# Modeling of Acoustic Vibration Theory Based on a Micro Thin Plate System and Its Control Experiment Verification

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis of Thin Plate Vibration

## 3. Finite Element Simulation Analysis

## 4. Experimental Results

#### 4.1. Vibration Mode Experiment

#### 4.2. Single Particle Control

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lee, T.; Kwon, H.B.; Song, W.; Lee, S.; Kim, Y.J. Microfluidic ultrafine particle dosimeter using an electrical detection method with a machine-learning-aided algorithm for real-time monitoring of particle density and size distribution. Lab Chip
**2021**, 21, 1503–1516. [Google Scholar] [CrossRef] - Chu, A.; Nguyen, D.; Talathi, S.S. Automated detection and sorting of microencapsulation via machine learning. Lab Chip
**2019**, 19, 1808–1817. [Google Scholar] [CrossRef] [Green Version] - Barman, U.; Lagae, L.; Jones, B. Capillary stop valve actuation by thermo- pneumatic-pressure for lab-on-chip systems. Microsyst. Technol.
**2021**, 27, 681–692. [Google Scholar] [CrossRef] - Monterosso, M.E.; Futrega, K.; Lott, W.B.; Vela, I.; Williams, E.D.; Doran, M.R. Using the Microwell-mesh to culture microtissues in vitro and as a carrier to implant microtissues in vivo into mice. Sci. Rep.
**2021**, 11, 5118. [Google Scholar] [CrossRef] - Baruffaldi, D.; Palmara, G.; Pirri, C.; Frascella, F. 3D Cell Culture: Recent Development in Materials with Tunable Stiffness. ACS Appl. Bio Mater.
**2021**, 110, 465–471. [Google Scholar] [CrossRef] - Chen, P.; Luo, Z.; Tasoglu, S. Microscale Assembly Directed by Liquid-based Template. Adv. Mater.
**2014**, 26, 5936–5941. [Google Scholar] [CrossRef] [Green Version] - Shen, F.; Li, X.J.; Li, P.C.H. Study of flow behaviors on single-cell Manipulation and shear stress reduction in microfluidic chips using computational fluid dynamics simulations. Biomicrofluidics
**2014**, 8, 021501. [Google Scholar] [CrossRef] [Green Version] - Jia, W.N.; Neild, A. Multiple outcome particle manipulation using cascaded surface acoustic waves (CSAW). Microfluid. Nanofluid.
**2021**, 25, 16. [Google Scholar] - Yiannacou, K.; Sariola, V. Controlled Manipulation and Active Sorting of Particles Inside Microfluidic Chips Using Bulk Acoustic Waves and Machine Learning. Langmuir
**2021**, 37, 4192–4199. [Google Scholar] [CrossRef] - Xu, D.; Cai, F.Y.; Chen, M. Acoustic manipulation of particles in a cylindrical cavity: Theoretical and experimental study on the effects of boundary conditions. Ultrasonics
**2019**, 93, 18–25. [Google Scholar] [CrossRef] - Ding, X.Y.; Lin, S.C.S.; Kiraly, B. On-chip manipulation of single microparticles, cells, and organisms using surface acoustic waves. Proc. Natl. Acad. Sci. USA
**2012**, 109, 11105–11109. [Google Scholar] [PubMed] - Hu, J.H. An introduction to acoustic micro/nano manipulations. Appl. Phys.
**2016**, 6, 114–118. [Google Scholar] [CrossRef] - Zhang, X.; Halvorsen, K.; Zhang, C.Z. Mechanoenzymatic Cleavage of the Ultralarge Vascular Protein von Willebrand Factor. Science
**2009**, 324, 1330–1334. [Google Scholar] [CrossRef] [Green Version] - Yang, A.; Moore, S.D.; Schmidt, B.S. Optical Manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides. Nature
**2009**, 457, 71–75. [Google Scholar] [CrossRef] - Zhu, X.; Li, N.; Yang, J.; Chen, X. Revolution of trapped particle in counter-propagating dual-beams optical tweezers under low pressure. Opt. Express
**2021**, 29, 11169–11180. [Google Scholar] [CrossRef] - Wright, W.H.; Sonek, G.J.; Berns, M.W. Parametric study of the forces on microspheres held by optical tweezers. Appl. Opt.
**1994**, 33, 1735–1748. [Google Scholar] - Zhukov, A.; Ipatov, M.; Churyukanova, M.; Kaloshkin, S.; Zhukova, V. Giant magnetoimpedance in thin amorphous wires: From manipulation of magnetic field dependence to industrial applications. J. Alloys Compd.
**2014**, 586, S279–S286. [Google Scholar] [CrossRef] - Snezhko, A.; Aranson, I.S. Magnetic Manipulation of self-assembled colloidal asters. Nat. Mater.
**2011**, 10, 698–703. [Google Scholar] [CrossRef] - Khademhosseini, A.; May, M.H.; Sefton, M.V. Conformal coating of mammalian cells immobilized onto magnetically driven beads. Tissue Eng. Part A
**2005**, 11, 1797–1806. [Google Scholar] [CrossRef] [Green Version] - Hu, N.; Wang, Y.; Li, J.; Wei, Q.; Jiang, Y.; Ma, L.; Yu, Z.; Zhou, K.; Long, H. Manipulation of nanostructured carbon films as field emitters in an electric-and-magnetic-field-assisted chemical vapor deposition process. Surf. Coat. Technol.
**2019**, 359, 459–467. [Google Scholar] - Chladni, E. Entdeckungen ber die Theorie des Klanges Weidmanns Erben und Reich; Bey Weidmanns Erben und Reich: Leipzig, Germany, 1787. [Google Scholar]
- Tuan, P.H.; Wen, C.P.; Chiang, P.Y.; Yu, Y.T. Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers. J. Acoust. Soc. Am.
**2015**, 1379, 2113–2123. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Luo, Y.; Feng, R.; Li, X.; Liu, D. TA simple approach to determine the mode shapes of Chladni plates based on the optical lever method. Eur. J. Phys.
**2019**, 40, 065001. [Google Scholar] [CrossRef] - Bialek, J.M. Nonlinear Continuum Mechanics for Finite Element Analysis. Nucl. Fusion
**1998**, 38, 776. [Google Scholar] [CrossRef] - Biro, O.; Preis, K. On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents. IEEE Trans. Magn.
**1989**, 25, 3145–3159. [Google Scholar] [CrossRef] - Geng, J.P.; Tan, K.; Liu, G.R. Application of finite element analysis in implant dentistry: A review of the literature. J. Prosthet. Dent.
**2001**, 85, 585–598. [Google Scholar] [CrossRef] - Hughes, T.R. The finite element method: Linear static and dynamic finite element analysis. Prentice-Hall
**2000**, 19, 096004. [Google Scholar] - Prathap, G. The Finite Element Method in Structural Mechanics; Springer: Dordrecht, The Netherlands, 1993. [Google Scholar]
- Schötzau, D. Mixed finite element methods for stationary incompressible magneto-hydrodynamics. Numer. Math.
**2004**, 96, 771–800. [Google Scholar] - Hu, W.N.; Ho, S.L. Extension of the Concept of Windings in Magnetic Field–Electric Circuit Coupled Finite–Element Method. IEEE Trans. Magn.
**2010**, 46, 2119–2123. [Google Scholar] - Rachid, F.; Noureddine, B.; Jean, B. Case Study of Laser Hardening Process Applied to 4340 Steel Cylindrical Specimens Using Simulation and Experimental Validation. Case Stud. Therm. Eng.
**2017**, 11, 15–25. [Google Scholar]

