寬頻激振下基於非線性振動控制(SSD)及壓電振能擷取(SSH)技術的數學建模

Abstract

The decrease in consumption of electronic components has allowed the growth of mobile wireless applications and with this rapid growth, the replacement and disposal of battery have become a problem. Therefore, alternative power sources from ambient environment recently grasped people's interest. The basic idea of energy harvesting consists of converting a given source to a more useful form of energy. Among the numerous available energy sources, piezoelectric materials that convert vibrational energy into electrical energy received much attention as low-level mechanical vibrations are available in many environments and as piezoelectric transducers allow the direct conversion of vibrations into electricity. In addition, piezoelectric materials feature high power density and have promising integration potentials. Recently, nonlinear techniques were proposed for vibration control and extended as an energy conversion interface in order to increase the efficiency of power harvesting using piezoelectric materials. The nonlinear interfaces consists in a switch device connected with the piezoelectric element. The basic concept of using nonlinear techniques is to turn on the switch when the vibration gets its maximum and minimum values and so the voltage would be inverted to hold the magnitude. The switching frequency depends on the electromechanical structural response and the input excitation. The nonlinear process therefore induces an additional piecewise voltage which could be seen as a dry friction effect on the system and leads to a vibration damping process. In a electromechanical point of view, the induced damping effect is explained by the increase of the converted energy by the piezoelectric element. The converted energy could be harvested and accordingly, the nonlinear technique has also been used in energy harvesting system, showing bright performance in monochromatic excitation. However, in practical application, the excitation would be broadband and random rather than single frequency and so the performance when using nonlinear techniques would be more complicated to evaluate. The purpose of this work is to construct a broadband modeling using the concept of frequency-domain self-sampling and self-aliasing and permit containing more frequency information. The broadband modeling is firstly discussed with vibration control techniques as an introductory section and then extended to energy harvesting techniques. The modeling is separated into two parts: displacement input and force excitation. With this broadband modeling, the systematic performance could be described directly instead of the classic recursive time-domain analysis considering a switching delay and with a switching frequency which could be other than $2omega_0$. The broadband modeling is also analyzed with several well-known excitation cases as theoretical analysis and the simulation results based on theoretical analysis and broadband modeling are then compared with the time-domain resolution (classic time-domain analysis) to show its effectiveness. The prediction of harvested power under a monochromatic force excitation is also compared with the experimental results in previous literature. Simulation results from theoretical analysis and numerical calculation based on broadband modeling match well with the time-domain resolution considering different excitations and the broadband modeling is validated to be effective. In addition, through the result of theoretical analysis, several phenomena due to the frequency-domain analysis like Gibbs phenomenon, Heisenberg's uncertainty principle and time-domain aliasing are discussed. From simulation results, the effect of switching delay is shown to be limited within a specific range of switching delay.