Sensors and Actuators A 109 (2003) 156–164 An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations

This paper presents an analytical model for support loss in clamped–free (C–F) and clamped–clamped (C–C) 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 (λT). Through the combination of these two theories and the Fourier transform, closed-form expressions for support loss in C–F and C–C beam resonators are obtained. Specifically, closed-form expression for the support loss in a C–C 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