# On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures

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## Abstract

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## 1. Introduction

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- detection of the occurrence of an unsafe irregularity;
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- identification of the geometric location of the irregularity;
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- determination of the magnitude or severity of the irregularity;
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- prognostic estimation of the remaining service life/strength.

_{w}(the velocity of the longitudinal or transverse acoustic waves in the wedge) must be smaller than c

_{phase}(the phase velocity of a desired wave mode at a selected frequency in the thin-wall structure). This can limit either the choices of wedge materials appropriate for the generation of a desired mode or the availability of modes that can be generated with a given wedge material. Secondly, spurious signals, resulting from wave reverberation inside the wedge, may deteriorate the quality of the useful signal, that is, the intended applied wave. Thirdly, due to beam spreading of acoustic waves propagating through the wedge to the structure’s surface, other wave modes beyond the mode of interest may be generated. This statement is confirmed by the results of [26], where it is reported that at a large enough wedge-specimen contact area, the undesirable aperture effects can appear.

## 2. The Experimental Investigation of Acoustic Waves Excited in the Plastic Panel under Study

^{®}), its mechanical properties were measured in a series of tests using a testing machine and further numerically processed. Used in subsequent experiments, the angle beam wedge actuator Olympus V414-SB-ABWS-3-45 was tested alone to reconstruct its characteristics, which were used in the development of its finite-element prototype. At the final stage, the angular and radial intensity distributions of the wave fields generated by this actuator in a plastic plate were investigated.

#### 2.1. Determination of Elastic Properties for the Material of the Studied Panel

^{st}bending vibration modes were used to calculate the Young’s modulus using the classical formula for the Euler–Bernoulli beam. The observable discrepancy between the moduli, which were calculated according to the different methods, did not exceed 3.5%. A comparison of the moduli measured for the specimens carved along two perpendicular directions of the sheet of material under study proved that the material can be considered quasi-isotropic. All data for the studied specimens are summarized in Table 1.

#### 2.2. Reconstruction of the Wedge Actuator Structure and Electro-Mechanical Properties

#### 2.3. Experimental Study on the Directivity of Acoustic Waves Excited by the Wedge Actuator in a Plastic Panel

## 3. Numerical Study of Acoustic Wave Propagation

#### 3.1. Dispersion Analysis of Acoustic Waves That Can be Excited in the Plastic Panel Under Study

#### 3.2. Finite Element Analysis of Acoustic Wave Propagation in the Studied Quasi-Isotropic Panel

#### 3.3. Analysis of Directivity forA_{0} Lamb and SS0 Horizontally Polarized Waves Excited by the Angle Beam Wedge Actuator

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The plastic panel under study: (

**a**) schematic view; (

**b**) photograph of studied plastic panel with installed angle beam wedge actuator and one pair of sensors.

**Figure 4.**Two kinds of the actuator’s driving signals used for determination of the generated wave speeds and of the actuator’s directivity: (

**a**) tone burst signal; (

**b**) signal with a smooth increase and stabilization of the amplitude. Both signals have the carrying frequency 30 kHz.

**Figure 5.**The dispersion curves for the wavespeed (

**a**) and wavelength (

**b**) of the Lamb wave A0 that can be excited in the studied panel at the frequencies 10–100 kHz together with the values of the wavespeeds and wavelenghts, which are computed by the postprocessing of FE simulation.

**Figure 6.**The dispersion curves for the wavespeed (

**a**) and wavelength (

**b**) of the horizontally polarized SS0 wave that can be excited in the studied panel at the frequencies 10–100 kHz together with the results of FE simulation.

**Figure 8.**The normalized directivity diagrams for the Lamb A0 waves (

**a**,

**c**,

**e**) and for the horizontally polarized SS0 waves (

**b**,

**d**,

**f**) at the modeled eigenfrequencies of actuator: 15 (

**a**,

**b**), 30 (

**c**,

**d**) and 65 kHz (

**e**,

**f**).

**Figure 9.**The radial distributions of the out-of-plane (

**a**,

**c**,

**e**) and in-plane (

**b**,

**d**,

**f**) amplitude displacements under footprint of angle beam wedge actuator exciting the studied plastic panel at the excitation frequencies 15 (

**a**,

**b**), 30 (

**c**,

**d**), and 65 kHz (

**e**,

**f**).

Young’s Modulus, GPa | Poisson Ratio | Density, kg/m^{3} |
---|---|---|

7.4 ± 1.1 | 0.33 ± 0.04 | 1230 ± 42 |

Actuator’s Part | Young’s Modulus, GPa | Poisson Ratio | Mass Density, kg/m^{3} | Loss Factor |
---|---|---|---|---|

Body | 6.0 | 0.33 | 1500 | 0.075 |

Backing layer | 50 | 0.1 | 7500 | 0.15 |

Matching layer | 6.0 | 0.3 | 1500 | 0.025 |

Lucite sound path | 4.0 | 0.33 | 1200 | 0.025 |

Active element (PZT-5H) | The elasticity, coupling, and relative permittivity matrices contain all data | 7500 | 0.15 |

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**MDPI and ACS Style**

Shevtsov, S.; Chebanenko, V.; Shevtsova, M.; Kirillova, E.; Rozhkov, E. On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures. *Actuators* **2019**, *8*, 64.
https://doi.org/10.3390/act8030064

**AMA Style**

Shevtsov S, Chebanenko V, Shevtsova M, Kirillova E, Rozhkov E. On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures. *Actuators*. 2019; 8(3):64.
https://doi.org/10.3390/act8030064

**Chicago/Turabian Style**

Shevtsov, Sergey, Valery Chebanenko, Maria Shevtsova, Evgenia Kirillova, and Evgeny Rozhkov. 2019. "On the Directivity of Acoustic Waves Generated by the Angle Beam Wedge Actuator in Thin-Walled Structures" *Actuators* 8, no. 3: 64.
https://doi.org/10.3390/act8030064