Matched-Compliance Benchmarking of Perforated and Uniformly Thinned Substrates for Piezoelectric Cantilever Energy Harvesters

Cellular and perforated substrate roots are stated to improve the output of piezoelectric cantilever energy harvesters, which serve as the primary vibration power source for self-powered wireless sensor nodes. The present work applies stricter control: a uniformly thinned root of equal substrate compliance. A single geometric family, defined by hole–footprint fractions and depth, contains through-cuts, skin-closed pockets and the thinned band. The family is analyzed with closed-form section mechanics, a validated segmented distributed-parameter model with active-coverage bounds for electrodes bridging holes, and coupled-field finite element analysis, and it is optimized in footprint, depth, thickness profile, and load in matched and frequency-free frames. At matched compliance and equal assumed damping, 1 m/s2 and 1 MΩ, the band delivers 27.8 µW against 20.7 (through-cut) and 25.8 µW (pocket), a 62% gain over the solid reference at equal footprint, at the lowest peak substrate stress of the three, and optimization terminates at the no-hole boundary. The through-cut’s +20% gain over the solid baseline reproduces the literature and is traced to root compliance. Sensitivity studies bound the claim. The power ordering holds for all patch thicknesses and coverages in the weak-coupling regime and at equal modal damping, reversing only if the band’s damping exceeds that of the pocket’s thinner skin and slender ribs. It flips in favor of the pocket under strong coupling at optimal load. The stress ordering reverses only with a damping contrast of 24–62%, an order of magnitude larger. Coupled finite element checks at three optimized designs confirm the model-frame conclusions: the best real-hole design at matched compliance delivers 16% less power than the plain band, while for a front-loaded thickness profile, a thinned root still delivers 9% more at 1.6-times the peak stress. Within this envelope, the benefits belong to thinning, not preformation.