In this study, we investigate the dynamic scaling laws of geometrically similitude models and systems for predicting their vibration characteristics accurately. A determination method of scaling laws based on least square method for calculating weighted powers of scaling factors is proposed for the first time. Taking geometric parameters as input (design) parameters and vibration characteristics parameters as output parameters, the weighted powers of scaling factors are calculated by least squares similitude method (LSSM) with several design models, and then scaling factors of the output parameters are obtained by combining weighted powers and corresponding scaling factors. Applicability of the LSSM is verified in the following two cases with rectangular plate and rotor-bearing system that the stiffness of supports is taken into account. The vibration characteristics are calculated by using finite element method in MATLAB and compared with simulation analysis software ANSYS. As a result, stable weighted powers and good predictions are obtained for two cases.

在这项研究中，我们研究了几何相似模型和系统的动态缩放定律，以准确预测其振动特性。首次提出了一种基于最小二乘法的比例尺定律确定方法。以几何参数为输入（设计）参数，以振动特性参数为输出参数，采用最小二乘相似度法（LSSM）结合几种设计模型，计算出比例因子的加权功率，再结合使用得到输出参数的比例因子。加权功率和相应的比例因子。在以下两种情况下，使用矩形板和转子-轴承系统验证了LSSM的适用性，其中考虑到了支撑的刚度。通过在MATLAB中使用有限元方法计算振动特性，并将其与仿真分析软件ANSYS进行比较。结果，在两种情况下获得了稳定的加权功率和良好的预测。