**Figure 3.**Analysis of mesh convergence. (

**a**) Square plate with mesh. (

**b**) The maximum eigenfrequency versus the number elements.

**Figure 13.**Analysis of experimental error. (

**a**) Area change of node line in simulation and experiment; (

**b**) Error histogram.

**Figure 14.**Experimental of non-contact manipulation of single particle. (

**a**) Before frequency excitation; (

**b**) During frequency excitation; (

**c**) End of frequency excitation.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jiao, X.; Tao, J.; Sun, H.; Sun, Q.
Modeling of Acoustic Vibration Theory Based on a Micro Thin Plate System and Its Control Experiment Verification. *Sustainability* **2022**, *14*, 14900.
https://doi.org/10.3390/su142214900

**AMA Style**

Jiao X, Tao J, Sun H, Sun Q.
Modeling of Acoustic Vibration Theory Based on a Micro Thin Plate System and Its Control Experiment Verification. *Sustainability*. 2022; 14(22):14900.
https://doi.org/10.3390/su142214900

**Chicago/Turabian Style**

Jiao, Xiaodong, Jin Tao, Hao Sun, and Qinglin Sun.
2022. "Modeling of Acoustic Vibration Theory Based on a Micro Thin Plate System and Its Control Experiment Verification" *Sustainability* 14, no. 22: 14900.
https://doi.org/10.3390/su142214900