LAUSR

A two-degree-of-freedom (2DOF) quarter-car model with a piecewise leaf spring for the rear suspension of a truck is presented. A leaf spring, which contains a main leaf and an auxiliary leaf, can be regarded as a model with piecewise-linear stiffness and damping, and the model is built with two load states according to whether the auxiliary leaf spring is at work at the static equilibrium. The incremental harmonic balance method is used to obtain the nonlinear dynamics of the presented quarter-car truck model. The accuracy of this method is verified by comparing the nonlinear responses, including the sub-harmonic resonance, with the Runge–Kutta method. Afterward, the effects of the auxiliary leaf spring’s stiffness, the sprung mass ratio and the main leaf spring’s damping on the dynamic responses of the system are investigated. It is found that the piecewise-linear system shares similar dynamic characteristics with a Duffing oscillator, and the proper design of the auxiliary leaf spring can contribute to the reduction in the fundamental resonance amplitudes of the system. The frequency response curve shows ‘snap-back’ features in the sub-harmonic resonance under a certain sprung mass and the leaf spring’s damping, which is due to the coupled nonlinearities of both DOFs. In addition, the increase of the main leaf spring’s damping can shrink or even eliminate the sub-harmonic or chaos resonances.