考虑变幂数的畸变动力学相似试验模型设计方法及试验研究

动力学相似理论广泛应用于大型结构的振动试验，其中畸变相似用于解决结构的设计参数不满足等比例缩放时的相似问题，针对畸变相似关系中幂数为定值导致预测精度低的问题，提出考虑变幂数的畸变动力学相似试验模型设计方法。首先，在敏感性分析与中心差分理论推导的幂数表达式的基础上，将中心差分的范围不断扩大得到一组随相似比变化的幂数。采用最小二乘法将这组幂数拟合为关于相似比的函数并建立相似关系。然后，在多盘转子系统的数值算例中将变幂数法与文献中的两种方法进行对比，结果表明，变幂数法的预测精度较文献中的方法有很大提高。最后，通过试验研究验证了数值算例中动力学模型及临界转速求解的正确有效性。相似关系的建立是以模型的临界转速为基础，因此也验证了数值算例中的相似预测结果。

Design Method of Distorted Dynamics Similitude Test Model Considering Variable Power and Experimental Study

Dynamics similitude theory is widely used in vibration test of large structures. Distorted similitude is used to solve the similitude problem that the design parameters of structures do not satisfy equal scaling. Aiming at the problem of low prediction accuracy caused by the fixed power in distorted scaling laws, this paper proposes a design method of distorted dynamics similitude test model considering variable power. Firstly, on the basis of the power of scaling factor deduced by the sensitivity analysis and the central difference theory, the range of the central difference theory is expanded to obtain a set of powers which is used to fit a function related with the scaling factor by the least square method. Then, the proposed method is compared with two methods in literatures in the numerical example of multi-disc rotor system. It is found that the accuracy of the proposed method is much higher than that of the methods in literatures. Finally, the dynamic model and its solution of the numerical example are verified by the experimental study. The prediction results in the numerical example are also considered verified since the scaling laws are developed based on the critical speeds of the dynamic model.