Abstract Piezoelectric energy harvesting is commonly considered to be a promising field of development for microelectronic devices due to its potential to address a variety of key supply problems. However, due to their geometric designs, traditional piezoelectric energy harvesters (PEHs) tend to only be able to cultivate energy from vibrations flowing in one direction. The results of PEHs only capable of harvesting mono-directional vibrations are that they suffer from narrow resonance frequency bands and low energy conversion efficiency. To overcome these difficulties, this paper proposes a PEH inspired by a line tooth (PEH-ILT) with the ability to collect three-dimensional stochastic vibrations. To do so, the PEH-ILT possesses a nonlinear geometric shape which can, in theory, be designed arbitrarily. An example PEH-ILT is illustrated in this paper as well corresponding nonlinear piezoelectric constitutive equations. The cylindrical spiral curve is inspired by the line tooth design and is intended to replicate a nonlinear electro-mechanical model and its electrical output. Furthermore, the PEH-ILT is evaluated in this study by interacting with the four basic vibrations such devices are expected to encounter. In addition, the broadband piezoelectric energy harvesting conditions of the PEH-ILT are parsed and determined through the Melnikov theory, providing a theoretical explanation to the broadband conditions of the harvester. And this study can lay the theoretical basis for practical applications.