Abstract Accurate and efficient models of the dynamics of a laminated transformer core structure are essential for the design of quiet power transformers. However, owing to the complex structure of the transformer core, the dynamic response of the core has not yet been accurately modelled. In this paper, the strains in different laminas and the strain differences between them are included as key parameters in the derivation of the equivalent bending stiffness of a beam subject to transverse vibration. As a result, the equivalent stiffness and loss factor of the beam are obtained as functions of the number of layers and strain difference ratio due to the inter-layer friction factor and the clamping force. The equivalent material properties are then used to determine the frequency response functions of laminated beams using the finite element method. Two sets of frequency response functions produced by different numbers of layers and different clamping forces are measured experimentally. A comparison between the simulated and measured frequency response functions shows good agreement with the relative error of the natural frequencies less than 6% for the first four natural frequencies.

中文翻译：

---

计算层状梁等效杨氏模量和损耗因子的新型动力学模型

摘要 叠层变压器铁心结构动力学的准确有效模型对于安静电力变压器的设计至关重要。然而，由于变压器铁心结构复杂，铁心的动态响应尚未被准确建模。在本文中，在推导受横向振动的梁的等效弯曲刚度时，不同薄层中的应变和它们之间的应变差是关键参数。结果，由于层间摩擦系数和夹紧力，梁的等效刚度和损耗系数是层数和应变差比的函数。然后使用等效材料属性来确定使用有限元方法的层压梁的频率响应函数。实验测量了不同层数和不同夹紧力产生的两组频率响应函数。模拟和测量的频率响应函数之间的比较表明，前四个固有频率的固有频率相对误差小于 6%。