Mode-Selective Nonlinearity in a Monolithic Slitted Piezoelectric Energy Harvester: Symmetry-Controlled Internal Resonance, Saturation, and Differential Bistability

Abstract

Abstract

Nonlinear elements in vibration energy harvesters conventionally act on coordinates that every structural mode shares, so added functionality detunes the power-carrying resonance. We analyse a different placement: a permanent-magnet pair mounted inside the slit of a monolithic slitted piezoelectric cantilever, acting only on the difference in the prong deflections. Because this coordinate is odd under the device mirror symmetry, an exact selectivity theorem holds: at equal tip masses, the element is invisible to the symmetric mode family at every order in amplitude, while a rank-one lever places the antisymmetric resonance across 33–60 Hz. Deliberate mass mistuning μ then opens a gated 2:1 internal resonance (coupling asymptotically ∝μ2, activation threshold ∝μ−3), verified against direct integration of the full cubic model to 0.1–2% and cross-checked by an independent finite element model. The two regimes trade off: at the mistuned design point, the first resonance shifts by 5.9%, and thresholdless transfer syphons 38% of its matched-load power at 0.05 g. The device serves a 43.3 Hz line at 16.6–20.1 μW, where the symmetric platform delivers 0.15–0.21 μW, integrates 448 vs. 354 μW⋅Hz over the band (1.27×), with unloaded/matched activation thresholds 0.017 g/0.079 g and an optimal load fraction ρ⋆≈0.34.