A reasonable fundamental form of a mathematical model of nonlinear oil-film force acting on an unsteady journal bearing is presented in the paper, and nonlinear oil-film whip instability of a rigid Jeffcott rotor supported by short journal bearings is discussed. It is proved that only three functions are needed to express a general reasonable mathematical model of oil-film force and the matrix consisted of the three functions is symmetric and positive. The obtained general analytical model is much convenient for global analysis of nonlinear oil-film instability of rotor. Using the explicit analytical formulae of the three functions for cylindrical short journal bearing, bifurcation diagrams are studied at varying rotating speed and with the nondimensional mass eccentricity ρ as parameter. Poincare maps are used to explore the motion of the rotor center. It is found that influences the motion seriously. Particularly in the vicinity of p=0.3, the motion becomes very complex, synchronous whirl, periodic doubling, quasi-periodic and chaos occur alternately. Comparing the result with that under steady nonlinear model. It is found that the threshold speed at which the rotor will lose stability is much higher than that of steady model. This is more accordant with practice. The analysis shows that this model is more reasonable for nonlinear oil-film instability analysis.
The global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under combined parametric and transverse excitations are investigated in this paper for the first time. The extended Melnikov method is generalized to investigate the multi-pulse chaotic dynamics of the non-autonomous nonlinear dynamical system. The main theoretical results and the formulas are obtained for the extended Melnikov method of the non-autonomous nonlinear dynamical system. The nonlinear governing equation of the honeycomb sandwich rectangular plate is derived by using the Hamilton's principle and the Galerkin's approach. A two-degree-of-freedom non-autonomous nonlinear equation of motion is obtained. It is known that the less simplification processes on the system will result in a better understanding of the behaviors of the multi-pulse chaotic dynamics for high-dimensional nonlinear systems. Therefore, the extended Melnikov method of the non-autonomous nonlinear dynamical system is directly utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the two-degree-of-freedom non-autonomous nonlinear system for the honeycomb sandwich rectangular plate. The theoretical results obtained here indicate that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the honeycomb sandwich rectangular plate. It also demonstrates the validation of the theoretical prediction.
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