Low frequency band gap of twin-beam metamaterial based on butterfly quasi-zero stiffness spring

To reduce the low frequency vibration and noise of transformers in residential areas and promote the environmental protection of transformers, a double-beam metamaterial with periodic configuration of Belleville quasi-zero stiffness spring (BQZSS) is proposed to achieve vibration and noise reduction for transformers. By establishing the theoretical model of statics of BQZSS, the analytical expressions of its restoring force-displacement and stiffness-displacement are deduced, and the quasi-zero stiffness characteristics at equilibrium position are analyzed as well. The mechanical properties of the BQZSS are verified through finite element simulation. On this basis, using Euler-Bernoulli beam theory, the cellular dynamics model of the double-beam metamaterial composed of BQZSS periodically coupled with silicon steel sheet and aluminum alloy beams is established. According to the continuous boundary conditions and Bloch theorem, the dispersion relation of the bending vibrations of double-beam metamaterial is derived, and its corresponding low frequency bandgap mechanism is investigated. Finally, the low frequency bandgap characteristics of the double-beam metamaterial are simulated and analyzed. The results show that the double-beam metamaterial formed by periodically coupling silicon steel sheet and aluminum alloy beams with BQZSSs can yield low frequency bandgap for suppression of low-frequency vibration and noise of transformers, and these bandgaps benefit from both Bragg scattering and local resonance mechanisms, which provides a new control strategy for low-frequency vibration and noise of transformers. © 2023 Chinese Vibration Engineering Society. All rights reserved.