Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Analysis of norditerpenoid alkalods in processing Radix Aconiti Lateralis preparata with Radix Glycyrrhizae Preparata by electrospray ionization tandem mass spectrometry

Norditerpenoid alkaloids in the processing of Radix aconiti lateralis preparata with Radix glycyrrhizae preparata was studied by electrospray ionization tandem mass spectrometry. A method of ESI-MS couple with internal standard was applied for semi quantitative analysis of norditerpenoid alkaloids before and after processing. The combined-decoction-to single-decoction-ratios of the relative abundance of toxic hypaconitine, mesaconitine and aconitine were 5. 67%, 4. 05% and 4. 88%, respectively. The chemical changes of processing can been comprehensive observed by ESI-MS/MS analysis. The scientific basis of reducing the toxicity of Radix aconiti lateralis preparata with Radix glycyrrhizae preparata was enlightened by compareing with the single-decotion, the combined-decoction and residue for the compatibility of Radix aconiti lateralis preparata and Radix glycyrrhizae preparata.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Nonequilibrium microstructures and their evolution in a Fe-Cr-W-Ni-C laser clad coating

The laser-solidified microstructural and compositional characterization and phase evolution during tempering at 963 K were investigated using an analytical transmission electron microscope with energy dispersive X-ray analysis. The cladded alloy, a powder mixture of Fe, Cr, W, Ni, and C with a weight ratio of 10:5:1:1:1, was processed with a 3 kW continuous wave CO2 laser. The processing parameters were 16 mm/s beam scanning speed, 3 mm beam diameter. 2 kW laser power, and 0.3 g/s feed rate. The coating was metallurgically bonded to the substrate, with a maximum thickness of 730 mu m, a microhardness of about 860 Hv and a volumetric dilution ratio of about 6%. Microanalyses revealed that the cladded coating possessed the hypoeutectic microstructure comprising the primary dendritic gamma-austenite and interdendritic eutectic consisted of gamma-austenite and M7C3 carbide. The gamma-austenite was a non-equilibrium phase with extended solid solution of alloying elements and a great deal of defect structures, i.e. a high density of dislocations, twins, and stacking faults existed in gamma phase. During high temperature aging, in situ carbide transformation occurred of M7C3 to M23C6 and M6C. The precipitation of M23C6, MC and M2C carbides from austenite was also observed.

Analytical Interaction of the Acoustic Wave and Turbulent Flame

A modified resonance model of a weakly turbulent flame in a high-frequency acoustic wave is derived analytically. Under the mechanism of Darrieus-Landau instability, the amplitude of flame wrinkles, which is as functions of the expansion coefficient and the perturbation wave number, increases greatly independent of the 'stationary' turbulence. The high perturbation wave number makes the resonance easier to be triggered but weakened with respect to the extra acoustic wave. In a closed burning chamber with the acoustic wave induced by the flame itself, the high perturbation wave number is to restrain the resonance for a realistic flame.

A Numerical Model of Rapid Solidification Processing of Ni-Al Alloy in Planar Flow Casting

A numerical model has been developed for simulating the rapid solidification processing (RSP) of Ni-Al alloy in order to predict the resultant phase composition semi-quantitatively during RSP. The present model couples the initial nucleation temperature evaluating method based on the time dependent nucleation theory, and solidified volume fraction calculation model based on the kinetics model of dendrite growth in undercooled melt. This model has been applied to predict the cooling curve and the volume fraction of solidified phases of Ni-Al alloy in planar flow casting. The numerical results agree with the experimental results semi-quantitatively.

Tailoring of dendritic microstructure in solidification processing by crucible vibration

We analyzed the effects of both natural convection and forced flows on solid–liquid interface morphology during upward Bridgman solidification of metallic alloys. Experiments were carried out on Al–3.5wt% Ni alloy, for a cylindrical sample. The influence of natural convection induced by radial thermal gradient on solidified microstructure was first analyzed as a function of the pulling rate. Then, the influence of axial vibration on solidification microstructure was experimentally investigated by varying vibration parameters (frequency and amplitude). Experimental results demonstrated that vibrations could be used to either attenuate fluid flow in the melt and obtain a uniform dendritic pattern or to promote a fragmented dendritic microstructure. However, no marked effect was observed for cellular growth. This pointed out the critical role of the mushy zone in the interaction between fluid flow and solidification microstructure.

