NONLINEAR STABILITY AND RESPONSE OF CAR-TRAILER COMBINATIONS

The technique of quasilinearization (describing function analysis) is used to study the effects of saturation of lateral tire force based on the traditional slip law concept. Due to trailer swing velocity, the dynamic slip angle is shown to be greater than the trailer angle. Thus nonlinear results are important even for small displacements. Significant changes in frequency and damping ratio from linear values are shown for the transient response of a one degree of freedom model. The forced response is shown to be of the classical left-leaning softening type, with jump/drop phenomenon. A two degree of freedom model is shown to have a very small amplitude limit cycle for operation above the critical velocity. Conversely, a three degree of freedom model is shown to have no stable limit cycle above the critical velocity. Thus, response above critical velocity appears to be unbounded. Also, an unstable limit cycle encloses the stable part of the equilibrium solution, providing a possibility for unbounded response below critical velocity.