Optimal Shape Design of Cantilever Structure Thickness for Vibration Strain Distribution Maximization

Energy harvesting systems face performance limitations, and existing optimizations are not always sufficient; this study addresses these gaps by enhancing piezoelectric energy systems. To improve the performance of piezoelectric energy harvesting systems, an optimization methodology is developed in this study. Since the mechanical strain distribution directly affects energy conversion efficiency, this issue is addressed through optimization of the thickness geometry of a common cantilever-type harvester elastic substrate element via a state-space gradient projection method combined with design sensitivity analysis. The gradient projection method is implemented in MATLAB R2024b software to determine the optimal elastic substrate design, after which the optimized design is simulated in COMSOL 6.3 Multiphysics for strain analysis in a transient study. The optimized cantilever designs are produced by 3D printing using a photopolymer and experimentally validated using piezo sensors and laser measurements for dynamic analysis. Theoretically compared with traditional uniform beams, the optimized cantilever designs maximize strain along the upper layer of the elastic substrate element, leading to a substantial increase in the energy conversion efficiency. This maximization is validated by experimental measurements showing a significant increase in strain in the elastic substrate (approximately 30% at the first eigenfrequency and 70% at the second). The correlation between the experimentally obtained data and the simulation results validates the optimization results. Deviation between the results did not exceed 3% and indicates that cantilever-type energy harvesters with optimized thickness profiles outperform traditional rectangular beams in energy conversion efficiency.