Abstract
Vibrations in mechanical structures are usually undesired and dangerous; hence many technologies have been developed in the past to dissipate their mechanical energy. However, it is advisable to harvest such energy, rather than let it dissipate. The harvested vibration energy may be readily used, for example, to independently power sensors due to the small amount of power required to operate them. Numerous linear and non-linear energy harvesters have been proposed in order to operate in a variety of vibratory environments with the intention of improving power production and/or frequency and dynamic range bandwidth of the generic device. In this paper, the suitability of a parametrically excited system versus a non-parametrically excited system for energy harvesting is investigated both numerically and experimentally. Parametrically excited systems show large periodic motion when excited near their region of instability. Firstly, the characteristics of a Single Degree of Freedom (SDOF) system with periodic stiffness are introduced theoretically. A periodic stiffness or parametric stiffness (described by a Mathieu equation) is then introduced into the dynamic equation in order to generate parametric resonance. A cantilever beam with a parametric spring attached along its length is considered. The periodically changing spring coefficient is obtained experimentally using a permanent magnet and two electromagnetic coils as an electromagnetic spring. It is shown that the cantilever beam, when excited parametrically, exhibits the same behaviour described by the Mathieu equation. Numerical and experimental results are in good agreement.
