Natural frequencies and mode shapes of vibration of transformer cores

Transformer-core vibrations, which are caused by magnetic and magnetostrictive forces, are responsible for the noise radiated by the tank. Since the core is a structure consisting of distributed mass and stiffness, it has an infinite number of natural frequencies, one of which may coincide with one of the harmonics of the above forces, resulting in increased noise level. Because of the nonuniformity of the core steel, vibrations may be excited, both in the plane of the core and normal to it. The paper sets out to show how these natural frequencies can be calculated for both directions, taking longitudinal vibrations, shear deformation and rotational inertia into account. A distinction is made between cores having a large overlap at the joints and those having mitred joints with small overlap. The correctness of the mathematical model and the validity of the assumptions made for the calculations were checked on two models and two transformer cores. Satisfactory correlation was achieved between the experimentally determined natural frequencies and those calculated with the help of a computer programme.