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Shock and Vibration
Volume 18 (2011), Issue 1-2, Pages 245-256

Particle Damping with Granular Materials for Multi Degree of Freedom System

Masanobu Inoue,1 Isao Yokomichi,2 and Koju Hiraki3

1Department of Mechanical Engineering, Kitakyushu National College of Technology, Fukuoka, Japan
2Professor Emeritus, Kitakyushu National College of Technology, Fukuoka, Japan
3Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Fukuoka, Japan

Received 12 February 2010; Revised 3 August 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A particle damper consists of a bed of granular materials moving in cavities within a multi degree-of-freedom (MDOF) structure. This paper deals with the damping effects on forced vibrations of a MDOF structure provided with the vertical particle dampers. In the analysis, the particle bed is assumed to be a single mass, and the collisions between the granules and the cavities are completely inelastic, i.e., all energy dissipation mechanisms are wrapped into zero coefficient of restitution. To predict the particle damping effect, equations of motion are developed in terms of equivalent single degree-of-freedom (SDOF) system and damper mass with use made of modal approach. In this report, the periodic vibration model comprising sustained contact on or separation of the damper mass from vibrating structure is developed. A digital model is also formulated to simulate the damped motion of the physical system, taking account of all vibration modes. Numerical and experimental studies are made of the damping performance of plural dampers located at selected positions throughout a 3MDOF system. The experimental results confirm numerical prediction that collision between granules and structures is completely inelastic as the contributing mechanism of damping in the vertical vibration. It is found that particle dampers with properly selected mass ratios and clearances effectively suppress the resonance peaks over a wide frequency range.