A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Effect of different heating methods on deformation of metal plate under upsetting mechanism in laser forming

In a laser forming process, different forming mechanisms have different deformation behaviors. The aim of laser forming is to acquire plane strain under an upsetting mechanism, while a plate undergoes a small bending deformation. In some industrial applications, the bending strain should not occur. To achieve high-precision forming, the deformation behaviors of a metal plate when an upsetting mechanism plays a dominant role are studied in the paper. Several heating methods are proposed to reduce the plane strain difference along the thickness direction and little bending deformation resulting from a small temperature difference between the top and bottom surfaces of the plate. The results show that negligible bending deformation and a uniform plastic plane strain field can be obtained by simultaneously heating the top and bottom surfaces with the same process parameters. A conventional scanning method needs a larger spot diameter and slower scanning speed under the upsetting mechanism, but a smaller spot diameter and quicker scanning speed may be selected using the simultaneous heating method, which can greatly widen the potential scope of process parameters.     

An analytical model based on the similarity in temperature distributions in laser forming

Laser forming of a metal plate involves a complex thermoplastic process. To accurately control the deformation of a metal plate, its temperature distribution must be obtained first. In this paper, three-dimensional finite element method simulations of the temperature field that account for the temperature dependence of the thermal properties of the materials were carried out. By defining a dimensionless temperature T* and a special Y-coordinate Y*, we found that temperature distributions in the Y′ direction are similar for different thicknesses. An analytical model of the temperature of the high-temperature zone in the Y′ direction is derived for the first time based on the similarity of temperature distributions and data obtained from regression analysis. The comparison of analytical and numerical results shows good agreement with respect to temperature distributions. This investigation is of significance for the prediction of a deformation field in future works.     

A novel acoustic emission beamforming method with two uniform linear arrays on plate-like structures

A novel acoustic emission (AE) source localization approach based on beamforming with two uniform linear arrays is proposed, which can localize acoustic sources without accurate velocity, and is particularly suited for plate-like structures. Two uniform line arrays are distributed in the x-axis direction and y-axis direction. The accurate x and y coordinates of AE source are determined by the two arrays respectively. To verify the location accuracy and effectiveness of the proposed approach, the simulation of AE wave propagation in a steel plate based on the finite element method and the pencil-lead-broken experiment are conducted, and the AE signals obtained from the simulations and experiments are analyzed using the proposed method. Moreover, to study the ability of the proposed method more comprehensive, a plate of carbon fiber reinforced plastics is taken for the pencil-lead-broken test, and the AE source localization is also realized. The results indicate that the two uniform linear arrays can localize different sources accurately in two directions even though the localizing velocity is deviated from the real velocity, which demonstrates the effectiveness of the proposed method in AE source localization for plate-like structures.     

Epitaxial growth of high-Tc superconducting Tl-Ca-Ba-Cu-O films by liquid phase epataxial process

Tl-Ca-Ba-Cu-O epitaxial films have been successfully grown on (001) MgO substrate by liquid phase epitaxial (LPE) process. The as-grown films showed an onset of superconductivity at about 140 K and zero resistance at 111 K. X-ray diffraction analysis suggests the films to be highly preferentially oriented with the c-axis perpendicular to the film surface. Observation from transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS) revealed the presence of both Tl-Ca₂Ba₂Cu₃O_y and TlCa₂Ba₃Cu₄O_y phases.     

Synthesis and superconducting properties of bscco including precipitates with high density

Bi₂Sr₂Ca₁Cu₂O _y (2212) superconductors including normal particles with high density were synthesized by a melt process, and the temperature and magnetic field dependence of the critical current density was estimated from the magnetization hysteresis. The temperature dependence of the irreversibility field, B_r, was expressed as (1-T/T_c)^3/2 above 50 K, and became weak below 50 K as compared with that in the single-crystalline (2212). The B_r, in the magnetic field parallel to the c-axis was about one order of magnitude lower than in a magnetic field normal to the c-axis.     

A method for phase reconstruction in the optical three-dimensional shape measurement

In the optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid the phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing the numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

An experimental investigation of underwater pulsed laser forming

Laser forming is a new forming technology, which deforms a metal sheet using laser-induced thermal stresses. This paper presents an experimental investigation of pulsed laser forming of stainless steel in water and air. The effects of cooling conditions on bending angle and morphology of the heat affected zone (HAZ) are studied. It is shown that the case of the top surface in air and the bottom surface immersed in water has the greatest bending angle based on the forming mechanism of TGM. The water layer above the sample decreases the coupling energy, leading to a small bending angle. For a thin water thickness (1 mm), the water effects on the HAZ are limited. As water layer thickness increases (5 mm), the concave shape of the HAZ is more remarkable and irregular because the shock waves by high laser energy heating water are fully developed. However, the area and the depth of the HAZ become less significant when water thickness is 10 mm due to the long pathway that laser undergoes.     

不同晶体取向下纳米压痕的多尺度模拟

采用准连续介质多尺度方法模拟面心立方金属铝单晶薄膜的纳米压痕变形过程.对薄膜分别采用三种不同的晶体取向(分别为x［1 1 1］,y［1 1 0］,z［1 1 2］; x［1 1 2］,y［1 1 1］,z［1 1 0］;x［1 1 0］,y［0 0 1］,x［1 1 0］)，得到载荷-位移响应曲线.加载过程中，对晶体内部变形比较剧烈的部分画出原子图，并从微观角度分析产生剧烈变形的原 关键词： 纳米压痕 准连续介质方法 晶体取向 位错成核     

Quasi-periodic wave solutions,soliton solutions,and integrability to a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation

In this paper, a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation is investigated, which can be used to describe the interaction of a Riemann wave propagating along y-axis and a long wave propagating along x-axis. The complete integrability of the gBK equation is systematically presented. By employing Bell’s polynomials, a lucid and systematic approach is proposed to systematically study its bilinear formalism, bilinear Bäcklund transformations, Lax pairs, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic wave solutions and soliton solutions of the gBK equation are derived. Finally, an asymptotic relation between the periodic wave solutions and soliton solutions are strictly established under a certain limit condition.