Investigation on Low Frequency Bandgap of Coupled Double Beam with Quasi-Zero Stiffness for Power Transformer Vibration Control

Abstract

To suppress low frequency vibration and noise generated by power transformer in residential area and achieve environment protection standards, a double-beam metamaterial is proposed, which is fabricated through periodically coupling silicon steel sheet and aluminum beams with Belleville quasi-zero stiffness spring (BQZSS). The double-beam metamaterial can be assembled with iron core of transformers as a whole to obtain the design of a low-noise transformer. Performing static analysis, the mechanical model of BQZSS is established and the relationship between restoring force, stiffness, and displacement can be obtained. Then, the mechanical properties of BQZSS are verified with the finite element method. On this basis, the governing equations of the unit cell of the double-beam metamaterial are derived using Euler–Bernoulli beam theory. According to Bloch theorem and boundary conditions, the dispersion relation of the double-beam metamaterial is deduced, and behaviors of flexural wave propagation in beams are investigated. The effects of structure parameters on bandgaps and dispersion properties are studied, and the low frequency vibration bandgap mechanism is revealed. Finally, the frequency response function (FRF) of the double-beam metamaterial with a finite length is calculated in ANSYS to verify the bandgap characteristics given by a theoretical model. The results show that the double-beam metamaterial can yield multiple low frequency bandgaps at 100 Hz, 200 Hz, 300 Hz, and 500 Hz for suppression of flexural vibration components of transformers, which benefits from Bragg scattering (BS) and the blend of BS and LR mechanisms. The opening and closing of the low frequency bandgaps and the attenuation constants within bandgaps can be tuned by choosing parameters of beams. These findings suggest that the coupling between beams can lead to novel dispersion properties, which provides a new control approach for low frequency vibration and noise in power transformer.