Thermoelastic Damping In Laminated Composite Microbeam And Microplate Resonators

The micromechanical resonator is a new type of microelectromechanical system (MEMS), which always operates at the natural frequency. The quality factor is an important parameter in the design of the micromechanical resonator. A higher quality factor means lower energy dissipation, increased sensitivity and improved stability for the system. Damping in MEMS resonators arises from two principal sources, namely external energy dissipation and intrinsic energy dissipation. The external dissipation mechanism includes air damping, anchor damping and surface loss. External dissipations can be minimized by proper design and modifying operating conditions. Thermoelastic damping is an internal energy dissipation mechanism in MEMS, and it cannot be controlled as easily as external dissipation mechanisms. For this reason, thermoelastic damping in MEMS has been an active area of current theoretical research for a long time.As MEMS technologies evolving, there is an increasing use of laminated composite architectures in MEMS devices. Three models for thermoelastic damping are presented in different laminated composite micromechanical resonators, respectively. The main work and contributions are as follows.First, this dissertation focuses on a thin Kirchhoff-Love bilayered microplate micromechanical resonator. The temperature field along the thickness direction in the bilayered microplate is presented using the generalized orthogonal expansion technique. In the framework developed by Bishop and Kinra, the total thermoelastic damping is defined as the total energy dissipated in all layers normalized by the maximum elastic energy stored in all layers. Therefore, an analytical model for thermoelastic damping in the bilayered fully clamped rectangular and circular microplates is developed by computing the energy dissipated and the maximum elastic energy in each layer. For thermoelastic damping in the bilayered cantilever and fixed-fixed microplates oscillating at the first natural frequency, an approximate analytical model is also developed based on Rayleigh’s method. The present analytical model for thermoelastic damping in bilayered microplate is validated by comparing its results with results obtained by the previous model for thermoelastic damping in homogeneous microplate and the numerical model (ANSYS). The results show that the thermoelastic damping spectrum is independent of the length, width (or radius) and the distribution of the external force, it only depend on the thickness of the microplate. Furthermore, the spectrum may exhibit two peaks when the Zener’s modulus of the first layer is much higher/lower than that of the second layer.Second, the dissertation focuses on a general Euler-Bernoulli trilayered microbeam resonator. The temperature filed of the trilayered microbeam with heat conduction only along the z-direction is solved using the generalized orthogonal expansion technique and the Green’s functions. Both methods lead to the same expression. Then an analytical model for thermoelastic damping in the general trilayered Euler-Bernoulli microbeam is developed. The present analytical model in trilayered microbeams is validated by comparing its results with those obtained by the ANSYS model. The limitation of the present analytical model is assessed. Furthermore, the present model for thermoelastic damping in a general trilayered microbeam can be readily reduced to those in homogeneous, bilayered and symmetric trilayered microbeams.Finally, the dissertation focuses on a general thin Kirchhoff-Love trilayered microplate resonator. The temperature filed of the trilayered microplate with heat conduction only along the z-direction is solved using the standard integral transform techniques. The expression of the temperature in the trilayered microplate is similar to that of the trilayered microbeam obtained by the Green’s functions, the difference between them is the term of the stress. Then an analytical model for thermoelastic damping in the general trilayered microplate is developed. The present analytical model in trilayered microbeams is validated by comparing its results with those obtained by the numerical model. The limitations of the present analytical model and the numerical model are assessed, respectively. The normalized temperature and the normalized thermoelastic damping in each layer are investigated. It is found that adiabatic condition is obtained when the time period of vibration much less than the time for thermal relaxation since heat has very little time to diffuse from the "hot" compressional side to the "cold" tensile side before the strain is reversed.