Mathematical Modeling of Deflection of a Beam: A Finite Element Approach

Azizi, Aydin; Dourali, Laaleh; Zareie, Shahin; Rad, Farid Parvari

doi:10.1109/icecs.2009.84

Cited by 2 publications

(1 citation statement)

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“…The eigen-value equation for the mode frequencies has been derived based on the boundary conditions satisfied by the beams. Azizi et al (2009) have presented a finite element approach for solving Euler-Bernoulli equation for beams to find their mode shapes in terms of Hermitian shape functions. In both approaches, the damping effects on the beams have been ignored.…”

Section: Introductionmentioning

confidence: 99%

An experimental analysis of electrostatically vibrated array of polysilicon cantilevers

et al. 2010

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Micromechanical cantilevers are one of the most fundamental and widely studied structures in micro-electromechanical systems. Dynamic response of such cantilevers has long been an interesting subject to researchers and different analytical and experimental approaches have been reported to determine it. Theoretical estimation of different damping mechanisms have been reported over years which are relevant particularly in studying the dynamics of the micro-mechanical structures. Most properties and functionalities of the MEMS devices are invariably dependant on the dynamic response of the devices, which in turn depends on the quality factor of the devices or in other words the overall damping present in the system. This paper presents a thorough experimental analysis of vibration characteristics of micro-mechanical cantilevers of different dimensions. Arrays of polysilicon micro-cantilevers of different dimensions have been designed and fabricated using surface micromachining process. The beams are resonated by electrostatic actuation and their vibration characteristics have been observed using Laser Doppler Vibrometer. Also a thorough analysis of modal behaviour of the beams is presented using analytical approach and finite element method based simulation. Different damping mechanisms have been critically reviewed and a semianalytical estimation of the overall damping is presented. The results are compared with experimental values.

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Section: Introductionmentioning

confidence: 99%