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

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.