Experimental analysis of the steady-state behaviour of beam systems with discontinuous support

This paper deals with the experimental analysis of the long-term behaviour of periodically excited linear beams supported by a one-sided spring or an elastic stop. Numerical analysis of the beams showed subharmonic, quasi-periodic and chaotic behaviour. Furthermore, in the beam system with the one-sided spring three different routes leading to chaos were found. Because of the relative simplicity of the beam systems and the variety of calculated nonlinear phenomena, experimental setups are made of the beam systems to verify the numerical results. The experimental results correspond very well with the numerical results as far as the subharmonic behaviour is concerned. Measured chaotic behaviour is proved to be chaotic by calculating Lyapunov exponents of experimental data.

---

Sommario Il presente lavoro concerne l'analisi sperimentale del comportamento a regime di travi lineari, su supporti elastici nonlineari discontinui, eccitate periodicamente. L'analisi numerica dei sistemi in esame ha evidenziato risposte subarmoniche, quasi-periodiche e caotiche, nonchè l'esistenza, nel caso di trave con una molla laterale, di tre differenti percorsi verso il caos. La relativa semplicità dei sistemi di travi ha consentito di procedere ad una verifica sperimentale dei risultati numerici e della varietà dei fenomeni nonlineari da essi evidenziati. La corrispondenza fra risultati sperimentali e numerici è molto buona nel caso di risposta subarmonica. Il comportamento caotico sperimentale è stato convalidato attraverso il calcolo degli esponenti di Lyapunov a partire dai relativi dati.

     

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions

Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg-Landau equation) and a nonlinear hyperbolic equation (the sine-Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact of boundary noise on the system evolution is also discussed.     

Effects of coating amount and particle concentration on the impact toughness of polypropylene/CaCO3 nanocomposites

The effects of the coating amount of surfactant and the particle concentration on the impact strength of polypropylene (PP)/CaCO₃ nanocomposites were investigated. Nanocomposites prepared with monolayer-coated CaCO₃ nanoparticles had the best mechanical properties, including Young’s modulus, tensile yield stress and impact strength because of the good dispersion of the nanoparticles in the polymer matrix. In addition, the good dispersibility of the monolayer-coated nanoparticles allowed us to study the effects of particle concentration on the impact strength of the nanocomposites. H-PP and E-PP, which were the low and high molecular weight PPs, respectively, were used as polymer matrices. Critical particle concentrations of 10 and 25 wt% corresponding to an abrupt increase in the impact toughness were determined for the E-PP and H-PP nanocomposites, respectively. Good particle dispersion in a polymer matrix is the prerequisite for the calculation of the critical ligament thickness using the critical particle concentration. We propose that the observed critical ligament thickness actually corresponds to the critical thickness at which the plane-strain to plane-stress transition occurs. In addition, the critical ligament thickness of a nanocomposite depends on the properties of the polymer matrix, such as molecular weight, even for a given type of polymer.     

Double impact periodic orbits for an inverted pendulum

There exist many types of possible periodic orbits that impact at the walls for the inverted pendulum impacting between two rigid walls. Previous studies only focused on single impact periodic orbits and symmetric periodic orbits that bounce back and forth between the two walls. They respectively correspond to Types I and II orbits in the Chow, Shaw and Rand classification. In this paper we discuss two types of double impact periodic orbits that have not been studied before. The equations need to be solved for double impact orbits are transcendental and it is very hard to see the structure of the solutions. Consequently the analysis of double impact orbits is much more difficult than that of Types I and II orbits. A combination of analytical and numerical methods is employed to investigate the existence, stability and bifurcations of these orbits. Grazing bifurcations, which do not present for Types I and II orbits, are also observed.     

Dual channel detection–diode array and mass spectroscopy (El or Cl)–in HPLC

Simultaneous recording of UV and mass spectra (electron impact or chemical Ionization) in conventional HPLC is described. The LC eluent is divided into two parts; one is directed into a diode array detector and the other is introduced into the mass spectrometer via a particle beam interface. The analysis of the steroid esters of a pharmaceutical formulation illustrates the possibilities of dual channel (DAD-MS) HPLC detection.     

Numerical aspects of improvement of the unsteady pipe flow equations

The paper presents an analysis of some recently proposed improvements of the water hammer equations, which concern the friction term in the momentum equation. A comparison of the experimental data and numerical results shows that the required damping and smoothing of the pressure wave cannot be obtained by modification of the friction factor only. In order to evaluate the significance of the introduced improvements into the momentum equation, the accuracy of the numerical solution has been analysed using the modified equation approach. The analysis shows why the physical dissipation process observed in the water hammer phenomenon cannot be reproduced with the commonly used source term in Darcy–Weisbach form, representing friction force in the momentum equation. Therefore, regardless of the proposed form of the friction factor for unsteady flow, the model of water hammer improved in such a way keeps its hyperbolic character. Consequently, it cannot ensure the expected effects of damping and smoothing of the calculation head oscillations. Copyright © 2007 John Wiley & Sons, Ltd.     

Impact response of an interface crack in a hybrid piezoelectric laminate

Summary  In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results for the dynamic stress intensity factor show the influence of the geometry and electric field. Received 29 June 2001; accepted for publication 3 December 2001     

五种典型硝基苯胺类炸药的静电势与撞击感度的关系研究

利用HONDO程序包,采用从头算法对硝基苯胺类炸药的分子结构和电偶极矩等性质以及 C-NO2键中点静电势等进行计算,讨论了硝基苯胺类炸药C-NO2键中点静电势最大值Vmidmax与其实验撞击感度之间的关系.研究表明:对于硝基苯胺类炸药,不宜单独用C-NO2键中点静电势最大值Vmidmax来表征撞击感度的变化,但可以用静电势最大值Vmidmax与电偶极矩的积来确定其撞击感度的变化趋势,讨论了硝基和胺基的相对位置以及硝基和胺基的数目对这类炸药感度的影响.     

抗冲聚丙烯微结构的研究

利用¹³C NMR对抗冲聚丙烯的微结构进行了研究.结果表明,由于抗冲聚丙烯聚合工艺的差别,4个抗冲聚丙烯样品中的乙烯链段的序列分布也不同.根据抗冲聚丙烯的¹³C NMR谱,计算出了丙烯段的次甲基和甲基的峰强度,由此建立了表征抗冲聚丙烯共聚物中丙烯链段的立构规整度的方法.     

硝基甲苯类炸药C-NO2键中点的静电势

利用HONDO程序包,采用从头计算法对硝基甲苯类炸药的分子结构及其C-NO2键中点的静电势进行了计算,讨论了硝基甲苯类炸药C-NO2键中点的静电势最大值Vmidmax与其实验撞击感度之间的关系.研究表明:对于硝基甲苯类炸药,可用其分子C-NO2键中点的静电势最大值Vmidmax来确定其撞击感度的变化趋势.以静电势为判据,讨论了硝基和甲基数目以及硝基和甲基的相对位置对这类炸药撞击感度的影响.