Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by laser Doppler vibrometer is presented in this paper. Silicon nanobeams test structures are fabricated from silicon-on-insulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value Δ L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including Δ L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to surface effect does not play a role in mechanical elastic behaviour of silicon nanobeams with the thickness larger than 200 nm.     

Mechanical properties an undercut evaluated resonance test and of silicon nanobeams with by combining the dynamic finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Circuit-field coupled finite element analysis method for an electromagnetic acoustic transducer under pulsed voltage excitation

This paper presents an analytical method for electromagnetic acoustic transducers (EMATs) under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation (FFT). In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting’s theorem. Then the currents under different frequencies are calculated according to Ohm’s law and the pulsed current excitation is obtained by inverse fast Fourier transformation (IFFT). Lastly, the sequentially coupled finite element method (FEM) is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board (PCB) coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Further- more, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied.     

Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

梯形截面硅基水平多槽纳米线定向耦合器全矢量分析

定向耦合器是构成各类光子器件的基础元件. 本文采用一种基于电场分量的全矢量有限元法, 分析由梯形截面硅基水平多槽纳米线构成的定向耦合器. 给出了准TE与准TM偶、奇模有效折射率、耦合长度及模场分布, 揭示了其模式的混合特性及模场分布特点. 分析结果表明, 准TE模与准TM模的耦合长度随波导间距的增大均呈指数增长, 其中准TE模的耦合长度对波导侧壁倾角的变化敏感, 而准TM模的耦合长度对槽厚及槽折射率的变化敏感. 恰当选择结构与材料参数, 可实现两偏振态下相同耦合长度, 定向耦合器在偏振无关条件下工作.     

Modal analysis of rib waveguide through finite element and mode matching methods

Two mode solvers based on the finite element and the mode matching methods are compared by way of analyzing rib waveguides. Differences between the normalized propagation constants provided by the two methods are always less than 10^–4 which is at least about one order of magnitude smaller than previously reported values. Results for lossy waveguides and field comparison are also presented.     

用有限电流元法识别HL-2A 装置的等离子体边界

在电流丝模型对HL-2A装置等离子体边界重建取得满意结果[3]、[5]的基础上，本文用有限电流元模型对HL-2A等离子体边界进行了重建研究。计算和实验结果表明，在通常情况下，有限电流元模型比固定电流丝模型的重建误差稍小，前者误差小于3mm，后者误差小于6mm。当部分有限电流元分布在等离子体边界之外时，用有限电流元模型仍然可以成功重建边界。有限电流元的位置在一定范围内变化时，重建的误差都很小。用普通奔腾4 2.4GHz PC机计算一组等离子体放电边界的时间不超过1ms。有限电流元法能准确而快速地识别等离子体的偏滤器位形，这对于HL-2A装置的实时位形控制是基本和重要的。     

有限元在大口径镜面研制中的应用

大口径光学反射镜镜面受自重影响变形较大,研究它在磨制和检测中的支撑结构和形式是非常重要的。采用有限元软件从理论上分析了Φ1330mm平面反射镜和Φ616mm非球面轻量化碳化硅主镜在磨制和检测中的支撑结构和形式,以使反射镜面形变形最小,保证其光学成像质量达到一定的技术要求。通过实际测量Φ616mm非球面碳化硅主镜在不同支撑状态下的面形变化情况,验证了理论分析结果。根据实际效果值用有限元进一步优化组合了最佳的支撑结构和形式,为今后对更大口径反射镜面的磨制和检测提供了指导。     

Optimal design and lifetime calculation of the belt chamber by finite element method

Abstract

A mixed numerical-analytical method for an optimal strength design is presented. Optimal number n of components and optimal radii r_j are calculated for an equivalent cylindrical model of the compound vessel. An iterative numerical method is proposed for evaluation of optimal overlaps Δr_j. A finite element method (FEM) elastic-plastic program has been developed to estimate the vessel lifetime.     

