A novel equivalent circuit approach for modeling piezoelectric energy harvesters in quarter and half-car suspension systems

Abstract This paper presented a rigorous modeling and validation study of equivalent electrical circuits for vibration energy harvesting from quarter-car (QCM) and half-car (HCM) suspension systems. The proposed approach relied on the force-voltage analogy to represent mechanical suspension systems and piezoelectric energy harvesters as equivalent electrical circuits. Energy harvesting was achieved using a piezoelectric stack modeled by the simplified Mason equivalent circuit and integrated in series with the suspension spring, preserving the overall system dynamics. To validate the equivalent circuit models, vehicle suspension dynamics were also simulated in MATLAB Simulink by solving the coupled equations of motion for the sprung and unsprung masses. Validation was conducted in two steps. First, the comparison between mechanical and electrical transmissibility ratios—without energy harvesting—showed excellent agreement, confirming the accuracy of the circuit-based dynamic representation. Second, the energy harvesting performance was evaluated in terms of output voltage and harvested power. The results indicated that the HCM configuration yielded up to 75% more harvested power than the QCM. A two-dimensional parametric study on electrical load resistance and smoothing capacitance revealed their strong influence on both power output and voltage stability. An optimal combination of load resistance and smoothing capacitance, R = 3.16 MΩ and C s = 1 μ F, was identified, balancing high energy recovery with reduced voltage ripple. Frequency-domain analyses further confirmed enhanced energy capture near resonance frequencies, particularly in the HCM. These findings demonstrated the accuracy and practical relevance of the proposed equivalent circuit approach and established a solid foundation for optimizing piezoelectric energy harvesters integrated into vehicle suspensions.