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针对具有不确定但有界参数的结构系统的固有振动频率问题,提出一种近似求解结构固有频率上、下界值的区间特征值摄动法.该方法基本上是两步法,首先,将结构系统的振动描述为区间数学中的广义区间特征值问题,形成矩阵方程.其次,把特征值看作是摄动矩阵的函数,利用区间分析和摄动理论计算特征值的上下界值,从而根据其值来估计结构固有振动频率的范围.通过两个数值例子表明,该方法在结构参数的不确定量较小时可得到满意的结果.
Aiming at the problem of natural frequency of structural system with uncertainties and bounded parameters, a method of interval eigenvalue perturbation to approximate upper and lower bounds of natural frequency of structures is proposed. The method is basically a two-step method. Firstly, The vibration of the system is described as a generalized interval eigenvalue problem in interval math, forming a matrix equation.Secondly, the eigenvalues are considered as a function of the perturbation matrix, and the interval analysis and perturbation theory are used to calculate the upper and lower bounds of eigenvalues, The value of which is used to estimate the range of the natural frequency of the structure.Through two numerical examples, it is shown that this method can obtain satisfactory results when the uncertainty of the structural parameters is small.