Novel dynamic model for calculating the equivalent Young's modulus and loss factor of layered beams

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.