基于有限元分析的大型固体激光器稳定性指标重分配

在大型固体激光器结构稳定性设计中,使用等概率分配方法的分配值作为光学元件稳定性设计指标常常会增加结构设计的难度,造成结构建造的巨大浪费。为此,提出了基于结构有限元分析的稳定性指标重分配方法,即将同一光路中光学元件振动响应引起靶点光束的定位误差作为各自的权重系数,采用线性加权和法对稳定性指标进行重新分配。稳定性指标重分配后,所得到的同一光路中各光学元件的安全系数相等。利用此方法对某大型固体激光装置主机装置靶区一条光路中光学元件的稳定性指标进行了重分配,得到每条光路上光学元件稳定性的安全系数均为1.229,满足结构稳定性设计要求。     

用有效折射率法和有限元法分析多量子阱条形光波导

本文提出了一种快速和精确分析多量子阱(MQW)条形光波导的新算法。它基于有效折射率法和有限元法的结合。首先,由等效的平面波导替换多量子阱条形结构,用有效折射率法从原来问题得到平面波导的折射率分布;然后,用有限元法计算等效结构中E_(mn)~x模和E_(mn)~y模的传播常数和场强分布。文中给出了任意阱数和不同宽度多量子阱的对称结构和不对称结构的结果。     

Functions for patch test in finite element analysis of the Mindlin plate and the thin cylindrical shell

Current patch test for Mindlin plate element only satisfies the zero shear deformation condition. The patch test of non-zero constant shear for Mindlin plate problem cannot be performed. For shell element, the patch test does not even exist. Based on the theory of enhanced patch test proposed by Chen W J (2006), the authors proposed the enhanced patch test function for Mindlin plate and thin cylindrical shell elements. This enhanced patch test function can be used to assess the convergence of the Mindlin plate and cylindrical thin shell elements. Supported by the National Natural Science Foundation of China (Grant Nos. 50479058 and 10672032)     

Analysis of the special hollow-core photonic crystal fibre by finite element method

Two kinds of fabricated hollow-core photonic crystal fibres （HC-PCFs） arc studied using finite element method （FEM） because the structures of the fibres are special, Normalized transmission spectra and transverse intensity distribution of the modes are calculated and measured. And the dispersion characteristics of these two kinds of HC- PCFs were analysed from 400 nm to 800 nm. Simulated and measured results show that the special structure could affect the properties of HC-PCFs, By comparing the simulated values with the measured results, it can be clarified that FEM is feasible and accurate for analysing photonic crystal fibres whose structures are irregular and complex.     

基于等效参数反演的敷设声学覆盖层的水下圆柱壳体声散射研究

应用了一种等效方法计算敷设声学覆盖层无限长圆柱壳体水下声散射特性.等效方法的核心是忽略复杂声学覆盖层内部的声学结构,将其作为具有等效材料参数的均匀阻尼层进行建模,该均匀阻尼层具有和原覆盖层相同的复反射系数.进而,应用COMSOL Multiphysics软件建立敷设均匀阻尼层圆柱壳体的有限元模型并求解其声散射特性.等效方法的关键是等效材料参数的获取.采用充水阻抗管实验和有限元数值实验两种方法获取声学覆盖层贴敷在与壳体具有相同厚度、相同材料背衬条件下的复反射系数,在此基础上,基于遗传算法反演材料的等效参数.研究表明,等效参数具有频变特性,且尽管等效杨氏模量和等效泊松比在频率范围内存在较大波动,但是等效前后复反射系数仍保持一致.为了验证等效方法求解壳体声散射特性的准确性,同时建立了敷设声学覆盖层壳体的完整有限元模型,将覆盖层内部声学结构进行精细建模,并求其声散射特性.结果表明,两种方法求得的形态函数符合得较好,在整个频率范围内平均误差大约为1 d B.     

The microdroplet test: experimental and finite element analysis of the dependance of failure mode on droplet shape

The microdroplet technique is usually designed as a fibre embedded in a drop of resin and subsequently pulled out while the drop is being supported by two knife edges, resulting in either debonding of the droplets from the fibres, or breakage of the fibres before debonding can occur. In this study, the microdroplet technique was performed using a platinum ring with a 40 μm hole instead of the usual two knife edges, giving an axisymmetric geometry, load and stress distribution. Glass/phenolic and glass/polyester composite systems were tested experimentally and subsequent finite element modelling studies were performed to assess the variation of droplet size, and contact angle between the droplet and fibre. It was found that contact angle is of major influence in the proposed failure model. This study characterizes the influence of the contact angle between the droplet and the fibre on the subsequent stress distribution in the microdroplet specimen.     

