Local resonant acoustic band gaps in two-dimensional square-arranged Helmholtz resonators array

In this study, a limited phononic crystal vibration isolation (LPCVI) model is constructed based on a vibration isolator used in the field of rail transit, and analyses of the characteristics of the bandgap, the vibration isolation effect, and the vibrational energy transfer of the model are presented. In this paper, the Boltzmann integration theory and the Bloch theorem are used to establish a mathematical model that analyzes the band structure based on the viscoelastic damping of the system. Additionally, by comparing the practical finite periodic structure model and the conventional mass-spring-damping vibration isolation model, explicit forms of the vibration isolation coefficients of the models are derived. It is found that when the external excitation frequency is within the forbidden band range, the vibration isolation coefficient of the LPCVI system with a harmonic oscillator is much smaller than that of the vibration isolation system with a general mass-spring. Furthermore, the Newmark-β integration method is adopted to solve the vibration equation of the LPCVI model. The energy input, distribution, and output of the system are obtained when the energy is under excitation in the forbidden band and bandpass frequencies. It is found that the external excitation does both positive and negative works on the vibration isolation system within a certain period under the action of the central frequency excitation of the forbidden band; therefore, the energy cannot be input into the isolation system. This makes it possible to achieve effective vibration isolation at lower frequencies.

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A study of the vibration isolation performance of a limited phononic crystal vibration isolator based on local resonance theory

Zhao

Gao

Wang

et al. 2020

Journal of Applied Physics

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Experiments on defect mode of one-dimensional phononic crystal containing Helmholtz resonators

Gao¹,

Zeng²,

Ze-Min³

et al. 2013

Acta Phys. Sin.

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In this paper, a local resonant phononic crystal is designed and fabricated based on Helmholtz resonators. Experiment is carried out to study the defect mode of the structure, in which a point defect is introduced. Due to the coupling of the defect cell and perfect cells, a narrow pass band appears in the local resonant forbidden band. Meanwhile, acoustic energy localization effect is observed around the defect resonator at the frequency of defect mode which changes with the defect parameter. However, the defect mode is close to the edge of the forbidden band, the localized energy is high. In addition, if the resonant frequency of the defect unit is smaller than that of the perfect unit, the localized energy is mostly distributed in the waveguide. In contrast, the energy is mostly localized in the resonators when the defect unit frequency is larger than that of the perfect unit. This work will be of help for designing new acoustic functional devices of filters and concentrators.

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Low-frequency band gaps in phononic crystals with composite locally resonant structures

Zhang¹,

Wu²

2013

Acta Phys. Sin.

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In this paper, a novel locally resonant structure with composite units is proposed. Formation mechanisms and low-frequency characteristics of the band gaps in the proposed structure are investigated using finite element methods. Frequency positions of band gaps depend on natural frequencies of the corresponding locally resonant modes. And the gap width is related to both the Q factor of the locally resonant modes and the interaction strength in-between the locally resonant structural units. Phononic crystal structures with composite units exhibit multiple resonances and band gaps in low-frequency range, depending on the arrangement of locally resonant units. Due to the mode degeneracy of the vertical and horizontal local resonances, the composite structures possess band gaps below 200Hz with the total gap width more than 60% and the lowest frequency down to 18Hz. The structures and results provide a new effective method for phononic crystal structures to obtain broadband gaps in low-frequency range.

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Local resonant acoustic band gaps in two-dimensional square-arranged Helmholtz resonators array

Cited by 9 publications

References 17 publications

A study of the vibration isolation performance of a limited phononic crystal vibration isolator based on local resonance theory

A study of the vibration isolation performance of a limited phononic crystal vibration isolator based on local resonance theory

Experiments on defect mode of one-dimensional phononic crystal containing Helmholtz resonators

Low-frequency band gaps in phononic crystals with composite locally resonant structures

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