含模糊参数桁架结构动力特性的模糊性分析

Fuzzy Analysis of Dynamic Characteristics of Truss Structure with Fuzzy Parameters

由于制作或施工存在误差,使得一般工程结构的参数具有一定的不确定性.这些不确定性可能是随机的,也可能是模糊的,甚至可能是随机且模糊的.这些结构参数不确定性,加上结构使用荷载的不确定性,必将干扰基于结构动力特性损伤识别结果的准确性.通过考虑材料强度特性、结构尺寸以及结构负载的模糊性,建立了桁架结构的刚度矩阵和质量矩阵,利用Rayleigh商法得到结构的自振频率,分析了材料强度特性、结构尺寸以及结构负载的模糊性对结构动力特性的影响.通过算例表明,当各结构参数取相同模糊因子时,结构杆件的截面面积和负载的模糊性对结构各阶自振频率的影响比较小,而材料的弹性模量、杆件长度以及密度对结构的各阶自振频率影响比较大;结构杆件的截面面积、杆件长度以及负载的模糊性对结构振型的影响比较小,而材料的弹性模量和密度对结构的振型影响比较大.

Due to the manufacture and constructional inaccuracy, the uncertainty is inevitable to exist in the structure parameters. All the uncertainty may be random or fuzzy,even both. It will effect the accuracy of damage identification results based on dynamic characteristic of structures. Considering the fuzzy proper- ties of the material strengths, structure dimensions and loadings,we have established the stiffness and mass matrixes of a truss structure. The frequency of the structure is obtained by using the Rayleigh Method. The effects of fuzzy material strength, structure size and loading on dynamic characteristics of structures are al- so analyzed. The results show that the effect of fuzziness of the structure members area and loading on structure frequency is less than those of the elastic modulus, length and density when each of the parameters is the same;and that the effect of fuzzyiness of the elastic modulus and density on structure model is greater than those of structure members area, length and loading.