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Abstract

The nonlinear oscillatory motion of an elastic sphere in contact with a rigid flat surface to different loads is clearly dominated by the damping mechanism of the system. However, the damping power law is unable to be identified using the decrement method due to the almost identical free vibration responses. In this paper, a procedure which allows identification of the nonlinear viscous damping from the free response data is presented. The procedure is based on the figure relating the damping restoring force and the velocity which is distinguishable for different damping laws. A dynamic experiment is described, and from the free vibration data obtained the damping restoring forces are extracted for spheres with different materials being steel and low density polyethylene (LDPE). Subsequently, based on the models and observations the characteristics of the damping law are estimated. The results show that a linear viscous damping model is a good representation for the steel sphere contact, which confirms earlier studies; whilst the LDPE sphere contact follows a nonlinear power law for the viscous damping function, which is newly obtained. The validity and accuracy of the proposed method are supported by the good agreement between numerical results and experimental results.

Keywords

Hertzian contact free vibration viscous damping restoring force method

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Identification of dissipation of a Hertzian contact from free vibration investigations

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