Reduced order model-based free vibration analysis method for beam structure

Abstract

The invention belongs to the field of aerospace complex beam structure component calculation, and provides a reduced order model-based free vibration analysis method for a beam structure. The method comprises the following steps: 1) obtaining a mass matrix and a stiffness matrix of a fine structure by using finite element software; 2) using a polynomial interpolation function to construct a reduced base vector, so as to realize order reduction of an original complex beam structure; and 3) solving a kinetic equation of the reduced order model, and obtaining the overall frequency and part of low-order frequencies of the structure. According to the method disclosed by the present invention, the polynomial interpolation function is used to construct the reduced base vector, nodes in a finite element model of the complex structure are condensed to the section centroid in the form of displacement interpolation so as to realize the order reduction of the original structure, and the calculation precision of the reduced order model can be controlled by polynomial orders. The method disclosed by the present invention has the advantages that: without depending on the experience of the user, the adverse influence of the difference of selection of the master and slave freedom degrees on the calculation precision is reduced; a large amount of matrix operation is not needed, so that the calculation efficiency of order reduction of the model is improved; and the obtained reduced order model has a wide application range.

Description

technical field [0001] The invention belongs to the calculation field of aerospace beam structure components, and relates to a beam structure free vibration analysis method based on a reduced-order model. Background technique [0002] With the development of computing science and technology, the processing speed and storage capacity of computers continue to increase, but at the same time, the scale and complexity of engineering and scientific problems requiring calculations also continue to increase. For the statics problems of complex engineering, it is possible to establish a finite element model with a large scale, a very dense grid, and a detailed description of the structural details and perform structural analysis on it, but the calculation amount of the structural dynamic analysis is larger than that of the static analysis. Several orders of magnitude, it is almost impossible to use such a model for structural dynamic analysis. In addition, in the initial stage of st...

AI Technical Summary

Problems solved by technology

[0006] The present invention mainly solves the problems of complex operation, large amount of calculation, and loss of low-order frequencies of the structure after model reduction in the existing model reduction method, and proposes a beam structure free vibration analysis method based on the reduction model, which is simple to operate, Make full use of the finite element model information of the original beam structure, combine the polynomial interpolation function to construct the reduced basis vector, and realize the order reduction of the beam structure

Images