Perturbation RICCATI Transfer Matrix Method For One Dimensional Structure With Parameter Uncertainties And Its Applications

In this paper, the perturbation RICCATI transfer matrix method was comprehensively investigated. The important developments achieved in theories include:1. Based on RICCATI transfer matrix method, the calculating formulas and equations for perturbation analysis of one-dimensional structural system with parameter uncertainties are derived. By making singular value decomposition, the unknown perturbing eigenvalues and unknown perturbing eigenvectors in the perturbation equations are separated, consequently, the theoretical basis for solving perturbation equations and for getting perturbation eigenvectors with high precision is established;2. General methods are presented to calculate the 2nd order perturbations of eigendatas for one-dimensional structural system with parameter uncertainties, the methods are applicable to both single and repeated eigendata problems as well as both real and complex eigendatas;3. It doesn't needed that solve the 2nd or the other higher order perturbation equations as the 1st order perturbations of eigenvectors are calculated for repeated eigenvalues, and the perturbation analysis of eigenvectors for repeated eigenvalue problems is simplified. This is different from the matrix perturbation method based on the FEM;4. Because the errors caused by truncating the high modals are avoided, the perturbation solutions of eigenvalues and eigenvectors are high accurate perturbation solutions;5. The perturbation method presented in this paper is a general method for any one-dimensional and like one-dimensional structural system.The achievements in applications include:1. Based on the perturbation RICCATI transfer matrix method, the calculating program are developed. The program can be used to the perturbation analysis and the sensitivity analysis of the real and complex, the single and repeated eigenvalues and eigenvectors for lateral vibration of rod and beam structures, especially suitable to the perturbation analysis and the sensitivity analysis of eigenvalues and eigenvectors for rotordynamic systems;2. The perturbation RICCATI transfer matrix method was applied to identify the parameters of the rotor for a boiler supply pump, and the accurate dynamic model of the rotor was archived. It is a important basis for advanced dynamic analysis and redesign;3. The application formulas based on this perturbation theory in some areas such as stochastic eigendatas, stochastic response, dynamic reliability, sensitivity analysis, parameter identification, optimal design are given.