Statistic Analysis On Dynamic Characteristics For Large Random Structures

Some research state clearly: random dynamic respond of large fluctuation levels can be given rise to random variability of structure's parameters and sometimes it becomes leading factor. For this reason, sufficient estimate and thorough research should pay close attention to dynamic reliability analysis and optimization design. The common analysis method would meet various problems in stochastic dynamic analysis of large-scale and complicated structural systems because of extremely large number of degrees of freedom. In view of this point, eigenvalue problems involving random variables of large fluctuation levels are researched. The main achievements are briefly mentioned as follows:1. Induce and summarize the research condition of eigenvalue problems involving random variables both at home and abroad; introduce concretely stochastic finite element method and its various algorithms; stress random space expression and perturbation stochastic finite element method on the basis of minor parameter perturbation, deterministic analysis and recursive equations.2. Introduce the recursive stochastic finite element method in details. Express random structural eigenvalues and eigenvections as non-orthogonal polynomials chaos; set up a series of deterministic recursive equations through non-orthogonal polynomials of the same order; derive the statistics of eigenvalues and eigenvections after solving these equations with the aid of the finite element method. Different from the previous stochastic finite element method, calculating time of the new method can be reduced largely and the method introduced here can also random eigenvalue problems involving random variables of large fluctuation levels.3. Present the theoretic basis of component modal synthesis method; introduce concretely classical C-B method. The computation results of typical examples indicate this method possesses enough accuracy for requirement of engineering calculation and it can also reduce greatly number of degrees of freedom of a complete structural system for the purpose of computation. Though a lot of calculations, theauthor obtains quantitatively the relation between the number of dynamic modes chosen and the computati6nal accuracy to meet the engineering requirement.4. A new kind of numerical method that the component modal synthesis method is combined with stochastic finite element method is used to study random eigenvalue problems of large-scale and complicated structural systems. This kind of method includes perturbation and recursive stochastic finite element method combining with component modal synthesis method, respectively called as perturbation stochastic component method and recursive stochastic component method those can also reduce greatly number of freedom degrees and save enormous calculating time. The typical examples indicate that results of two combination methods are found in good agreement with those obtained by perturbation and recursive stochastic finite element method, respectively. Compared with perturbation stochastic component method, results of recursive combining with component method to random eigenvalue problems of large-scale and complicated structural systems involving random variables of large fluctuation levels can better approximate those of Monte-Carlo simulation.