Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.     

激光干涉任意转角测量信号的获得及误差补偿技术

采用信号处理的方法对激光干涉测角系统的特性进行线性化处理,需要产生两路正交信号。采用空间互相垂直的两套干涉系统获得信号难免会使系统复杂、调整困难,因此提出了一种插值处理方法,可以利用测量得到的一路信号获得线性输出信号。输出信号的非线性误差较处理前大大减小了,但是无法满足高精度测量的要求。还提出了针对误差产生的原因进行的误差补偿技术。实验结果表明,提出的方法可以实现任意转角的高精度测量,光程差的测量误差小于±0 2μm,对应的转角测量误差为0 63″。     

杯突试验机夹紧参数校准技术研究

介绍了杯突试验机夹紧参数校准的工程背景和技术现状,提出了一种用于校准夹紧参数的十字型悬臂梁式力传感器的解决方案,建立了夹紧参数计算的数学模型．对力传感器的应力状态、制作以及整个校准装置的标定、非线性误差修正和测量数据处理等问题进行了论述,为杯突试验机夹紧参数的全面校准提供了充分的技术依据．     

Experimental characterization of non-linear behavior of monolithic glass

This paper presents the results of a combined experimental and analytical study on one-dimensional slender elements of monolithic glass subjected to simultaneous compression and bending, which progressively increased up to the collapse. The experiments were performed on 32 quintuplets; each quintuplet was composed of five identical specimens, while the quintuplets differed from each other in the geometry and glass of the specimens. The load and restraints applied to a specimen of a quintuplet were different from those applied to the other specimens of the same quintuplet; hence, five different types of tests were performed on the 160 specimens. In each test, the load and the displacements were measured continuously.The collapse, which occurred when the maximum tensile stress reached glass tensile strength (first cracking), exhibited large deflections. Cracking always initiated away from the edges, since the tests had been designed to avoid edge effects. The results proved that geometric non-linear behavior of glass members cannot be described using the same model as steel structures. An analytical model was then constructed to describe the behavior of glass members subjected to combined compression and bending, which predicts the load-carrying capacity and allows safety to be assessed.     

Theoretical calculation of acoustic non-linearity parameter B/A of binary mixtures

Acoustic non-linearity parameter B/A is calculated for five binary liquid mixtures using Tong and Dong equation along with the Flory’s statistical theory. Similar to other excess thermodynamical quantities an excess non-linearity parameter (B/A)^E is defined for binary liquid mixtures. The interactions in the liquid mixtures are explained on the basis of the excess non-linearity parameter.     

Bestimmung der Materialkennwerte einer drei-dimensionalen Theorie zur Beschreibung des tertiären Kriechverhaltens austenitischer Stähle auf der Basis der Experimente

Übersicht Eine tensoriell nichtlineare Theorie für tertiäres Kriechen isotroper Werkstoffe ist gegeben. Die anisotropen Kriechschädigungen werden mit einem zweistufigen Schadenstensor beschrieben. Zur Ermittlung der Materialkonstanten der Materialgleichung und Evolutionsgleichung werden einachsige Kriechversuche an Flachproben aus dem austenitischen Stahl X8 CrNiMoNb 16 16 durchgeführt.

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Global structure stability of impact-induced tensile waves in a rubber-like material

^** Corresponding author. Email: makong{at}cityu.edu.hk This paper concerns the global structure stability of impact-generatedtensile waves in a 1D bar made of a rubber-like material. Becausethe stress–strain curve changes from concave to convexas the strain increases, the governing quasi-linear system ofpartial differential equations, though hyperbolic, fails tobe ‘genuinely non-linear’ so that the standard formof the initial-boundary value problem corresponding to impactis not well-posed at all levels of loading. However, Knowles(2002, SIAM J. Appl. Math., 62, 1153–1175) constructedthe solutions of the initial-boundary value problem correspondingto impact. Based on this, in this paper we prove the globalstructure stability of the impact-generated tensile waves constructedby Knowles. The method of the proof is constructive.     

Photopolymerisation kinetics and electro-optical properties in mixtures of dichroic dye-doped nematic liquid crystal and photocurable polymer

This work reports the effect of dye on the photopolymerisation and electro-optical properties of polymer dispersed liquid crystal (PDLC) composite films. Dichroic PDLC (DPDLC) films based on a photocurable polymer and nematic liquid crystal (LC) with an azo dichroic dye were prepared by photopolymerisation-induced phase separation method. Polarising optical microscopy has been used for monitoring the phase separation kinetics and two-phase morphology evolution in the DPDLC system. LC domains with radial structures during initial period of phase separation adopted a resultant morphology of bipolar configuration over the course of polymerisation. The phase separation and morphology of LC domains was found to be dependent on the amount of dye used. Moreover, the addition of small amount of dye reduced the switching voltage, and enhanced the contrast ratio with improved switching time in the PDLC films. It was shown that, under the application of an electric field, the molecular orientation and absorbance of dichroic dye can be controlled in DPDLC to induce non-linearity and colour contrast without the use of polarisers.     

BESⅢ TOF前端读出电子学系统原型设计和实验结果

作为北京谱仪(Beijing Spectrometer, 简称BES)的改造, BESⅢ将把TOF(time-of-flight)测量精度提高到一个新的水平, 总时间分辨不大于90ps. 其中要求前端电子学(Front End Electronics, FEE)对时间测量的不确定性贡献小于25ps. 本文介绍了TOF前端读出电子学系统原型电路的设计和初步的测试结果.     

非线性项在零点非渐进增长的四阶边值问题单侧全局分歧

We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x"+kx"+lx=λh(t)x+g(t, x,λ), 0< t< 1,x(0)=x(1)=x'(0)=x'(1)=0. Under some natural hypotheses on the perturbation function g:(0,1)×R²→R, we show that (λ_k, 0) is a bifurcation point of the above problem. And there are two distinct unbounded continuas, C_k⁺ and C_k^-, consisting of the bifurcation branch C_k from (λ_k, 0), where λ_k is the k-th eigenvalue of the linear problem corresponding to the above problems. As an application of the above result, the global behavior of the components of nodal solutions of the following problem x"+kx"+lx=rh(t)f(x), 0< t< 1, x(0)=x(1)=x'(0)=x'(1)=0 is studied. We obtain the existence of multiple nodal solutions for the problem if f₀=∞, f_∞ ∈ (0, ∞), f₀=f(s)/s, f_∞=f(s)/s.