Abstract. In this work we study a dynamical system with a complicated nonlinearity, which describes oscillation of a turbine rotor, and give an algorithm to compute Melnikov functions for analysis of its chaotic behavior. We first derive the rotor model whose nonlinear term brings difficulties to investigating the distribution and qualitative properties of its equilibria. This nonlinear model provides a typical example of a system for which the homoclinic and heteroclinic orbits cannot be analytically determined. In order to apply Melnikov's method to make clear the underlying conditions for chaotic motion, we present a generic algorithm that provides a systematic procedure to compute Melnikov functions numerically. Substantial analysis is done so that the numerical approximation precision at each phase of the computation can be guaranteed. Using the algorithm developed in this paper, it is straightforward to obtain a sufficient condition for chaotic motion under damping and periodic external excitation, whenever the rotor parameters are given.Key words. mathematical modeling, Melnikov function, chaos, modulus of continuity, oscillatory integrand AMS subject classifications. 34C28, 34C37, 34C45 DOI. 10.1137/S10648275034207261. Introduction. The oscillation phenomenon of the turbine rotor has long been observed in industry. Many efforts [7,8] have been made to analyze and control the mode and scale of such oscillations, which are caused by a number of factors, e.g., unbalanced centrifugal force. However, to eliminate such vibrations effectively, which are harmful to the quality and life span of the system, it is necessary to examine the underlying nature of those nonlinear oscillations and to find the relationship between the oscillatory behavior and the physical parameters of the real system.Consider the shaft of a rigid rotor supported symmetrically by four equal bearings at the ends on a low-speed balance platform, as shown in Figure 1. The elasticity in each bearing can be modeled equivalently as a spring. Let L denote the length of the shaft, and let c and K denote the length and stiffness of each relaxed spring, respectively. The following linear model is often used [3,4,18,27]: