# Investigation on the Acoustical Transmission Path of Additively Printed Metals

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Experimental Design and Implementation

_{damp}, of a sinusoidal wave is time-dependent, the following expression (1) can describe the acceleration over time. The widely used logarithmic decrement is not applicable because some of the measured datasets show a superimposed oscillation. With the shown equation, it is possible to calculate the R

^{2}value for each point and thus exclude those data from global evaluation. For comparability, it is assumed that the oscillation could be described as a cosine function, starting (t = 0) with the maximum deflection initiated through the impulse hammer.

_{damp}(t) cos(ω

_{0}t)

_{damp}, an initial function had to be chosen. Referring to the aim of this research approach, which is concerned with the investigation of damping, it had to be an asymptotic function converging to zero. In the context of damped oscillations, first- and second-order (2) exponential functions are widely used.

_{damp}(t) = A

_{1}e

^{d1 t}+ A

_{2}e

^{d2 t}

d

_{1}= D

_{1}ω

_{0}

d

_{2}= D

_{2}ω

_{0}

_{1}and d

_{2}in the exponent are dependent on the damping factors D

_{1}and D

_{2}and the angular natural frequency ω

_{0}.

^{2}parameter, it was free from external acceleration.

## 4. Results

_{1}, A

_{2}, d

_{1}and, d

_{2}were determined. For each geometry variant and each parameter, the distribution and median were calculated. The results of this calculation are shown in Table 1. It can be seen that the influence on energy decay is highly related to the shape of the inner geometry and the orientation of the shapes in relation to excitation.

_{2%}in Table 2.

## 5. Discussion

_{1}and A

_{2}is connected with the geometry variants and seems not to be bonded to a specific shape of inner geometry. A possible reason for this is an external dynamical interspersion in the measurement setup while measuring variants VH4 to VH6. The influence cannot be seen in the evaluation of parameter A

_{2}, which has a lower influence on the decay curve than parameter A

_{1}.

## 6. Conclusions

_{1}. With the aim of damping where a started oscillation is damped as quickly as possible, a high value of parameter d

_{1}seems to be the first criterion for evaluating the damping capacity. Other studies found that the height of the excitation has an important influence on the damping capacity; this could not be proven in this study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Concepts of traditional particle dampers: 1—impact damper; 2—particle damper; 3—multi-unit particle damper.

**Figure 6.**Measurement setup for the free oscillation test and the cross section of a sample. (

**left**: mesurment setup,

**right**: crosssection of sample VH5)

**Figure 9.**Acceleration data and fitted curve for a printed bar with a rectangular inner shape (force- orthogonal).

Measured Sample | d_{1} | A_{1} | d_{2} | A_{2} |
---|---|---|---|---|

Geom VH1: Drawn bar | −280.9 | 0.31 | −48.9 | 0.21 |

Geom VH2: 3D-printed bar | −203.2 | 0.62 | −54.6 | 0.12 |

Geom VH3: 3D-printed bar with rectangular inner shape (force−parallel) | −40.6 | 0.38 | −6.3 | 0.07 |

Geom VH4: 3D-printed bar with rectangular inner shape (force−orthogonal) | −785.4 | 2.62 | −51.8 | 0.19 |

Geom VH5: 3D-printed bar with inner ellipsoidal geometry | −520.0 | 1.19 | −56.1 | 0.04 |

Geom VH6: 3D-printed bar with inner spherical geometry | −617.4 | 1.64 | −37.4 | 0.01 |

Geom VH7: 3D-printed bar with triangular inner shape (top-up) | −282.3 | 0.50 | −0.6 | 0.00 |

Geom VH8: 3D-printed bar with triangular inner shape (top-down) | −397.5 | 0.95 | −28.1 | 0.01 |

Geometry | VH1 | VH2 | VH3 | VH4 | VH5 | VH6 | VH7 | VH8 |
---|---|---|---|---|---|---|---|---|

t_{2%} in sec. | 0.049 | 0.033 | 0.191 | 0.012 | 0.014 | 0.008 | 0.044 | 0.011 |

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**MDPI and ACS Style**

Rehmet, R.; Lorenz, S.; Hahn, V.; Lohrengel, A. Investigation on the Acoustical Transmission Path of Additively Printed Metals. *Appl. Sci.* **2023**, *13*, 180.
https://doi.org/10.3390/app13010180

**AMA Style**

Rehmet R, Lorenz S, Hahn V, Lohrengel A. Investigation on the Acoustical Transmission Path of Additively Printed Metals. *Applied Sciences*. 2023; 13(1):180.
https://doi.org/10.3390/app13010180

**Chicago/Turabian Style**

Rehmet, Raphael, Swenja Lorenz, Vincent Hahn, and Armin Lohrengel. 2023. "Investigation on the Acoustical Transmission Path of Additively Printed Metals" *Applied Sciences* 13, no. 1: 180.
https://doi.org/10.3390/app13010180