# Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Models

#### 2.1. Structure Model and Basic Governing Equations

#### 2.2. Band-Gap Formulations of an Infinite LR Plate

#### 2.3. Vibration and Radiation Formulations of a Finite LR Plate

## 3. Results and Discussion

#### 3.1. Band-Gap Properties

^{3}, approximately twice that of the base plate’s density. As shown above, the introduction of water fluid decreases the Bragg frequency from 1973.2 Hz to 1386.7 Hz, and this decrease is also caused by the attached mass. By comparing Equation (44) to (47), a general relation of Bragg frequency between the plate with water fluid and without fluid can be given as

#### 3.2. Vibration and Sound Radiation Performance

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic of a finite locally resonant plate baffled in an infinite rigid baffle and single-side submerged in the infinite fluid (SSB: simply supported boundary).

**Figure 3.**Dispersion curves of the water-loaded locally resonant plate and corresponding band gap (BG).

**Figure 4.**Dispersion curves of the locally resonant plate (

**a**) with air load and without load, and (

**b**) with water load and without load (w.o.: without, BG: band gap).

**Figure 5.**(

**a**) Dispersion curves of the LR plate with water load and without (w.o.) fluid load; (

**b**) normalized effective density (d.c.: dispersion curve).

**Figure 6.**Normalized effective density with water load as a function of frequency with frequency range (

**a**) from 0 Hz to 1 kHz and (

**b**) from 460 Hz to 560 Hz (BG: band gap; HM: homogeneous; LR: locally resonant).

**Figure 8.**(

**a**) Band-gap frequency and (

**b**) band-gap width of the locally resonant plate with and without (w.o.) water fluid as a function of the resonant frequency.

**Figure 9.**(

**a**) Average velocity level and (

**b**) radiation power level of the water-loaded LR plate (BG: band-gap).

**Figure 10.**Comparison of (

**a**,

**b**) average velocity level and (

**c**,

**d**) radiation power level between water-loaded locally resonant (LR) plate and water-loaded homogeneous (HM) plate (BG: band-gap).

**Figure 11.**Comparison of (

**a**,

**b**) average velocity level and (

**c**,

**d**) radiation power level between locally resonant (LR) plate with fluid and that without fluid (BG: band gap; w.o.: without).

**Figure 12.**Comparison of radiation efficiencies between a water-loaded locally resonant (LR) plate and a water-loaded homogeneous (HM) plate (BG: band gap).

**Figure 13.**Spatial distributions of the normalized displacement (norm. disp.) at 518 Hz in (

**a**) a homogeneous plate and (

**b**) a locally resonant plate.

**Figure 15.**(

**a**) Average velocity level and (

**b**) radiation power level of a water-loaded homogeneous (HM) plate and a water-loaded locally resonant (LR) plate with damped and undamped periodic resonators.

**Figure 16.**(

**a**) Average velocity level and (

**b**) radiation power level of a water-loaded locally resonant plate with various damping parameters of the resonator.

Band-Gap Start Frequency | Band-Gap Cut-off Frequency | Band-Gap Width | |
---|---|---|---|

Present model | 510.1 Hz | 512.8 Hz | 2.7 Hz |

FEM model | 510.0 Hz | 512.8 Hz | 2.8 Hz |

Band-Gap Start Frequency | Band-Gap Cut-off Frequency | Band-Gap Width | |
---|---|---|---|

without fluid load | 510.1 Hz | 561.6 Hz | 51.5 Hz |

with air load | 510.1 Hz | 561.6 Hz | 51.5 Hz |

with water load | 510.1 Hz | 512.8 Hz | 2.7 Hz |

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**MDPI and ACS Style**

Guo, Z.; Sheng, M.; Zeng, H.; Wang, M.; Li, Q. Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate. *Machines* **2023**, *11*, 590.
https://doi.org/10.3390/machines11060590

**AMA Style**

Guo Z, Sheng M, Zeng H, Wang M, Li Q. Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate. *Machines*. 2023; 11(6):590.
https://doi.org/10.3390/machines11060590

**Chicago/Turabian Style**

Guo, Zhiwei, Meiping Sheng, Hao Zeng, Minqing Wang, and Qiaojiao Li. 2023. "Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate" *Machines* 11, no. 6: 590.
https://doi.org/10.3390/machines11060590