Vibrations due to impact in a non ideal mechanical system with a non-linear Hertzian contact model

This work analyses the post impact behavior of a mechanical system consisting of an oscillator and an unbalanced non-ideal electrical motor. The impact between the mechanical system and a rigid wall is based on the assumption that the impacting bodies undergo local deformations. The method used in the present work is similar to the Discrete Element Method for particle systems modeled with a soft-sphere mechanism. The contact forces are modeled using a nonlinear damped Hertzian Spring-Dashpot system. The mathematical model of the mechanical system is represented by a set of nonlinear ordinary differential equations. The transient and steady-state responses are discussed. As the motor is considered a non ideal energy source, the Sommerfeld effect is also analyzed. The impact model is first applied for a single freely falling particle and then in the proposed mechanical system. Non-dimensional expressions for the contact force and numerical simulations of the mechanical system behavior are also presented.