A new mechanism of energy dissipation in nanomechanical resonators due to the Casimir force

Abstract

In this study, we report a new energy dissipation mechanism of nanomechanical resonators due to the Casimir effect originating from quantum fluctuation of the vacuum electromagnetic field at the nanoscale. An analytical study on the evaluation of the Casimir effect-induced energy loss in nanobeam resonators undergoing in-plane flexural vibration is presented. Two-dimensional elastic wave theory is employed to determine the energy transmission from the vibrating resonator to the substrate. Fourier transform and Green's function technique are adopted to solve the problem of wave motions on the surface of the substrate excited by the Casimir force. Analytical expressions of the Casimir effect-induced energy loss in terms of the quality factor, taking into account both pressure wave propagation in the noncontact substrate and shear wave propagation in the supporting substrate, as well as linear and nonlinear terms of time-varying Casimir force, have been derived. Effects of beam geometry, initial separation gap, and structural boundary conditions on energy loss are examined. Results of the present study demonstrate that the Casimir effect-induced energy loss plays an important role in the dissipation of the nanobeam resonators, in which the influence of shear wave propagation is remarkable. Also, as reflected by our results, the influence of nonlinear terms of time-varying Casimir force on the energy dissipation cannot be neglected for large-amplitude vibration, which is obviously a feature of nonlinear damping. Furthermore, we propose a possible way to experimentally measure the Casimir force by using the energy dissipation mechanism due to the Casimir force.