Incorporating Dissipated Impact into Random Vibration Analyses through the Modified Hertzian Contact Model: Fid-Bau Portal

Incorporating Dissipated Impact into Random Vibration Analyses through the Modified Hertzian Contact Model

Xu, M. / Wang, Y. / Jin, X. L. / Huang, Z. L. / Yu, T. X.

Abstract

The Hertzian contact model, which is usually used in analyzing the response of vibroimpact system with elastic contact, cannot deal with the dissipated contact problem in general. A modified Hertzian contact model that was developed through recent experiments, however, provides an opportunity to break this limitation. The random response of vibrating system with dissipated impact subjected to Gaussian white noise is investigated in this paper, and the dissipated impact is incorporated into random analysis through this modified model. The inelastic contact force can be separated into two parts: elastic restoring component and dissipative component. The restoring component is expressed as the gradient of the potential energy preserved in the system and the dissipative component is approximated by a damping force with energy-dependent damping coefficient through energy dissipation balance technique. The Itô stochastic differential equation with respect to the total energy of the system, which is a one-dimensional Markov process, is derived through the stochastic averaging of the energy envelope. The stationary probability density of system total energy, the joint probability density of system displacement and velocity, and the statistics of system response are analytically obtained from the associated Fokker-Planck-Kolmogorov equation. The agreement between the analytical results and Monte-Carlo simulations validates the effectiveness of the proposed technique.