Vibration Modeling of Arc-Based Cantilevers for Energy Harvesting Applications

Cantilever beams are widely used for designing transducers for low-frequency vibration energy harvesting. However, in order to keep the dimensions within reasonable constraints, a large tip mass is generally required for reducing the resonance frequency below 100 Hz which has adverse effect on the reliability. This study provides a breakthrough toward realizing low-frequency micro-scale transduction structures. An analytical out-of-plane vibration model for standalone arc-based cantilever beams was developed that includes provisions for shear and rotary inertia, multidirectional arcs, and multiple layers. The model was applied to a multilayered cantilever beam (10-mm wide and 0.1-mm thick) composed of three arcs, and the results indicate that the fundamental bending mode of the beam was 38 Hz for a silicon substrate thickness of 100 μm. The model was validated with modal experimental results from an arc-based cantilever made out of aluminum.