Bandwidth-Enhanced Low-Frequency Piezoelectric Energy Harvesting via Multimodal Response of a Planar Fermat Spiral Harvester

Enhancing the bandwidth of low-frequency vibration energy harvesting remains challenging for conventional piezoelectric cantilever harvesters because their effective response is usually confined to a narrow resonance band. This study proposes a compact Fermat spiral piezoelectric energy harvester that exploits geometry-induced multimodal responses to enhance the low-frequency response over multiple resonant modes. By extending the effective beam length within a limited planar footprint, the spiral configuration reduces the resonant frequencies and enables multiple vibration modes without introducing additional nonlinear components or multi-beam arrays. A non-uniform rational B-spline (NURBS)-based isogeometric electromechanical model is developed to describe the coupled dynamic and electrical behavior of the discretely patched spiral structure. The Fermat spiral centerline is represented within a geometry-consistent isogeometric framework, while patch-wise indicator functions are introduced to capture the localized piezoelectric coupling. An external benchmark against published experimental data yields deviations of 1.17% in resonant frequency and 7.72% in peak open-circuit voltage. Numerical cross-verification with finite element simulations shows good agreement in natural frequencies, mode shapes, voltage responses, and normalized power spectra, with relative errors of the first four natural frequencies below 0.6%. The results further reveal direction-dependent modal dominance, where different excitation directions activate distinct electromechanical coupling patterns along the spiral structure. Parametric studies show that increasing the number of spiral turns extends the effective beam length and shifts the modal responses toward lower frequencies. The resulting effective bandwidth and peak power vary non-monotonically due to changes in modal spacing, modal participation, and lead zirconate titanate (PZT) strain distribution. The spiral expansion parameter further governs a clear trade-off between effective bandwidth and peak power by modifying the characteristic length scale, curvature distribution, and modal spacing of the structure. These results demonstrate that the Fermat spiral geometry provides a structurally simple and tunable strategy for bandwidth-enhanced low-frequency piezoelectric energy harvesting through geometry-induced multimodal response. In this paper, bandwidth enhancement refers to the effective bandwidth formed by the combined half-power intervals of the multimodal power response, rather than broadening of every individual resonance peak.