# A Comparison between Numerical Simulation Models for the Prediction of Acoustic Behavior of Giant Reeds Shredded

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Phenomenological and Numerical Models’ Descriptions

#### 2.1. Phenomenological Model

_{m}and of the complex wave number k

_{m}, as indicated in the following equations:

- ${\rho}_{0}$ is the density of air (kg/m
^{3}) - c is the sound speed (m/s)
- $Y$ is the porosity
- s is the structure factor
- $\gamma $ = cp/cv is the ratio of the specific heat at a constant pressure and volume of the air
- f is the frequency (Hz)

- c is the sound speed (m/s)
- n is an integer, n = 0 corresponds to the first value of the maximum
- d is the thickness of the sample (m)
- f
_{2n+1}is the corresponding frequency of the first value of the maximum of the measured absorption coefficient (Hz)

- ${R}_{1}$ is the resistivity (Ns/m
^{4}) - $Y$ is the porosity
- ${\rho}_{0}$ is the density of air (kg/m
^{3}) - s is the structure factor
- ${N}_{pr}$ is the Prandtl number

_{m}and the complex wave number k

_{m}have been calculated, we can define the acoustic impedance Z for a porous material, with a thickness of d, as follows:

#### 2.2. Numerical Model

_{1}, …, x

_{n}), called network inputs, into a set of dependent variables y = (y

_{1}, …, y

_{k}), called network outputs. The precise form of these functions depends on the internal structure of the network and on a set of values w = (w

_{1}, …, w

_{n}), called weights. We can therefore write the function of the network in the following form:

- x
_{j}is the jth input - w
_{j}is the jth weight - b is the bias
- y is the output

- An input layer
- A set of hidden layers
- An output layer

## 3. Materials and Methods

#### 3.1. Giant Reeds Characterization

- only wooden parts with an average size of 40 mm long, 10 mm wide, and 3.0 mm thick;
- mixed composed of wooden and bark parts of various sizes;
- only parts of bark.

#### 3.2. Acoustic Feature Measurements

- ${\rho}_{m}$ (kg/m
^{3}) is the apparent density of the material - ${\rho}_{solid}$ (kg/m
^{3}) is the density of the material

#### 3.3. Models Comparison

## 4. Results and Discussion

#### 4.1. Measurement Results

#### 4.2. Phenomenological Model Simulation

#### 4.3. Artificial Neural Network Model

- mean (x) represent the mean of the variable x
- sd (x) is the standard deviation of the variable x

- mean = 0
- standard deviation = 1

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Three layers Artificial Neural Network (ANN) architecture with nodes and weighted connections.

**Figure 3.**Detail of the shredding operations (to the left), and the average size of the crushed material (to the right).

**Figure 4.**Kundt’s tube for the absorbent acoustic coefficient measurement at normal incidence (to the left), and giant reeds loose material in the sample holder (to the right).

**Figure 6.**Sound absorption coefficient values of 4 cm and 8 cm thick samples and for mixed, only wooden part, and only bark.

**Figure 7.**Sound absorption coefficient values comparison between measured and simulated. The figure shows a 4 cm thick sample (

**a**,

**c**,

**e**) and 8 cm thick sample (

**b**,

**d**,

**f**) for only the wooden part (

**a**,

**b**), mixed (

**c**,

**d**), and only bark (

**e**,

**f**).

**Figure 9.**Simulated versus measured sound absorption coefficients. The figure shows a 4 cm thick sample (

**a**,

**c**,

**e**) and 8 cm thick sample (

**b**,

**d**,

**f**) for only the wooden part (

**a**,

**b**), mixed (

**c**,

**d**), and only bark (

**e**,

**f**).

**Table 1.**Resistivity and porosity values for each type of loosed granular material (mixed, only wooden part, and only bark).

Loosed Granular Material | Resistivity [Rayl/m] | Porosity |
---|---|---|

only wooden part | 1100 | 0.35 |

fine mixed | 850 | 0.45 |

only bark | 870 | 0.80 |

RMSE | MAE | Person’s Correlation Coefficient |
---|---|---|

0.300 | 0.253 | 0.666 |

RMSE | MAE | Person’s Correlation Coefficient |
---|---|---|

0.036 | 0.028 | 0.986 |

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**MDPI and ACS Style**

Ciaburro, G.; Iannace, G.; Puyana-Romero, V.; Trematerra, A.
A Comparison between Numerical Simulation Models for the Prediction of Acoustic Behavior of Giant Reeds Shredded. *Appl. Sci.* **2020**, *10*, 6881.
https://doi.org/10.3390/app10196881

**AMA Style**

Ciaburro G, Iannace G, Puyana-Romero V, Trematerra A.
A Comparison between Numerical Simulation Models for the Prediction of Acoustic Behavior of Giant Reeds Shredded. *Applied Sciences*. 2020; 10(19):6881.
https://doi.org/10.3390/app10196881

**Chicago/Turabian Style**

Ciaburro, Giuseppe, Gino Iannace, Virginia Puyana-Romero, and Amelia Trematerra.
2020. "A Comparison between Numerical Simulation Models for the Prediction of Acoustic Behavior of Giant Reeds Shredded" *Applied Sciences* 10, no. 19: 6881.
https://doi.org/10.3390/app10196881