Design, modeling, and optimization of a stepped-beam piezoelectric energy generator under friction-induced vibration

Abstract A stepped-beam piezoelectric energy generator (PEG) is proposed to harness energy from friction-induced vibration. First, a mathematical model incorporating beam vibration theory, friction model, and piezoelectric equation is developed to describe the dynamics of the system. The energy output of the PEG is evaluated by transient charging simulation, which is validated by experiment in previous literature. A piezoelectric stepped beam prototype is fabricated, and experimental tests under different conditions are conducted to validate the model. Subsequently, a convolutional neural network—long short-term memory neural network is proposed and trained with simulation data, functioning as a surrogate model for predicting the charging process. The well-trained model is used as the fitness function, and genetic algorithm (GA) is employed for parameter optimization. Optimizations under constant total mass (CTM) and varying total mass (VTM) conditions are conducted. The thickness of different sections <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> is selected as the tuning parameter. Improvements in energy output are achieved when comparing the best and worst fitness values, validating the feasibility of using GA for optimizing the geometry. With a 10% variation ratio and friction locations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>d</mml:mi> <mml:mrow> <mml:mtext>f</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> = 0.09, 0.18, and 0.27 m, the results under CTM exhibit improvements of 42.9%, 30%, and 37.3%, while the results under VTM show improvements of 24.4%, 15.0%, and 23.2%. Further improvement can be achieved by further tuning the variation ratio and incorporating additional parameters. A potential application in wind energy harvesting and sensing is demonstrated, and the results indicate the feasibility of simultaneous energy harvesting and sensing.