Stochastic perturbation method oriented to dense frequency structural vibration characteristic value

Abstract

The invention discloses a stochastic perturbation method oriented to a dense frequency structural vibration characteristic value. The method firstly caries out spectral factorization on a rigidity matrix and a mass matrix, then carries out displacement on the characteristic value and converts a dense frequency system into a repetition frequency system. Then, the revised characteristic value is subjected to perturbation analysis, and a matrix equation about the first order perturbation item of the dense frequency structural vibration characteristic value after a structure parameter is subjected to disturbance is obtained. Then, through a polynomial chaos expansion method, an agent model of the first order perturbation item of the dense frequency structural characteristic value is constructed. The perturbation method is combined with an agent model technology are combined to put forward an approximate calculation method oriented to the dense frequency structural vibration characteristic value, and the expression of a mean value and a variance of the dense frequency structural characteristic value under a parameter disturbance situation is further obtained on the basis of the approximate calculation method. The stochastic perturbation method solves the problem that the statistical characteristics of the dense frequency structural characteristic value can not be directly researched since the dense frequency structural characteristic value can not be expressed by the structure parameter in a traditional perturbation method.

Description

technical field [0001] The present invention is applicable to the analysis of vibration eigenvalues ​​of structural systems with densely distributed natural frequencies, and is used to solve the statistical characteristics of vibration eigenvalues ​​and the variation range of eigenvalues ​​of structural systems with densely distributed natural frequencies when subjected to various parameter disturbances , the invention can provide guidance for eigenvalue analysis technology, model update, structure analysis and design optimization of dense frequency structure system. Background technique [0002] In practical engineering structures, dense frequency structures or repetitive frequency structures are more common. In fact, dense frequency structures are more common than repetitive frequency structures, because repetitive frequency structures can be regarded as a special case of dense frequency structures, that is, densely distributed frequency intervals degenerate to zero. It s...

AI Technical Summary

Problems solved by technology

The present invention solves the difficulty that in the traditional random perturbation method, the first-order perturbation quantity of the dense frequency structure eigenvalue cannot be explicitly expressed, so it is impossible to further directly study the statistical characteristics of the dense frequency eigenvalue, and the present invention solves the difficulty based on The perturbation method of Taylor series expansion can only deal with the application bottleneck of small-scale variation of design parameters

Images