Finite element modelling of atomic force microscope cantilever beams with uncertainty in material and dimensional parameters

Copyright © 2014 by Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, PolandThe stiffness and the natural frequencies of a rectangular and a V-shaped micro-cantilever beams used in Atomic Force Microscope (AFM) were analysed using the Finite Element (FE) method. A determinate analysis in the material and dimensional parameters was first carried out to compare with published analytical and experimental results. Uncertainties in the beams’ parameters such as the material properties and dimensions due to the fabrication process were then modelled using a statistic FE analysis. It is found that for the rectangular micro-beam, a ±5% change in the value of the parameters could result in 3 to 8-folds (up to more than 45%) errors in the stiffness or the 1st natural frequency of the cantilever. Such big uncertainties need to be considered in the design and calibration of AFM to ensure the measurement accuracy at the micron and nano scales. In addition, a sensitivity analysis was carried out for the influence of the studied parameters. The finding provides useful guidelines on the design of micro-cantilevers used in the AFM technology.The research was supported by Sichuan International Research Collaboration Project (2014HH0022)

Electro-spraying and catalytic combustion characteristics of ethanol in meso-scale combustors with steel and platinum meshes

© 2018 Elsevier Ltd An experimental study on electro-spraying and catalytic combustion of ethanol at meso-scale is carried out. The electro-spraying process of ethanol is visualized and four typical spraying modes are identified. Based on droplet size measurements by a Phase Doppler Anemometer, the spraying at the cone-jet or multi-jet mode is suitable for meso-scale combustion. Two meso-combustors without and with the platinum catalyst, denoted as combustor A and combustor B, respectively, are designed to conduct the comparative experiments. The flame temperature at the cone-jet mode is higher than those at other modes when equivalence ratio φ = 1.0, and for the combustor with catalyst, fuel-lean conditions are favorable for stable combustion. It is also found that the carbon monoxide mole fraction in the exhaust decreases by at least 25% due to the catalytic effect. At the cone-jet electro-spraying mode, the combustion efficiencies of ethanol reach the highest value for both combustor A and combustor B due to smaller droplet size and more uniform droplet size distribution. Under the same conditions, combustion efficiency of ethanol can be improved by 4.5% for combustor B, which proves that the platinum catalyst can accelerate the decomposition of ethanol

Regular Composition for Slice-Regular Functions of Quaternionic Variable

A regular composition for slice regular function is introduced using a non commutative version of the Faa` di Bruno's Formul

Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate $\gamma$ for the KHI decreases with increasing the width of velocity transition layer ${D_{v}}$ but increases with increasing the width of density transition layer ${D_{\rho}}$. After the initial transient period and before the vortex has been well formed, the linear growth rates, $\gamma_v$ and $\gamma_{\rho}$, vary with ${D_{v}}$ and ${D_{\rho}}$ approximately in the following way, $\ln\gamma_{v}=a-bD_{v}$ and $\gamma_{\rho}=c+e\ln D_{\rho} ({D_{\rho}}<{D_{\rho}^{E}})$, where $a$, $b$, $c$ and $e$ are fitting parameters and ${D_{\rho}^{E}}$ is the effective interaction width of density transition layer. When ${D_{\rho}}>{D_{\rho}^{E}}$ the linear growth rate $\gamma_{\rho}$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].Comment: Accepted for publication in PR

Optimized Design Method of Microstrip Parallel-Coupled Bandpass Filters with Compensation for Center Frequency Deviation

Abstract An optimized design method is presented to compensate for the open-end effect in parallel-coupled microstrip bandpass filters. The analysis of the relationship between center frequency deviation and microstrip open-end effect is given. Based on the theoretical analysis, a design example of 10GHz bandpass filter is presented, which has proved the validity of this method