Uniaxially Strained Graphene: Structural Characteristics and G-Mode Splitting

The potential use of graphene in various strain engineering applications requires an accurate characterization of its properties when the material is under different mechanical loads. In this work, we present the strain dependence of the geometrical characteristics at the atomic level and the Raman active G-band evolution in a uniaxially strained graphene monolayer, using density functional theory methods as well as molecular dynamics atomistic simulations for strains that extend up to the structural failure. The bond length and bond angle variations with strain, applied either along the zigzag or along the armchair direction, are discussed and analytical relations describing this dependence are provided. The G-mode splitting with strain, as obtained by first principles’ methods, is also presented. While for small strains, up to around 1%, the G-band splitting is symmetrical in the two perpendicular directions of tension considered here, this is no longer the case for larger values of strains where the splitting appears to be larger for strains along the zigzag direction. Further, a crossing is observed between the lower frequency split G-mode component and the out-of-plane optical mode at the Γ point for large uniaxial strains (>20%) along the zigzag direction.

Simulation of the frequency split of the fundamental air cavity mode of a loaded and rolling tire by using steady-state transport analysis

It has been found that when a tire deforms due to loading, the fundamental air cavity mode splits into two due to the break in geometrical symmetry. The result is the creation of fore-aft and vertical acoustic modes near 200 Hz for typical passenger car tires. When those modes couple with structural, circumferential modes having similar natural frequencies, the oscillatory force transmitted to the suspension can be expected to increase, hence causing increased interior noise levels. Further, when the tire rotates, the frequency split is enlarged owing to the Doppler effect resulting from the airflow within the tire cavity. The current research is focused on determining the influence of rotation speed on the frequency split by using FE simulation. In particular, the analysis was performed by using steady-state transport analysis which enables vibroacoustic analysis in a moving frame attached to tire in the frequency domain. The details of the modeling are described and results are given for a tire under different rotation speeds, presented in terms of dispersion curves that illustrate the interaction between structural and acoustical modes. The results are compared to those for static tires and tires spinning without translational velocity to highlight the effects of rolling.

A Novel Method for Estimating and Balancing the Second Harmonic Error of Cylindrical Fused Silica Resonators

The cylindrical resonator gyroscope (CRG) is a type of Coriolis vibratory gyroscope which measures the angular velocity or angle through the precession of the elastic wave of the cylindrical resonator. The cylindrical fused silica resonator is an essential component of the CRG, the symmetry of which determines the bias drift and vibration stability of the gyroscope. The manufacturing errors breaking the symmetry of the resonator are usually described by Fourier series, and most studies are only focusing on analyzing and reducing the fourth harmonic error, the main error source of bias drift. The second harmonic error also is one of the obstacles for CRG towards high precision. Therefore, this paper provides a chemical method to evaluate and balance the second harmonic error of cylindrical fused silica resonators. The relation between the frequency split of the n = 1 mode and the second harmonic error of the resonator is obtained. Simulations are performed to analyze the effects of the first three harmonic errors on the frequency splits. The relation between the location of the low-frequency axis of n = 1 mode and the heavy axis of the second harmonic error is also analyzed by simulation. Chemical balancing experiments on two fused silica resonators demonstrate the feasibility of this balancing procedure, and show good consistency with theoretical and simulation analysis. The second harmonic error of the two resonators is reduced by 86.6% and 79.8%, respectively.