Analysis of bias DC voltage effect on thermoelastic damping ratio in short nano-beam resonators based on nonlocal elasticity theory and dual-phase-lagging heat conduction model

摘要

Thermoelastic damping (TED) is a fundamental dissipation mechanism in microano-scale resonators. Therefore, it is crucial to minimize this dissipation in design of these resonators. The problem has been formulated by the nonlocal theory of elasticity to take into account the small scale effect. Moreover, the Timoshenko beam model has been used to capture the transverse shear deformation and rotary inertia effects. The coupled thermoelastic equations have been derived using the generalized thermoelasticity theory based on dual-phase-lagging heat conduction model for transverse vibration of an electrostatically deflected short beam. A step-by-step linearization method has been used to escape from the nonlinearity. Afterwards, the Galerkin's weighted residual method has been applied to discretize the coupled dynamic equations of a beam resonator with both ends clamped and isothermal. Then, the complex-frequency approach has been utilized to obtain eigenvalue solution and TED ratio. The numerical results addressing importance of the nonlocal effect on the TED ratio of the short beam resonators have been presented.