| Technology of linear vibration mode analysis has become one of the common methods to judge the natural vibration characteristics of the system in practical engineering.However,it is obvious that the above linear vibration analysis of the strong nonlinear system is insufficient,leading the vibration damping design and vibration control of the complex nonlinear system is still open problems.Since Rosenberg first proposed the concept of nonlinear normal modes in the 1960 s,nonlinear modal theory has made great strides,including nonlinear normal modes defined by Shaw and Pierre based on the invariant manifold theory and nonlinear normal modes constructed by Nayfeh.Shaw-Pierre theory transforms a multi-degree-of-freedom system into a form of single nonlinear mode superposition by constructing the nonlinear coordinate transformation of the system,which has some value for the study of the natural vibration response of weakly nonlinear systems.The nonlinear modal theory developed by Nayfeh can effectively analyze complex resonance trigger conditions and their nonlinear response characteristics.This paper attempts to combine the nonlinear normal modes proposed by Shaw-Pierre and Nayfeh to analyze the nonlinear normal modes of the nonlinear rotor-bearing system,and furtherly to study the primary resonance/ subharmonic resonance/ constant load excitation and instability characteristics of the system,which including:1.This paper compares and distinguishes the characteristics of the existing nonlinear modal theories.First,the invariant manifold method proposed by Shaw-Pierre is used to construct the nonlinear normal modes of the system,and the nonlinear modal characteristics and natural vibration response characteristics of the Jeffcott rotor-bearing system in the sense of this theory are analyzed,and the results are compared with the results of numerical analysis.2.Based on the classical literature,the nonlinear modal theory of Nayfeh is adopted to obtain the triggering conditions of four nonlinear normal modes in the primary resonance regions under the constant load.Furthermore,the resonant position and hysteretic characteristics of the main resonance are analyzed with the variation of system parameters such as constant load and damping.3.Finally,based on the study of nonlinear normal modes of primary resonance,the 1/2-order subharmonic resonance response and its instability regions of the system are analytically studied by using the Multi-Scale Method and the First Lyapunov Method,and verify with the numerical results.In addition,determine the influence of constant load on the instability regions.In this paper,two classical nonlinear modal theories from Shaw-Pierre and Nayfeh are used to study the nonlinear modal characteristics and complex resonance response behavior of a Jeffcott rotor-bearing system.Considering the analytical results with the aid of the nonlinear normal mode theory,the influence laws of the constant load on the hysteretic characteristics and instability regions of system resonance are clarified.The related research in this thesis has definitely theoretical innovations and engineering practical significances. |
