ANALYSIS OF THE EFFECT OF THE THERMAL AXIAL FORCE ON THE THERMOELASTIC DAMPING IN BI-LAYERED MICRO BEAMS

In recent years, there have been many publications on the TED of composite laminated beam/plate resonators. However, the contribution of the thermal axial force (or thermal membrane force) on the thermoelastic damping (TED) in the resonators were neglected in all those investigations. It is well known that if the distribution of material properties along the thickness is asymmetric about the geometric midplane of a beam/plate resonator then the physical neutral surface will deviate from it. As a result, the temperature field in the resonator arising in the thermoelastic coupling vibration will produce both the thermal bending moment and the thermal axial/membrane force each of them will produce the TED. In this paper, based on the Euler-Bernoulli beam theory and the classical heat conduction theory, mathematical formulations for the thermo-elastically coupled free vibration of bi-layered laminated micro beams with rectangular cross sections are established in which the contribution of the thermal axial force on the internal energy dissipation is considered accurately. Then, analytical solutions of the thermal axial force and bending moment are found in terms of the geometric quantities representing the beam deformation. Furthermore, the complex frequency of the system and the TED represented by the inverse quality factor are obtained. As an example of numerical analysis, a bi-layered micro beam with homogenous layers of silver (Ag) and silicon nitride (Si₃N₄) is selected to quantitatively examine the effects of the thermal axial force on the TED by changing the volume fractions of the laminas and the total thickness of the beam. The numerical results show that neglection of the thermal axial force will underestimate the TED in the bi-layered beam resonators. Especially, for the resonator with the volume fraction of the silver at 70% (that of the silicon nitride at 30%), the TED will be underestimated about 16.3% if the thermal axial force is neglected.