Periodic sticking motion in a two-degree-of-freedom impact oscillator

Periodic sticking motions can occur in vibro-impact systems for certain parameter ranges. When the coefficient of restitution is low (or zero), the range of periodic sticking motions can become large. In this work the dynamics of periodic sticking orbits with both zero and non-zero coefficient of restitution are considered. The dynamics of the periodic orbit is simulated as the forcing frequency of the system is varied. In particular, the loci of Poincaré fixed points in the sticking plane are computed as the forcing frequency of the system is varied. For zero coefficient of restitution, the size of the sticking region for a particular choice of parameters appears to be maximized. We consider this idea by computing the sticking region for zero and non-zero coefficient of restitution values. It has been shown that periodic sticking orbits can bifurcate via the rising/multi-sliding bifurcation. In the final part of this paper, we describe three types of post-bifurcation behavior which occur for the zero coefficient of restitution case. This includes two types of rising bifurcation and a border orbit crossing event.     

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.

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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.     

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.