石墨烯/羟基磷灰石复合材料力学性能的数值研究

为了研究石墨烯/羟基磷灰石复合材料力学性能（弹性模量和泊松比）,开发了石墨烯/羟基磷灰石复合材料的随机分布模型自动生成算法及相应的计算程序;建立石墨烯/羟基磷灰石复合材料的有限元模型,计算添加不同质量分数的石墨烯对复合材料力学性能的影响,通过与实验数据对比验证算法的有效性.结果表明：添加0.25%~1.25%（质量分数）的石墨烯可使复合材料的弹性模量增加12%~50%,表明添加少量石墨烯即能有效地改善羟基磷灰石的力学性能.     

Fundamental accuracy of time domain finite element method for sound-field analysis of rooms

This paper presents an assessment of the accuracy and applicability of a time domain finite element method (TDFEM) for sound-field analysis in architectural space. This TDFEM incorporates several techniques: (1) a hexahedral 27-node isoparametric acoustic element using a spline function; (2) a lumped acoustic dissipation matrix; and (3) Newmark time integration method with an absolute diagonal scaled COCG iterative solver. Sound fields in an irregularly shaped reverberation room of 166 m³ are computed using TDFEM. The computed values and measured values for 125-500 Hz are compared, revealing that the fine structure of the computed band-limited impulse responses agree with measured ones up to 0.1 s, with a cross-correlation coefficient greater than 0.93. The cross-correlation coefficient decreases gradually over time, and more rapidly for higher frequencies. Moreover, the computed decay curves, and the reverberation times, agree well with the respective measured ones, and with a better fit the higher the frequency (up to 500 Hz).     

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors(SRM).Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics,a three-dimensional(3-D)nonlinear viscoelastic constitutive model incorporating with damage is developed.The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm,and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method.A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus.The material subroutine is validated through typical examples.Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy,and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.     

Design and optimization of carbon nanotube/polymer actuator by using finite element analysis

In recent years,actuators based on carbon nanotube(CNT) or graphene demonstrate great potential applications in the fields of artificial muscles,smart switches,robotics,and so on.The electrothermal and photothermal bending actuators based on CNT/graphene and polymer composites show large bending actuations,which are superior to traditional thermaldriven actuators.However,the influence of material parameters(thickness,temperature change,etc.) on the actuation performance needs to be further studied,because it is a critical point to the design and fabrication of high-performance actuators.In this work,finite element analysis(EEA) is employed to simulate the actuation performance of CNT/polymer actuator,which has a bilayer structure.The main focus of this work is to design and to optimize material parameters by using computational method.FEA simulation results show that each layer thickness of actuator has an important influence on the actuation deformation.A maximum curvature of 2.7 cm~(-1) is obtained by simulation,which is much larger than most of the actuator curvature reported in previous experiments.What is more,larger temperature change and larger difference of coefficient of thermal expansion(CTE) between two layers will result in larger bending actuation.This study is expected to provide valuable theoretical reference for the design and realization of CNT-based thermal actuator with ultra-large actuation performance.     

计算超薄镜最接近球面的非球面梯度法及有限元分析

利用超薄镜的弹性变形,通过主动光学技术将超薄球面镜变形为所需精度的非球面镜,可以避开大口径超薄非球面镜的制造难题。在分析了传统的非球面超薄镜最接近球面选择原则的基础上,提出了以非球面梯度作为选择原则的依据。针对一个实例,用非球面梯度法和最小二乘法分别求出两个最接近球面并对它们进行有限元法的变形分析,对它们变形后的面形精度和最大应力进行了比较。结果表明,在相同的边界条件、加载个数和加载位置的条件下,以非球面梯度法求出的最接近球面在变形后不仅应力小,且更有利于提高面形精度。