Influence of the Processing Conditions on the Characteristics of the Clad Layers Produced with Laminar Plasma Technology

Laminar plasma technology was used to produce ceramic hardened layers of Al2O3-40% mass Ni composite powders on stainless steel substrates. In order to investigate the influences of processing conditions on the morphologies of the surface modified layers, two different powder-feeding methods were tested, one with carrier gas called the powder injection method, and the other without carrier gas called powder transfers method. The microscopic investigations demonstrate that the cross-section of the clad layers consists of two distinct microstructural regions, in which the Al2O3 phases exhibit different growth mechanisms. When the powder transfers method is adopted, the number density and volume fraction of the Al2O3 particles increase considerably and their distributions exhibit zonal periodical characteristics. When the powder-feeding rate increases, the microstructure of the Al2O3 phases changes from a small globular to a long needle shape. Finite element simulations show that the transient thermo-physical features of the pool substances, such as solidification rate and cooling rate, influence strongly the mechanisms of the nucleation and the directional growth of the Al2O3 phases in the thermal processing.

Determination of Proper Processing Conditions of Material Surface Heat Treatment Through Finite Element Method

A two-dimensional model has been developed based on the experimental results of stainless steel remelting with the laminar plasma technology to investigate the transient thermo-physical characteristics of the melt pool liquids. The influence of the temperature field, temperature gradient, solidification rate and cooling rate on the processing conditions has been investigated numerically. Not only have the appropriate processing conditions been determined according to the calculations, but also they have been predicted with a criterion established based on the concept of equivalent temperature area density (ETAD) that is actually a function of the processing parameters and material properties. The comparison between the resulting conditions shows that the ETAD method can better predict the optimum condition.

Numerical and Analytical Study on the Pull-in Instability of Micro-Structure under Electrostatic Loading

The one-mode analysis method on the pull-in instability of micro-structure under electrostatic loading is presented. Taylor series are used to expand the electrostatic loading term in the one-mode analysis method, which makes analytical solution available. The one-mode analysis is the combination of Galerkin method and Cardan solution of cubic equation. The one-mode analysis offers a direct computation method on the pull-in voltage and displacement. In low axial loading range, it shows little difference with the established multi-mode analysis on predicting the pull-in voltages for three different structures (cantilever, clamped-clamped beams and the plate with four edges simply-supported) studied here. For numerical multi-mode analysis, we also show that using the structural symmetry to select the symmetric mode can greatly reduce both the computation effort and the numerical fluctuation.

Three-Dimensional Modeling of Heat Transfer and Fluid Flow in Laminar-Plasma Material Re-Melting Processing

Modeling study is performed concerning the heat transfer and fluid flow for a laminar argon plasma jet impinging normally upon a flat workpiece exposed to the ambient air. The diffusion of the air into the plasma jet is handled by using the combined-diffusion-coefficient approach. The heat flux density and jet shear stress distributions at the workpiece surface obtained from the plasma jet modeling are then used to study the re-melting process of a carbon steel workpiece. Besides the heat conduction within the workpiece, the effects of the plasma-jet inlet parameters (temperature and velocity), workpiece moving speed, Marangoni convection, natural convection etc. on the re-melting process are considered. The modeling results demonstrate that the shapes and sizes of the molten pool in the workpiece are influenced appreciably by the plasma-jet inlet parameters, workpiece moving speed and Marangoni convection. The jet shear stress manifests its effect at higher plasma-jet inlet velocities, while the natural convection effect can be ignored. The modeling results of the molten pool sizes agree reasonably with available experimental data.

Numerical Simulation of Transient Thermal Features in the Remelting Processing of Stainless Steel

应用有限元方法对层流等离子体射流不锈钢表面重熔工艺中的瞬态热物理现象进行了数值模拟研究.针对不同加热距离,确定了材料熔化和凝固过程中的瞬态温度场、温度梯度和凝固率的时间和空间分布特征.通过引入等效温度面积密度概念,研究了不锈钢重熔热处理的适合条件.结果表明,9～13mm的范围是较为适宜的加热距离,该结果与试验观察基本符合.

Analytical Study of Idealized Two-Dimensional Cellular Detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general.

Preliminary Investigations on Low-Pressure Laminar Plasma Spray Processing

The usual plasma spraying methods often involve entrainment of the surrounding air into the turbulent plasma core and result in coated materials having relatively high porosity and low adhesive strength. Therefore, exploration of new plasma spraying methods for fabricating high quality coatings to meet the requirement of special applications will be quite important. In this study, an alternative plasma spraying method, i.e. the low-pressure laminar plasma spraying process, is investigated and used in an attempt for spraying thermal barrier coatings (TBCs). Investigations on the characteristics of the laminar plasma jets, feeding methods for the ceramic powder and the formation process of the individual quenched splats have been carried out. The properties of the TBCs sprayed by laminar plasma jet process, such as the adhesive strength at the interface of the ceramic coating/bond coat, the surface roughness and microstructure, are examined by tensile tests and scanning electron microscope (SEM) observations.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.