An Analytical Model for Low-Frequency Vibration Energy Harvesting in a Cantilever Beam with a Piezoelectric Patch: Development and Qualification Using Experimental Data

Vibration-based piezoelectric energy harvesting provides a potential power source for low-consumption devices; however, its prediction requires a consistent representation of localized structural properties and experimentally identified modal behavior. This study presents the structural and modal qualification of an analytical electromechanical model for a 6061-T6 aluminum cantilever beam carrying a finite one-sided PZT-5J piezoelectric patch, with unequal beam and patch widths, under base excitation. The specific contribution is the traceable integration of local neutral-axis relocation, spatially varying mass and flexural rigidity, a finite-patch indicator function, d31 electromechanical coupling, multimodal projection, and mode-specific reduced-order equations. Two beam lengths, 275 and 250 mm, were investigated using broadband shaker excitation, accelerometry, and scanning laser vibrometry. The measured first and second bending frequencies were 16.56 and 110.31 Hz for the 275 mm beam and 19.14 and 125.00 Hz for the 250 mm beam. Experimental damping ratios obtained from the frequency-response functions ranged from 6.54×10−3 to 1.55×10−2. The analytical formulation reproduced the increase in modal frequencies produced by reducing the beam length and captured the measured transverse mode-shape trends. Experimentally identified frequencies, base accelerations, and damping ratios were subsequently introduced into the reduced model to obtain experimentally parameterized model outputs. The largest calculated peak voltage and estimated average electrical power were 155.99 mV and 1.22 μW, respectively, for the first mode of the 275 mm beam across a reference 10 kΩ resistive load. The reported qualification is restricted to the structural and modal response of the two tested configurations; the electrical quantities are calculated outputs rather than independent electrical measurements.