Focusing Impact Energy into Specific Modes

It is clear from Figure 26 and as expected from Figure 19, all modes of the spring / mass system were excited. The amount of energy transferred from the impact to a specific mode depended on the impact location, initial energy of the impactor, and the shape of the input pulse from the impact (i.e., modulus and radius of curvature of the contact areas). In general, however, it is likely that the device used to convert mechanical energy to electrical energy in the energy harvester is more efficient if excited only at specific modes of the system. For example, consider the impact target of a pinned- pinned beam with a piezoelectric device that spans the entire length of the beam. Since the generated charge from the piezoelectric device is proportional to the strain in the beam, any mode that consists of both positive and negative strains will generate charges that would tend to cancel out, thus reducing the efficiency of the energy conversion. Therefore, the first mode of the beam would then generate the most charge as compared to the other modes of the beam (see Figure 27). It would be prudent to ensure that the impact only excites those modes of the target system that efficiently convert mechanical energy to electrical energy.

Figure 27 – Modes of a pinned-pinned piezoelectric beam: example of charge generation per mode One method of achieving the desired “impact to modal” energy transfer is to utilize dynamic

vibration absorber technology. The target system of the impact should be designed such that it is as close to a one dimensional spring / mass system as possible, thereby only exhibiting a single natural frequency. For example, a block of steel supported by a small diameter all-thread rod would be such a target system. Since it would be difficult to excite the very high frequency modes in the block or the rod, a majority of the impact energy would then be transferred into the fundamental spring / mass mode of the system. The energy conversion device is then connected to the one dimensional spring / mass system and is designed to behave as a dynamic vibration absorber for the target system. Therefore, by proper design of the energy conversion device (or dynamic vibration absorber), the majority of the impact energy will be transferred into the energy conversion device improving the efficiency of the energy harvester.

4.5.1. Focused Impact Energy for Multiple Degree of Freedom System

As a simple example, the five degree of freedom spring / mass system in section 4.4 is used as the energy conversion device and, therefore, is also used as the effective dynamic vibration absorber. The one degree of freedom spring / mass system in section 4.3 is used as the target system (see Figure 28).

Figure 28 – System used as an example for focused energy transfer from impact to target mode Assuming that the energy conversion device (the five degree of freedom spring / mass system) is most efficient when vibrating at the first mode, then the target system is designed to also vibrate at the first mode of the energy conversion device. The energy of the impact will excite the fundamental mode of the target system, which will then be transferred into the first mode of the excitation device, due to the “tuning” of the attached effective dynamic vibration absorber. The results are presented in Figure 29. As a second example, it is assumed that the conversion device is most efficient when vibrating at the third mode (see Figure 30).

Figure 29 – Energy transfer between impactor, target, and 5-DOF spring / mass system during impact: focus on the 1st _{mode of 5-DOF spring / mass system}

Figure 30 – Energy transfer between impactor, target, and 5-DOF spring / mass system during impact: focus on the 3rd _{mode of 5-DOF spring / mass system}

As can be seen from Figures 29 and 30, by designing the target mass to provide a fundamental system natural frequency that approximately equals the mode of interest with respect to the energy conversion device, a majority of the impact energy can be focused into the corresponding modes,

while minimizing parasitic energy loss due to mechanical damping at other system frequencies and minimizing the reduction of conversion efficiency due to the generation of conflicting charges.

However, the use of dynamic vibration absorber technology does have a few disadvantages. The total mass of the energy conversion device (i.e., the dynamic vibration absorber) should be relatively small (< 5% to 10%) as compared to the total mass of the target to ensure a small impact of the dynamics of the one dimensional spring / mass system. If the energy conversion device is a design constraint, then the mass of the target, and therefore the impactor, must then be 90% to 95% more massive than the conversion device. However, if the impactor is a design constraint, this will then set the mass of the target, while the mass of the energy conversion system will need to be designed to be 90% to 95% of the impactor. In practical implementation, this should not be an issue.

Also, since the focus of this work is on piezoelectric devices, the electrical load of the conversion device will have an effect on the dynamic vibration absorber stiffness and damping, which will shift the mode of interest in real-time. Therefore, designing a target system to match the mode of interest in practice will be difficult. Nonetheless, the ability to focus the majority of the impact energy into system modes that increase the efficiency of the energy conversion device outweigh any of these design challenges.