# Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Study

#### 2.1. Vibration Decomposition

#### 2.2. Nonlinear Identification

## 3. Materials and Methods

^{3}and 240 GPa, respectively. The beam has a rectangular geometry, 80 × 12.75 mm, with a thickness of 0.08 mm. The analysis is carried out in two different fluid media, namely air and water. Thus, the terms “dry” and “wet” will be used here to represent the beam in air and liquid environments, respectively. The air and water density are 1.26 kg/m

^{3}and 997 kg/m

^{3}, respectively.

#### 3.1. Experimental Setup

#### 3.2. Numerical Simulation

## 4. Nonlinear System Identification

#### 4.1. Dry Model Analysis

#### 4.2. Wet Model Analysis

## 5. Analytical Approximation Methods

#### 5.1. Analytical Model

#### 5.2. Validation of Natural Frequencies

#### 5.3. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) The time series of velocity at $x$ = 8 cm, and the 3D plot of velocity in various frequency and beam length of (

**b**) the experimental model and (

**c**) the numerical model.

**Figure 9.**(

**a**) The time series of velocity at $x$ = 8 cm and the frequency series of (

**b**) the experimental model and (

**c**) the numerical model.

**Figure 11.**(

**a**) The time series of velocity at $x$ = 8 cm and the frequency series of (

**b**) the experimental model and (

**c**) the numerical model.

**Figure 13.**(

**a**) Time series of the velocity at the tip of the beam, (

**b**) velocity amplitude vs. frequency at several locations along the beam, and (

**c**) time series of the first and second decomposed signals.

**Figure 15.**The backbone curves estimated from the envelope of (

**a**) the first mode of numerical models, (

**b**) the second mode and (

**c**) the third mode of the experimental models.

**Figure 16.**The damping curves extracted from, (

**a**,

**b**) the numerical models and (

**c**) the experimental models.

**Figure 21.**(

**a**) The backbone curve, and the damping curves with respect to (

**b**) displacement and (

**c**) velocity.

Dry | ||

Exp. (Hz) | Calc. (Hz) | Error (%) |

12.0313 | 11.5328 | 4.1431 |

71.9531 | 72.2747 | 0.4469 |

202.2656 | 202.3712 | 0.0522 |

393.7500 | 396.5668 | 0.7154 |

Wet | ||

Exp. (Hz) | Calc. (Hz) | Error (%) |

2.7344 | 2.6935 | 1.4947 |

18.6719 | 16.8799 | 9.5972 |

55.3125 | 47.2642 | 14.5506 |

96.1719 | 92.6190 | 3.6943 |

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**MDPI and ACS Style**

Syuhri, S.N.H.; Zare-Behtash, H.; Cammarano, A.
Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification. *Vibration* **2020**, *3*, 521-544.
https://doi.org/10.3390/vibration3040032

**AMA Style**

Syuhri SNH, Zare-Behtash H, Cammarano A.
Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification. *Vibration*. 2020; 3(4):521-544.
https://doi.org/10.3390/vibration3040032

**Chicago/Turabian Style**

Syuhri, Skriptyan N. H., Hossein Zare-Behtash, and Andrea Cammarano.
2020. "Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification" *Vibration* 3, no. 4: 521-544.
https://doi.org/10.3390/vibration3040032