Thermoelastic damping in micromechanical and nanomechanical resonators

Thermoelastic damping (TED) is a fundamental mechanism of material damping in which energy is dissipated by the irreversible conduction of heat across thermoelastic temperature gradients within an oscillating structure. The first studies of TED were conducted over 85 years ago. Since that time, thermoelastic damping has been extensively studied, especially when it became clear in 1990 that TED can be a major mechanism of damping in microelectromechanical systems (MEMS). Nevertheless, as revealed by a careful survey of the literature, many aspects of TED remain to be investigated and understood. In this thesis, four such topics are addressed using a combination of analytical and numerical techniques.For monolithic beams, thermoelastic damping can be computed using a closed-form expression. Similar expressions were lacking for flexural-mode bilayer resonators, consisting of a substrate coated with a thin film, which are widely used in MEMS. To fill this gap in knowledge, a closed-form expression was developed for calculating TED in bilayers, and the formula was used to explore the nature and structure of the thermoelastic dissipation over several decades of frequency in a large set of materials and structures. This exploration showed that TED exhibits a rich variety of spectral features and provided useful information into the existence of multiple well-resolved dissipation peaks. Previously, numerical studies of TED in plates and membranes had concluded that TED can be decreased by subjecting the structures to in-plane tensile stresses. To gain a better understanding of the underlying mechanisms, simple closed-form analytical formulas were developed for the energy dissipated per cycle (ΔW) and TED for nanomembranes subjected to uniform biaxial, in-plane, tensile stresses. The results show that the effects of stress on dissipation are quite subtle: depending on the frequency, ΔW can increase, remain constant, or decrease when the structure is stressed in tension. The majority of the literature on TED is based on a linear analysis of damping. The sparse literature on nonlinear TED focuses on nonlinearities that have their origins in large deformations (that is, geometrical nonlinearities) or due to interactions with other energy domains (for example, electromechanical nonlinearities in electrostatically-actuated microresonators). In this thesis, a new type of dissipative nonlinearity (also called thermal nonlinearity) is studied. A finite-difference scheme was developed to solve the nonlinear governing equation and explore the effects of the dissipative nonlinearity on TED in stress-free silicon microcantilever beams and highly-stressed silicon nitride nanomembranes.Finally, the thesis considers an emerging topic in studies of TED, namely, computing dissipation using large-scale atomistic simulations. Classical molecular dynamics was used to simulate damping in the longitudinal-mode of single-crystal nickel resonators. Isothermal simulations were performed using the Nosé-Hoover thermostat to control the temperature. A protocol was devised for estimating the specific damping capacity and phase angle by identifying the factors that must be considered while selecting simulation parameters, and establishing criteria for convergence and linearity.

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