Next Article in Journal
Microfluidic Biosensor Array with Integrated Poly(2,7-Carbazole)/Fullerene-Based Photodiodes for Rapid Multiplexed Detection of Pathogens
Next Article in Special Issue
A Wireless MEMS-Based Inclinometer Sensor Node for Structural Health Monitoring
Previous Article in Journal
A Partially Distributed Intrusion Detection System for Wireless Sensor Networks
Previous Article in Special Issue
Design and Implementation of a Micromechanical Silicon Resonant Accelerometer
Article Menu

Export Article

Open AccessArticle
Sensors 2013, 13(12), 15880-15897;

Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports

State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Author to whom correspondence should be addressed.
Received: 9 September 2013 / Revised: 4 November 2013 / Accepted: 8 November 2013 / Published: 25 November 2013
(This article belongs to the Special Issue Modeling, Testing and Reliability Issues in MEMS Engineering 2013)
Full-Text   |   PDF [854 KB, uploaded 21 June 2014]


Normally, the boundaries are assumed to allow small deflections and moments for MEMS beams with flexible supports. The non-ideal boundary conditions have a significant effect on the qualitative dynamical behavior. In this paper, by employing the principle of energy equivalence, rigorous theoretical solutions of the tangential and rotational equivalent stiffness are derived based on the Boussinesq’s and Cerruti’s displacement equations. The non-dimensional differential partial equation of the motion, as well as coupled boundary conditions, are solved analytically using the method of multiple time scales. The closed-form solution provides a direct insight into the relationship between the boundary conditions and vibration characteristics of the dynamic system, in which resonance frequencies increase with the nonlinear mechanical spring effect but decrease with the effect of flexible supports. The obtained results of frequencies and mode shapes are compared with the cases of ideal boundary conditions, and the differences between them are contrasted on frequency response curves. The influences of the support material property on the equivalent stiffness and resonance frequency shift are also discussed. It is demonstrated that the proposed model with the flexible supports boundary conditions has significant effect on the rigorous quantitative dynamical analysis of the MEMS beams. Moreover, the proposed analytical solutions are in good agreement with those obtained from finite element analyses. View Full-Text
Keywords: equivalent stiffness; flexible supports; micro-beams; resonance frequency shift; dynamics equivalent stiffness; flexible supports; micro-beams; resonance frequency shift; dynamics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Zhong, Z.-Y.; Zhang, W.-M.; Meng, G. Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports. Sensors 2013, 13, 15880-15897.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Sensors EISSN 1424-8220 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top