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本文论述一个具有任意粘性阻尼和振动频率几乎重合的结构在单点动态试验后进行模态参数的识别问题。阻尼值不一定很低,并且不采用可在保守结构固有振型的基础上使阻尼矩阵对角线化的限制条件。结构数学模型的迁移率-位移函数系数是利用理论值与实验结果的最小二乘配合来计算的。建立了误差的变分公式,以此通过使形式为J(Z)=12(AZ,Z)-(b,z)的二次泛函取极小值的方法来估价未知的系数。式中,A和b分别是实验数据的非负定矩阵和矢量函数:Z代表要识别的系数矢量。然后,把识别出的迁移率一位移函数分解成有理分式就可得到模态系数。本文列举了按模态试验结果来识别的一些例子,以说明该方法在困难情况了评价结构模态特性的精确值的情况。
This paper deals with the problem of identifying modal parameters after a single dynamic test with a structure that has almost arbitrary viscous damping and almost coincident frequencies. The damping values are not necessarily low and do not employ the restriction that diagonalizes the damping matrix on the basis of the natural mode of the conservative structure. MATHEMATICAL MODEL MIGRATION - The displacement function coefficient is calculated using the least squares fit of the theoretical and experimental results. The variational formula of the error is established to estimate the unknown coefficients by taking the quadratic function of the form J (Z) = 1 2 (AZ, Z) - (b, z) . In the formula, A and b are the negative definite matrix and vector function of experiment data respectively: Z represents the coefficient vector to be identified. The modal coefficients are then obtained by decomposing the identified mobility-displacement function into rational fractions. In this paper, some examples identified according to the results of modal testing are given to illustrate how this method can evaluate the exact value of structural modalities in difficult situations.