Electromechanical modelling of l-shaped bending-torsion piezoelectric energy harvesting systems

Piezoelectric energy harvesting (PEH) has become an important concept in recent years, aiming to harvest energy from various mechanical vibrations. However, a significant gap has been noticed in the multimodal and multidirectional analytics of PEHs. In this context, this paper proposes an innovative approach to introduce a novel multimodal and multidirectional PEH design, which exploits both the face extension mode (d31) and the face shear mode (d36), to target low-frequency environments. The study investigates three bending-torsion l-shaped bimorph PEHs, namely H₁, H₂, and H₃. To evaluate the performance of the proposed PEHs, a distributed parameter model is developed based on the assumptions of the Euler-Bernoulli beam. The validity of the model is confirmed by analytical, numerical, and experimental results from previous work. The exploitation of the d36 mode enhances the power output of H₁, H₂, and H₃ by 67.95 %, 43.66 %, and 31.83 respectively. The three PEHs performances are compared quantitatively and qualitatively, and H₁ is found to be the most efficient among them. The PEH H₁ requires a single excitation to perform the coupled bending-torsion motions, resulting in an outstanding average power output of 54.66 µW, which outperforms the other two PEHs by tenfold. The use of the d36 modes to expand the frequency bandwidth and improve the power output presents an excellent innovative and practical value for piezoelectric energy harvesting.