A Floquet–Bloch approach is employed to demonstrate the stop bands for an infinite locally resonant plate. In addition, the effects of the connection stiffness of the unit cells on the band gap and dynamic performance of a locally resonant plate are analysed. The results show that the degree of inhibition of elastic waves in the band gaps increases rapidly when the connection stiffness of the unit cells increases within the scope of the transition stage stiffness. However, outside of the range of transition stage stiffness, the degree of inhibition of elastic waves in the band gaps basically remains unchanged. This discovery widens the application scope for vibration and noise control using locally resonant plates.

The dynamic and vibrational properties of various structures have always been a topic of interest to scholars [

The locally resonant plate is suitable for vibration and noise control within different frequency ranges and has strong vibration and noise absorption ability in a narrow frequency range. However, typical narrowband properties hinder the application of locally resonant plates. To expand applicability, domestic and overseas scholars have proposed various strategies for the expansion of the band-gap frequency range of locally resonant plates. Peng et al. [

This study is presented in four sections. Following the introduction, Section

The locally resonant plate with elastic unit cell edges is shown in Figure

Schematic view of an infinite locally resonant plate.

Definitions of the elements and nodes for a unit cell.

With no consideration of the damping effect, the motion equation of the periodic unit cell under the excitation of a harmonic force is expressed in the following matrix form [

Equation (

The unit cell of the locally resonant plate in this section is composed of a plate and a mass spring system, as shown in Figure

The material properties of the locally resonant plate are given in Table

Material properties and dimensions of the unit cell.

Density | |

Poissonʼs ratio | |

Elasticity modulus | |

Thickness | |

The size of unit cell |

Dispersion surfaces for a locally resonant plate.

Assuming that the support connection stiffness coefficients

The band-gap frequencies of the locally resonant plate vary with different support connection stiffness coefficients of the unit cell.

Figure

The band-gap frequencies of the locally resonant plate vary with different rotation connection stiffness coefficients of the unit cell.

The internal physical mechanisms for these phenomena can be interpreted as follows: the small connection stiffness coefficients actually lead to weak coupling of the unit cells, reducing the interaction of the resonators and the original structure to a certain degree, and the large connection stiffness coefficients lead to a high structural coupling of the unit cells, resulting in no free wave propagation, which is possible in a frequency region around the resonance frequency of the mass spring system.

In this study, a finite plate is derived by repeating the unit cell

Frequency response curves for the locally resonant band-gap plate with different support connection stiffness coefficients of the unit cell.

Frequency response curves for the locally resonant band-gap plate with different rotation connection stiffness coefficients of the unit cell.

The effect of connection stiffness coefficients on the vibration transfer function of the locally resonant plate can be shown by taking the rotation connection stiffness coefficient

The velocity amplitude distribution of the locally resonant plate (

The above discussion proves that there exists a “transition stage stiffness” for the unit cell, within which the band gap and the degree of inhibition of elastic waves increase rapidly when the connection stiffness coefficients of the unit cells increase. Outside of the transition stage stiffness range, the band gap and the degree of inhibition of elastic waves basically remain unchanged.

In this study, a computational model of a locally resonant plate based on the elastic connection of unit cells was established, and the influence of connection stiffness coefficients on the band gap and vibration performance of a local resonant structure was analysed. It was found that the band gaps can be tuned using the connection stiffness of the unit cells, and the bandwidth and degree of inhibition increase rapidly in the range of the transition stage stiffness. The effect of vibration reduction of local resonant structures is not affected if the corresponding connection stiffness coefficients are adjusted above the transition stage. This new discovery is of great significance to the practical application of local resonance plates in vibration and noise control.

The data generated or analysed to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest.

This project was supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN201800726).