The Influence of the Non-linear Stiffness on the Vibration Parameters of a Half-Vehicle

The considered model has two degrees of freedom, a vertical linear displacement of the center of weight and the rotation about this center of weight. The elastic stiffnesses (for the front part and for the back part of the automobile) are considered to be expressed by polynomials of different (or possibly equal) degrees. In this paper the authors determine the responses of the suspension consisting in quasi-amplitudes of the vibrations and the quasi-periods of the vibrations (translation and rotation) as functions of the parameters of the excitations. The excitation is considered to be a harmonic one and lasting for a certain period of time. It is characterized by amplitude, period and the lasting period. In the present paper the authors consider only suspensions for which the stiffnesses are given as odd degree polynomials (for which the vertical descendent position of equilibrium is unique). The authors also determine the equilibrium positions.