities have been integrated into the existing systems to improve their performance, correspondingly, based on a selected criterion. In addition, the OFRF method has been employed in the analysis, design and optimisation of all the systems considered.