Kirigami-Graded Metabeam for Broadband Piezoelectric Energy Harvesting: A Numerical Analytical and Finite-Element Study

Self-powered sensor nodes need vibration harvesters that work over a band of frequencies, but the arrays and graded metamaterials that provide such bandwidth need many separately clamped resonators. This numerical study presents a kirigami-graded metabeam in which U-shaped slits in one 250 × 16 × 0.5 mm aluminum sheet release four tabs of graded length (44–62 mm); the sheet is folded and clamped at both ends, and a PZT-5A patch straddling each root feeds its own resistive load. A distributed-parameter cell model is verified against a three-dimensional coupled-field finite-element model within 1% in frequency and 2% in power. In the finite-element model, each cell mode is confined to one tab (off-diagonal amplitudes ≤ 0.09) and the cells deliver 0.59–1.44 µW per (m s−2)2 at 130–274 Hz; their band-mean power is 3.6 times that of a single clamped tab and 0.9 times that of four separately clamped tabs, with two clamps instead of four. Interleaving the cells so that frequency-adjacent cells are not spatial neighbors keeps the modes localized on an 18 Hz grid and gives a continuous 212–284 Hz band with 1.1 times the four-tab power. One root-compliance parameter places 18 cell frequencies within 2–3%, and the sensitivity of the results to the assumed damping is quantified. No measurement is reported; the experimental characterization of the prototype is left to a separate study.