Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

TL;DR

This study investigates the dynamic response of a single degree of freedom mechanical system with a particle damper, revealing non-monotonic effective mass behavior including overshoot phenomena in both small and tall container limits.

Contribution

It demonstrates that the effective mass can overshoot the expected limits in particle dampers, challenging previous assumptions of monotonic approach to the asymptotic mass.

Findings

Effective mass overshoot occurs in small containers.

Similar overshoot behavior is observed in tall containers.

Implications for industrial damping applications are discussed.

Abstract

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.