含模糊参数振动系统的Taylor级数展开法

为研究模糊参数约束条件下振动结构模糊有限元平衡方程特征值的问题,通过模糊集合理论中隶属度的性质,把振动结构的不确定模糊参量表示成区间形式,得到区间有限元平衡方程,利用所提Taylor级数展开法求解可以得到特征值所在的区间集.将α水平截集下得到的区间解,通过模糊分解定理构造出振动结构模糊有限元平衡方程的模糊解,从而可以得到模糊参数约束条件下振动结构的固有频率的变化范围,为结构的模糊可靠性评价奠定了基础.通过数值算例表明了所提方法的可行性.

Taylor series expansion method for vibration system with fuzzy parameters

To study the eigenvalues problem of vibration structure with fuzzy parameters, the Taylor series expansion method was proposed. Based on the property of membership level, the uncertain fuzzy parameters were expressed in the interval forms, and accordingly the fuzzy finite element equilibrium equation could be expressed by interval finite element equilibrium equation. The Taylor series expansion method was used to compute the eigenvalues interval sets of interval finite element equilibrium equation for the purpose of calculating the eigenvalues variety range of vibration structure with fuzzy parameters. The fuzzy result sets of eigenvalues could be constructed by interval result sets gained from computing the interval finite element equilibrium equation under every a-level through fuzzy decompose theorem. Consequently the variety range of natural frequencies can be obtained concerning vibration structures with fuzzy parameters and establish the foundation for fuzzy reliability evaluation. A numerical example is considered to illuminate the practicability of the method presented.