Modeling additively-manufactured particle dampers as a 2DOF frictional system

Abstract

In this paper, a two-mass model for the dynamics of additively manufactured structures with embedded particle dampers (EPDs) is proposed and verified experimentally. It is proposed to model the structure’s dynamics as a linear spring-mass-dashpot system, with an added lumped mass, representing the particles, that slides relative to the structure’s mass. The friction caused by the sliding motion introduces nonlinear effects into the model that are similar to those observed in particle dampers. The two-mass model is thoroughly studied numerically and analyzed with Hilbert-transform-based tools, used to identify the instantaneous parameters of an equivalent single-degree-of-freedom system. The analysis reveals that the system’s dynamics is linear up to a certain acceleration response amplitude, above which the system exhibits nonlinear behavior, where its natural frequency and damping ratio vary with the response amplitude. This transition from linear to nonlinear behavior is attributed to the onset of sliding motion due to the inertial forces exceeding the friction force. In the nonlinear regime, the natural frequency increases and approaches a limiting value with increasing excitation frequency, while the damping ratio increases, reaches a peak and then decreases back and approaches its original value. To verify the model, a beam structure with EPDs was fabricated and excited to characterize its dynamic behavior. The same Hilbert-transform-based analysis tools were used for the investigation of the beam, providing a comprehensive description of its dynamics. The investigation revealed that the beam exhibits similar behavior to the two-mass model: transition from a linear to a nonlinear regime at an inertial threshold, and the same variations pattern of the instantaneous natural frequency and damping ratio with increasing excitation amplitude. The similarities drawn from particle dampers to the simple two-mass system shed light on the underlying mechanisms that affect the behavior of these dampers: the transition from linear to nonlinear behavior above a certain acceleration response amplitude is explained by the inertial forces acting on the particles exceeding the friction force between the particles and the structure. Above this amplitude, the particles move more freely, collide and rub more with one another, dissipating more energy overall. When the response amplitude is increased even further, the relative energy dissipated by the particles decreases, similar to what is observed in the two-mass system model. Since the model successfully reproduces the nonlinear phenomena observed in the beam with EPDs, it can be calibrated and used to predict the beam’s response to a given excitation.