Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Atomistic simulations can be used to compute damping from first principles and gain unprecedented insights into the mechanisms of dissipation. However, the technique is still in its infancy and many foundational aspects remain unexplored. As a step toward addressing these issues, we present here a comparative study of five different methods for estimating damping under isothermal conditions. Classical molecular dynamics was used to simulate the fundamental longitudinal-mode oscillations of nanowires and nanofilms of silicon and nickel at room temperature (300 K) in the canonical ensemble using the Nosé-Hoover thermostat. In the subresonant regime, damping was quantified using the loss tangent and loss factor during steady-state harmonic vibration. The quality factor was obtained by analyzing the spectrum of thermomechanical noise and also from the Duffing-like nonlinearity in the frequency response under harmonic excitation. In addition, the nonlinear logarithmic decrement was obtained from the Hilbert transform of freely decaying oscillations. We discuss the factors that must be considered while selecting simulation parameters, establish criteria for convergence and linearity, and highlight the relative merits and limitations of each method.