Energy generation from friction-induced vibration of a piezoelectric beam

The primary challenge in harnessing vibration energy with piezoelectric materials is the discrepancy in frequency between the energy source and the energy generator, which lowers the efficiency of energy harvesting. To address the challenge, a piezoelectric beam under friction-induced vibration (FIV) is designed, modeled, and studied for the first time to realize the pronounced FIV contributing to energy generation by adapting the vibrations of the continuum structure to align close to its resonant frequencies. The Stribeck friction model is applied to characterize the variation of friction based on the relative sliding velocity v_r between contacting objects. The analytical solution is derived to solve the dynamic responses, and transient charging simulation validated by the experiment is utilized to assess energy output. Furthermore, parameter studies are conducted based on the validated model with regard to the material properties of the beam and piezoelectric material, electrode connections of piezoelectric patches, and friction model parameters to investigate their influences on energy output. Considering the same dimensional properties, materials with low Young's modulus E and density ρ are desired for the host structure to facilitate large dynamic strain in piezoelectric materials. With an exponential decay factor C = 8, representing optimal material contact interface, pronounced higher FIV mode can be induced leading to higher output power. A root mean square charging power $P_e^{\text{RMS}}$ of 42.4 mW and a peak instant charging power P_{e − peak} of 263 mW can be achieved. In the current study, the model is implemented on a beam coupled with one piezoelectric patch, which has potential applicability to non-uniform beams with various layouts of piezoelectric patches. The presented model enables efficient optimization of continuum structural design for higher piezoelectric energy generation under friction.