| The work presented in this dissertation offers theoretical analysis of thermoelastic dissipation of micro/nano beam resonators operated with linear small-amplitude vibration or non-linear large-amplitude vibration under adiabatic or isothermal surface conditions. The aim is to find better design and better operating conditions for beam resonators of MEMS/NEMS for less thermoelastic dissipation. The beam resonators studied in this dissertation (which have not been studied in existing literature) include hollow tubular beams, solid beams of elliptical, triangular, or arbitrary rectangular cross-section, layered composite beams of circular and rectangular cross-sections, and stepped-beams of rectangular cross-section. For each case, detailed formulas are derived for quality factor (Q-factor) due to thermoelastic dissipation under adiabatic and isothermal surface conditions. In addition, thermoelastic dissipation in beam resonator of rectangular cross-section is analyzed for non-linear large-amplitude vibration under adiabatic or isothermal surface thermal condition with comparison to the results of small-amplitude linear vibration.;The obtained results offer useful guiding ideas for design of beam resonators to achieve higher Q-factor with thermoelastic dissipation. For example, the present results show that, to achieve higher Q-factor , hollow tubular resonators with isothermal and adiabatic surface conditions are best to operate at low and high frequencies, respectively, as compared to beam resonators of solid circular or rectangular cross-section. Beam resonators of elliptical and triangular cross-sections are best to operate at high frequencies compared to solid rectangular cross-sections of same cross-sectional area and width irrespective of surface thermal conditions. In case of layered composite beams under either of the two surface thermal conditions, two-layered circular cross-sections is found better at high frequencies than three-layered rectangular cross-section of same material combination and layer sizes. Results for doubly-clamped stepped-beams show that a real beam resonator of rectangular cross-section with an undercut at a clamped end, known as a stepped-beam with single step having a change in cross-sectional size at the step in lateral direction only, provides higher Q-factor than a uniform beam of same thickness for all real lengths found in the literature. This dissertation also confirms that non-linear large-amplitude vibration is preferable over linear small-amplitude vibration for doubly-clamped beam resonators under adiabatic surface condition for which the Q-factor increases monotonically with amplitude of vibration, while the opposite is true under isothermal surface condition. The large-amplitude effect on thermoelastic dissipation becomes more significant for higher vibration frequencies than lower ones. |
