Design and FEM simulation study of the electro-thermal excitation resonant beam with slit-structure
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TECHNICAL PAPER
Design and FEM simulation study of the electro-thermal excitation resonant beam with slit-structure Huichao Shi • Shangchun Fan • Weiwei Xing Cheng Li • Jinhao Sun • Zhongwu Jing
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Received: 9 June 2012 / Accepted: 1 October 2012 / Published online: 30 October 2012 Ó Springer-Verlag Berlin Heidelberg 2012
Abstract This paper proposes a slit-resonant beam based on the double clamped resonant beam theory of silicon micro-machined resonant pressure sensors. The slit structure can enhance surface alternating stress in the root area of beam while vibrating. Finite element method (FEM) is applied to calculate the stress concentration magnification, and we carry out a computational study of the effects of size and location of slit structure in terms of mechanical properties of resonant beam, such as stress concentration on resonant beam and natural frequency of resonant beam, as well as sensing performance, such as resonant beam amplitude sensitivity. Our simulations show that the slit structure could strengthen the stress concentration and increase the amplitude detection sensitivity, and the variations of these parameters can substantially influence the performance of slit structure. The research of stress concentration, caused by silt structure, could provide reference for further optimization and design for the resonant beam. Abbreviations L Length of the resonant beam B Width of the resonant beam H Thickness of the resonant beam l Length of slit H. Shi (&) S. Fan W. Xing C. Li J. Sun Z. Jing School of Instrument Science and Opto-electronics Engineering, Beihang University, Beijing 100191, China e-mail: [email protected] H. Shi S. Fan W. Xing J. Sun Z. Jing Science and Technology on Inertial Laboratory, Beihang University, Beijing 100191, China C. Li State Key Laboratory of Virtual Reality Technology and System, Beihang University, Beijing 100191, China
b h s d l/b Rsc Rrsc Fnfr AR pL pT rL rT Sd eðxÞ
Width of slit Thickness of slit Space distance of two slits The distance of slit location from the resonant beam clamped end Aspect ratio (length/width) of the slit Average stress magnification radio Reference average stress magnification radio Natural frequency ratio Single side cross-sectional area of the U-shaped detection resistor Longitudinal piezoresistive coefficient Transverse piezoresistive coefficient Longitudinal stress of the detection resistor Transverse stress of the detection resistor Amplitude detection sensitivity Rate of detection resistance variation
1 Introduction In recent years, the resonant sensor based on measuring resonant frequency attracts many researchers (Langdon 1985; Bouwstra et al. 1990). Silicon micro-machined resonant pressure sensor measures pressure by the change of nature frequency of the resonant beam. It has good characteristics of frequency output (without A/D converter) and easier interface to computers, long term stability, and high repeatability (Qingfeng et al. 2012); However, the resonator of the device must be excited into vibration and
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