Thermoelastic Damping in Asymmetric Three-Layered Microbeam Resonators

Thermoelastic damping (TED) has been recognized as a significant mechanism of energy loss in vacuum-operated microresonators. Three-layered microbeams are common elements in many microresonators. However, only the model for TED in the three-layered microbeams with symmetric structure has been developed in the past. The first and the third layers in these beams have the same thickness and material properties. Thus, the temperature field is symmetric in these beams. In this paper, an analytical expression for TED in the asymmetric three-layered microbeams is developed in the form of an infinite series. The temperature fields in the asymmetric three-layered microbeams are asymmetric. The total damping is obtained by computing the energy dissipated in each layer. It is seen that the values for TED computed by the present model agree well with those computed by the finite-element model. The limitations of the present model are assessed. A simple model is also presented by retaining only the first term. The accuracy of the simple model is also discussed. The present model can be used to optimize the design of three-layered microbeams.