On the undamped free vibration of a mass interacting with a Hertzian contact stiffness

Three methods are used to determine the natural frequency of undamped free vibration of a mass interacting with a Hertzian contact stiffness. The exact value is determined using the first integral of motion. The harmonic balance method is used on a transformed equation for an approximate solution, and the multiple scales method is used on an approximate equation. The maximum initial displacement avoiding contact loss is also determined, and the corresponding exact natural frequency is also obtained analytically. The methods are evaluated by studying the free vibration of an elastic sphere on a flat rigid surface. © 2011 Elsevier Ltd © 2011 Elsevier Ltd. All rights reserved.

Keywords

Hertzian contact stiffness, Natural frequency, Undamped free vibration, Approximate equation, Approximate solution, Contact loss, Elastic sphere, First integral, Free vibration, Harmonic Balance method, Hertzian contacts, Multiple scales methods, Rigid surfaces, Natural frequencies, Spheres, Stiffness