Summary: Sensors and Actuators A 109 (2003) 156164
An analytical model for support loss in micromachined
beam resonators with in-plane flexural vibrations
Zhili Haoa,, Ahmet Erbilb, Farrokh Ayazia
a School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive, Atlanta, GA 30332-0250, USA
b School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332-0430, USA
Received 18 June 2003; received in revised form 22 September 2003; accepted 24 September 2003
This paper presents an analytical model for support loss in clampedfree (CF) and clampedclamped (CC) micromachined beam
resonators with in-plane flexural vibrations. In this model, the flexural vibration of a beam resonator is described using the beam theory. An
elastic wave excited by the shear stress of the beam resonator and propagating in the support structure is described through the 2D elastic
wave theory, with the assumption that the beam thickness (h) is much smaller than the transverse elastic wavelength (T). Through the
combination of these two theories and the Fourier transform, closed-form expressions for support loss in CF and CC beam resonators
are obtained. Specifically, closed-form expression for the support loss in a CC beam resonator is derived for the first time. The model
suggests lower support quality factor (Qsupport) for higher order resonant modes compared to the fundamental mode of a beam resonator.
Through comparison with experimental data, the validity of the presented analytical model is demonstrated.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Support loss; Beam resonator; Quality factor; Micromachining; Elastic wave; Flexural vibration
Micromachined beam resonators are of great interest for