## 1 Introduction
To comprehensively address real-world operational factors in piezoelectric energy harvester design, the recent literature has emphasized the impact of external variables, such as mounting configuration, temperature fluctuations, and electrical matching strategies. In their article, [PERSON] et al. [24] explored how varying the installation angle of an airfoil-based harvester can significantly influence its aerodynamic flutter threshold and power output, demonstrating that moderate angles improve performance. [PERSON] et al. [25] investigated the thermal sensitivity and frequency-dependent behavior of laminated macro-fiber composite harvesters, revealing the influence of environmental temperature on structural response and electrical generation. In line with electrical optimization, [PERSON] et al. [26] proposed a real-time impedance tracking approach using a Zeta converter and MPPT-based control system, achieving rapid power adaptation under dynamic environmental changes and ensuring efficient power transfer. In the context of non-linear mechanisms, magnetic coupling has received growing interest for performance enhancement. [PERSON] et al. [27] analyzed magnetic plucking dynamics in a frequency-upconverting harvester, uncovering key resonance conditions for energy amplification via repeated magnetic interactions. [PERSON] et al. [28] further expanded this concept by experimentally examining the dynamical behavior of piezoelectric harvesters influenced by variable magnetic interaction speeds, confirming non-linear frequency up-conversion effects. Finally, [PERSON] et al. [29] proposed a 2 + 1 degree-of-freedom equivalent circuit model for a LiNbO\({}_{3}\)/metal/LiNbO\({}_{3}\) bimorph piezoelectric cantilever, enabling more accurate prediction of its electromechanical behavior and offering insights valuable for broadband vibration energy harvesting design. Some designs do not necessarily come from math--it could be bioinspired. Such a structural design can significantly enhance the performance of vibration-based energy harvesters. Notably, [PERSON] et al. examined a trunk-shaped piezoelectric cantilever beam inspired by the caudal peduncle of the electric fish _Gnathonemus petresii_[30]. The structure incorporates delta wing-shaped extensions that emulate the morphology of the fish's tail, which is naturally evolved for efficient electrical signal generation. In their study, the biomimetic beam outperformed a conventional rectangular cantilever, yielding up to 45% more electrical output under vibrational excitation. This enhancement was attributed to improved strain distribution and potential non-linear amplification effects within the PVDF piezoelectric layer. The results suggest that evolutionary morphology, such as that found in electrogenic fish, may offer valuable templates for designing more efficient energy harvesting devices. Despite the advancements in the mentioned literature, a notable limitation is the underexplored potential of optimizing non-linear thickness profiles for specific eigenfrequencies. While width variation and topology optimization are widely applied, thickness remains either constant or adjusted without explicitly considering its effect on modal strain energy alignment. Since electromechanical coupling in piezoelectric materials is strongest when high strain regions align with polarized material, shaping the thickness presents a promising strategy. This approach can significantly enhance energy output, particularly when optimized for the fundamental vibration mode. This work aims to improve the electromechanical performance of piezoelectric energy harvesters by optimizing the thickness profile of a cantilever beam while preserving its first natural frequency. This objective was addressed through a combined numerical and experimental approach, involving gradient-based optimization, finite element modeling, and validation via interferometric and base-excitation testing.