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An efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems

Lookup NU author(s): Dr Harriet Grigg, Dr Barry Gallacher


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The design of high-Q resonators such as Xylophone Bar Resonators (XBRs) capable of being fabricated using Micro-Electro-Mechanical Systems (MEMS) processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance. This paper is concerned with vibration analysis and Q optimisation of an XBR, with the method extending directly to other planar frames and straightforwardly to more complex structures. The Rayleigh–Ritz method is discussed in some detail, first treating the discrete case, followed by developing and applying a kinematical procedure to an L-frame structure. Attention is given to geometric interpretation of the Rayleigh–Ritz procedure and to developing an intuitive understanding the method before turning to the XBR case. Having developed an approximation for system dynamics, the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support Qfactor. Natural frequencies, mode shapes, and support Q values are presented and compared to Finite Element models of the same problem, with excellent agreement observed at substantially lower computational cost. For the first time in the literature, the geometric impedance tuning principle underlying the XBR design is validated and quantified, including sensitivity to manufacturing error.

Publication metadata

Author(s): Grigg HTD, Gallacher BJ

Publication type: Article

Publication status: Published

Journal: Journal of Sound and Vibration

Year: 2014

Volume: 333

Issue: 19

Pages: 4724-4749

Print publication date: 14/09/2014

Online publication date: 22/05/2014

Acceptance date: 29/03/2014

ISSN (print): 0022-460X

ISSN (electronic): 1095-8568

Publisher: Elsevier


DOI: 10.1016/j.jsv.2014.03.040

Notes: First author 37 page paper in a high impact Q1 journal. One chapter of thesis.


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