A Dynamic Analysis of a Cantilever Piezoelectric Vibration Energy Harvester with Maximized Electric Polarization Due to the Optimal Shape of the Thickness for First Eigen Frequency

This study presents an analytical and experimental approach to enhance cantilever-based piezoelectric energy harvesters by optimizing thickness distribution. Using a gradient projection algorithm within a state-space framework, the unimorph beam’s geometry is tailored while constraining the first natural frequency. The objective is to amplify axial strain within the piezoelectric layers, thereby increasing electric polarization and maximizing the conversion efficiency of mechanical vibrations into electrical energy. The steady-state response under harmonic base excitation at resonance was modeled to evaluate the harvester’s dynamic behavior against uniform-thickness counterparts. Results show that the optimized beam achieves significantly higher output voltage and energy harvesting efficiency. Simulations reveal effective strain concentration in regions of high piezoelectric sensitivity, enhancing power generation under resonant conditions. Two independent experimental setups were employed for empirical validation: a non-contact laser vibrometry system (Polytec 3D) and a first resonant base excitation setup. Eigenfrequencies matched within 5% using a Polytec multipath interferometry system, and constant excitation tests showed approximately 30% higher in optimal shapes electrical potential value generation. The outcome of this study highlights the efficacy of geometric tailoring—specifically, non-linear thickness shaping—as a key strategy in achieving enhanced energy output from piezoelectric harvesters operating at their fundamental frequency. This work establishes a practical route for optimizing unimorph structures in real-world applications requiring efficient energy capture from low-frequency ambient vibrations.