Size-dependent damping of a nanobeam using nonlocal thermoelasticity: extension of Zener, Lifshitz, and Roukes’ damping model

Abstract

Thermoelastic damping is an important issue for micro-/nanoscale mechanical resonators. In this work, an Euler–Bernoulli beam with different types of mechanical boundary conditions at the two ends is adopted. Once it bends, the half compressed (stretched) will be heated (cooled), then a transverse heat conduction appears, and energy dissipation occurs. First, size-dependent thermoelasticity based on generalized thermodynamics is introduced by combining the nonlocal elasticity and hydrodynamic heat-conductive model heat conduction, and the governing equations of the nonlocal thermal Euler–Bernoulli beam are sequently formulated. Second, an analytical solution to the inverse quality factor is obtained by using the complex-frequency approach, and it is observed that the solution is related to the nonlocal parameter of both elastic and thermal fields, as well as material constants. Meanwhile, another numerical method to get the inverse quality factor is proposed. Third, the effects of nonlocal parameters of both thermal and elastic fields, the height of the beam, and the material constants on the quality factor are evaluated. Finally, conclusive remarks are summarized. The predicted results are expected to be beneficial to micro-/nanomechanical resonators design.