IJAM, Volume 26, No. 5 (2013)

Abstract. This paper analyzes the dynamic of the spray system that consists of a spray tower mounted on trailer and his main contribution was to consider a gap at the junction point between trailer and spray tower. The analysis of the dynamic stability of the system, especially the spray tower, is of fundamental importance because the mechanical vibrations of the system can affect the quality and efficiency of application during the work in the field. The mathematical model of this agricultural implement has three degrees of freedom and, with periodic vibrations at the junction, the system of differential equations is nonlinear, second-order with time-periodic coefficients. For the analysis of the problem, we used a technique based on the Chebyshev polynomial expansion, the iterative Picard and transformation of Lyapunov-Floquet (LF). In the numerical simulations, we did the phase planes and the diagram of stability, varying the torsional stiffness, the amplitude and the frequency of vibration in the joint point. We verified that there is instability in the system to some set parameters, which can produce chaotic motions in the spray tower.