Manipulating post-buckled compliant mechanisms

Buckling mode interaction as a novel method of stiffness compensation

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Bistable vibration energy harvesters are an interesting alternative to their linear counterparts. They allow for large amplitude oscillations between their stable equilibria, from which much energy can be generated. However, the stable equilibria are separated by a potential energy barrier that has to be overcome. Therefore, we cannot guarantee these oscillations, and the performance advantage diminishes. As a solution to this, a novel method of stiffness compensation in compliant bistable mechanisms is explored to lower the potential barrier. This method makes use of interaction between the buckling modes. Whereas this phenomenon is most undesired in structures due to their increasing proneness to catastrophic failure, we cleverly use it to our advantage. During the deflection required for the large amplitude oscillations, a transition between these buckling modes occurs, causing the increase in potential energy. By bringing the corresponding buckling loads closer together, the transition is eased and the potential barrier is lowered. An analytical framework was set up as a fundamental test of this method. Using a discrete analytical model of a bistable buckled four-bar linkage with torsion springs, it was shown that the potential barrier can be flattened upon matching the first two critical buckling loads, resulting in static balancing. This was achieved by making two torsion springs three times stiffer with respect to the other two springs. To put theory into practice, three compliant mechanisms were designed using the ratio between the first two buckling loads. Their force-deflection characteristics were experimentally determined and it was shown that the stiffness may be tuned according to the ratio between the buckling loads. Furthermore, it was shown that in designs having the first two buckling loads equal to each other, near zero stiffness is achieved. Hence, this method is proven a successful addition to the arsenal of methods in stiffness compensation and static balancing of compliant mechanisms.