Thermoelastic dissipation in stepped-beam resonators

Abstract

In recent years, stepped beam resonators have found broad application in MEMS/NEMS devices. A beam resonator with an undercut at the support, produced due to isotropic etching of the supporting substrate during fabrication, has also been characterized as stepped beam in the literature. The present study deals with thermoelastic dissipations of clamped–clamped stepped beam resonators under adiabatic surface thermal conditions having j (j = 1, 2, …., n) number of sections defined by (j − 1) number of steps along the length. Numerical results are obtained for three different types of stepped beams of rectangular cross-section having single step such as beams with cross-sectional change at the step only in lateral direction (type-1), in bending direction (type-2), and in both lateral and bending directions (type-3) where the section on the right of the step possesses smaller cross-sectional size compared to the other. The obtained results show that Q-factors vary significantly with step positions in all the three types of stepped beams. For constant length, the Q-factor increases in the type-1 while it decreases in other two types of stepped beams as the step position moves from the left support to the right along the length. Moreover, Q-factors in a type-1 stepped beam depend on the widths of different sections and can be higher than a uniform beam of same thickness for some particular step positions. For most common lengths of stepped beams in real applications with the step close to the left support, type-1 stepped beams provide higher quality factors than the other stepped beams provided that they have the same cross-sectional area.