P-Bifurcation Analysis of a Quarter-Car Model with Inerter-based Pendulum Vibration Absorber: A Wiener Path Integration Approach

Abstract

In this theoretical study, a recently developed inerter-based pendulum vibration absorber (IPVA) coupled with energy harvesting capabilities is applied to the quarter car model with class C road conditions (ISO 8608). The impact of varying the pendulum length parameter on power harvesting, ride comfort (sprung mass acceleration), and road handling is investigated. It is discovered that P-bifurcation of the probability density function (PDF), can simultaneously occur with enhanced output power (40% improvements), low sprung mass acceleration (60% improvements), and better road handling (60% improvements) when compared with the linear benchmark system. To predict this bifurcation, a Wiener path integration (WPI) method coupled with curvature checking is developed for the PDF. An efficient bifurcation detection algorithm is developed which leads to the prediction of monomodal, bimodal, and rotation PDF regions in the noise intensity-electrical damping plane. Using Monte Carlo simulations (MCS), the performance metrics were then compared against the optimal linear benchmark for varying driving speed on a class F road while varying the electrical damping so that the system is at or near P-bifurcation. Energy transfer into the electrical domain and power harvested is shown to be up to 43% and 20% higher than for the optimized linear system, respectively. Electrical efficiency considerations show that generator selection is also a factor. Ride comfort and road handling still saw improvements of at least 59%. Finally, the new algorithm effectively reduces an exhaustive MCS for various parameter configurations when qualitative changes in the PDF are linked to performance.