Mechanical behavior analysis of a clamped-clamped micro-beam with stepped viscoelastic layer under electrostatic excitation

Document Type: Research Paper


Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Mofatteh Avenue, P.O. Box 15719-14911, Tehran, Iran



In this study, static deflection, natural frequency and nonlinear vibration in bi-layer clamped-clamped microbeam are investigated. In this configuration, the second layer is the viscoelastic layer which covers a part of the microbeam length. This model is the main element of many chemical microsensors. The governing equations of motion for the system are obtained by Lagrange method and discretized using the assumed mode method. The non-uniform micro-beam modes shape are used as the comparison function in the assumed mode method. Initially, considering the DC voltage, system static response and natural frequency around the static position are obtained. Then, considering the AC voltage, the dynamic response around the dynamic position is calculated by both analytical (perturbation method) and numerical methods (Rung-kutta) and compared for validation purposes. The effect of different geometrical parameters of the viscoelastic layer on the static and dynamic behaviors of the system is also analyzed. The results indicate that the dimensions and location of the viscoelastic layer significantly affect the static and dynamic behavior of the system. Therefore, by using this property and considering the application of microsensors, their behaviors can be made efficient. For sensors operating based on resonance frequency shift, the optimum shift of frequency state can be obtained by varying the dimensions and position of the viscoelastic layer. Moreover, time of response can be optimized when the system is operating based on changes in the capacity of a capacitor. The results also represent that convergence in the assumed mode method used in this paper is feasible even using a single mode, whereas in previous works and using the Galerkin method, convergence was fulfilled in the presence of 3 modes.


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Volume 51, Issue 2
December 2020
Pages 486-497
  • Receive Date: 31 August 2020
  • Revise Date: 11 October 2020
  • Accept Date: 15 October 2020