The Numerical Integration Method Of Accurate Solution Of Non-linear Dynamic Systems Applied In Rotor Dynamics Of Coupling Vibrations Of Bending-torsional-pendular

Solving the non-linear dynamic systems by numerical integration method is improved by the thesis. The nonlinear differential equation is reconstructed as an equivalent non-linear ordinary differential equation, in which the main terms, linear part, construct the continuous linearization equation, and the remains represent the high-order remainder of the non-linear function, so it is unnecessary to expand and to calculate high-order remainder. However, the improved method doesn't change the nature of the systems without any assumption and doesn't disperse time of the non-linear item. The Duhamal convolution integration gives the expression of precision solution of the initial problem of the nonlinear differential equations. Using the Newton-Raphson iteration, in the time steps the accurate solution converge quickly with in given accuracy. Using step by step integration, the nonlinear instantaneous responses in inertial stage and long time steady state responses of nonlinear systems are obtained in whole time domain exactly. The Duhamel integration solutions are continuously satisfied system differential equations not in discrete form with algebra equations, so that is really integration method, which differs from all of the traditional finite difference method satisfied system equation at the end of time steps only. The truncation error is unlimited by original of method and determined by the calculating accuracy with in given accuracy. The reconstructed equivalent non-linear differential equation breakthrough the traditional iteration with linearized increment equation, and it is simple and has widely acceptability. The Duhamel integration breakthrough the traditional Euler's form of finite difference methods, which the truncation error is limited, the proposed method not only has high accuracy, but also avoid all of the troubles presented in finite difference methods, the period elongation, artificial damping, overshoot an stability problem.Mostly argumentation that the method of calculating matrix exponential function, considering by numeration precision and time effect, the precise time step integration method can give precise numerical results approaching to the exact solution at the integration points. Based upon the proposed theory and numerical method, some numerical examples have been calculated and analyzed. The responses of a forced vibration of linear and nonlinear systems show the high accuracy and verify the advantage of the proposed method.Based upon the study of bending vibration, torsional vibration and bending-torsional vibration by former, the thesis establishes the equation of rubbing rotor with coupling vibrations of bending-torsional-pendular when thinks over unbalance character and rubbing character. Using the numerical integration method of accurate solution of non-linear dynamic systems calculates the equation, and study that the general differential equations of coupling bending, torsional and pendular nonlinear vibration about rotor. The bifurcation and chaos behavior especially the influence on bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of rotor rotating speed and quantity of eccentricity are analyzed by using the numerical value analysis method. At the same time, the thesis also establishes the equation of rubbing rotor with non-linear radial rigidity based upon the third chapter. Using the same method study the bifurcation and chaos behavior caused by the parameters of rotor nonlinear rigidity. The analysis results provide the theoretical bases for safely operating, identifying the combination-resonance fault of the rotor and selecting the material of rotating axes.