Vibration analysis of two-layered microplate based on the modified couple stress theory using penalty approach

Document Type : Research Article

Authors

1 ,Ph.D. Candidate, Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran.

2 M.Sc. Student, Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran.

3 Assistant Professor, Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran.

Abstract

Predicting the vibration behavior of microsystems is of great importance. In this study, the vibration behavior of a microsensor modeled as a two-layer microplate is investigated. The effect of size has been investigated through the modified couple stress theory. The first natural frequency is extracted using the penalty approach. Boundary conditions are modeled using linear or torsional springs. Finally, changes in the natural frequency of the microsystem are presented according to different values ​​of the microplate parameters such as the thickness of the silicon layer and material of the second layer. The results show that the natural frequency decreases as the thickness of the second layer increases. In addition, despite the different first natural frequencies for different parameters, the natural frequency diagram shows the same behavior in terms of system parameters under various boundary conditions. Finally, the effect of the thicknesses ratio   and material length scale parameters ratio  on the natural frequency is investigated.   Predicting the vibration behavior of microsystems is of great importance. In this study, the vibration behavior of a microsensor modeled as a two-layer microplate is investigated. The effect of size has been investigated through the modified couple stress theory. The first natural frequency is extracted using the penalty approach. Boundary conditions are modeled using linear or torsional springs. Finally, changes in the natural frequency of the microsystem are presented according to different values ​​of the microplate parameters such as the thickness of the silicon layer and material of the second layer. The results show that the natural frequency decreases as the thickness of the second layer increases. In addition, despite the different first natural frequencies for different parameters, the natural frequency diagram shows the same behavior in terms of system parameters under various boundary conditions. Finally, the effect of the thicknesses ratio   and material length scale parameters ratio  on the natural frequency is investigated.   

Highlights

  • Sensor modeling is performed as a two-layer micro-plate.
  • The Rayleigh-Ritz method is used to extract the natural frequency
  • The penalty approach is used to solve the governing equations

Keywords

Main Subjects

References

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Journal of Theoretical and Applied Vibration and Acoustics
Volume 8, Issue 1
January 2022
Pages 1-12

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