On mechanical damping of cantilever beam-based electromagnetic resonators

Often when optimising a vibration energy harvester, the mechanical damping is given little significance and is usually assumed to be a constant. This paper analyses the importance of mechanical damping variation in modelling the behaviour of a cantilever beam-based electromagnetic resonator. It is shown that for beam volumes above 100 mm³, material damping dominates thermoelastic and air damping, hence becoming the major contributor towards the mechanical damping. A novel method is proposed to define material damping in terms of the maximum critically damped stress at resonance. The new method is shown to be simpler and more accurate than previous methods. Using the developed governing equations, the conditions of optimum load resistance are derived for two particular cases. A comparison is made between the mechanical damping model and the constant mechanical damping assumption in terms of maximum power output. Different trends were noted between the two compared methods, suggesting that the constant mechanical damping assumption can lead to large errors in power prediction. Further analysis describes the existence of an optimum mass ratio for electromagnetic resonators operating under a low magnetisation parameter. Lastly, this paper shows that different frequency tuning methods are preferable under different operating conditions.