Effect of stiffness nonlinearity on the transduction coefficient of a vibration based electromagnetic energy harvesting device - Low, Pei Sing (2017)
The concept of harvesting energy from ambient to power applications has been gaining attention from researchers in recent times due to its self-sustaining power source solution. Traditionally, the linear system has been used to harvest the energy. However, the limitation due to the difficulty in matching between the natural frequency of the device and the ambient frequency makes it less favourable. This is even worst when the ambient frequency varies with time, which leads to the narrow bandwidth for the device to perform. Presently, the nonlinear system has been introduced to overcome the limitation of the linear system. This thesis analyses the improvement of bandwidth performance at the maximum response in the nonlinear system. Despite of the bandwidth performance, the closed form performance characteristic for the nonlinear system in terms of transduction coefficient and optimum power has yet to be established. A theoretical study is conducted using the harmonic balance method to analyse the dynamic characteristics of the system. The harmonic balance method is further employed to determine the jump frequencies and to deduce the new optimum power expression for the nonlinear system. Apart from that, the initial conditions selection that creates the limitation to the nonlinear system is investigated using the basin of attraction. In this thesis, a proof of concept device with adjustable magnet gap is fabricated. The nonlinearity of the device is varied by adjusting the magnet gap. The dynamic characteristics of the proposed device are investigated experimentally. The quasi-static measurement is adapted to estimate the amount of nonlinearity using the force - deflection relationship. In the dynamic measurement, the dynamic characteristics are studied in terms of displacement and induced voltage. Further studies involve the effect of nonlinearity on the transduction coefficient and setting the limit of using the linear transduction coefficient on the nonlinear system. The limit is characterized from the analysis of the harmonic ratio. Ultimately, the optimum power at the maximum response of the device for the nonlinear system is measured to study the new optimum power expression deduced theoretically. From the theoretical results, it shows that the dynamic characteristics of the nonlinear system are affected by the nonlinearity and damping of the system. Meanwhile, the new optimum power expression is found to be proportional to the transduction coefficient and thus opens up question on the lower bound limit of the transduction coefficient. As for the limitation of the nonlinear system, the results show that a strong nonlinear system that may have bandwidth widen to a much frequency is restricted by the initial conditions selection especially near the maximum response region. In the experimental analysis, the quasi-static results reveal that the nonlinear system gradually converges to linear system as the magnet gap increases. The bandwidth region in the response curves obtained from the dynamic measurements also shows decrement as the magnet gap increases. In the study involving the transduction coefficient, the limit is characterized based on the harmonic ratio analysis. The results show that the linear transduction coefficient is applicable to the nonlinear system when the harmonic ratio is less than five percent at the multi-stable solutions region. For the highest power obtained experimentally, it is achieved when the transduction coefficient is the highest in the strongest nonlinear system with the transduction coefficient being considered at the maximum displacement.