基于时滞惯性流形的浅拱动力屈曲研究

从动力学观点,浅拱受冲击是一种无穷维或者连续的动力系统,论文针对抛物线浅拱,应用有关薄壁结构的基本理论和非线性几何关系推导并建立其控制微分方程。然后,利用时滞惯性流形的思想,提出一种求解这类强非线性偏微分方程的新方法,即基于时滞惯性流形的非线性Galerkin方法。通过这种方法,把原始方程的解投影到由控制方程中线性算子的特征函数所张成的完备空间内,并构造出无限维子空间内的动力行为与有限维子空间内的动力行为之间的耦合作用,该耦合作用认为高低阶分量间的相互作用并不是一种简单的瞬时行为,而是与模态发展的历史有关。通过数值分析得到：系统存在两个稳定平衡位置,与传统的Galerkin方法相比,所提出的基于时滞惯性流形的非线性Galerkin方法可以大幅度地降低方程的维数,提高计算速度,有效地降低对计算机内存的需求和减少计算时间。某种程度上,时滞惯性流形为系统的非线性动力行为如屈曲、分岔、突跳等动态模拟和数值分析提供了一个新的更为合理的研究手段。     

Discussion of compensating faults in modelling of NMR system reliability

To obtain realistic estimates of reliability of systems with N-tuple Modular Redundancy (NMR) the effect of compensation of logical faults should be considered. Throughout the analyses made up to date, different models of compensating faults have been considered, producing results that are rather impractical and yield very complex mathematical formulas for reliability indices. In this paper a general model is presented that combines the ideas most commonly applied. As a main result some useful estimates are given of upper and lower bounds of reliability indices of NMR systems with compensating faults.     

Planar waveguides formed by Ag+-Na+ ion exchange in nonlinear optical glasses: diffusion and optical properties

All-optical communication systems are the subject of intense research related to the integration of nonlinear optical materials. In sodiocalcic borophosphate glasses that contain niobium oxide and exhibit high nonlinear optical indices, planar waveguides have been formed by a Ag(+)-Na(+) ion-exchange technique. WKB analysis has been used to characterize the diffusion profiles of silver ions exchanged in glass substrate samples chemically by an electron microprobe technique and optically by an M-line technique. These methods permit the Ag(+) penetration depth and diffusion profile shape and index profiles to be determined. The results are analyzed and discussed in relation to Ca(2+) concentration and exchange conditions in glasses. The Ag(+) diffusion in these glasses can be almost entirely controlled for index-profile engineering.     

Computational analysis of geometric nonlinear effects in adhesively bonded single lap composite joints

It is well known that geometric nonlinear effects have to be taken into account when the ultimate strength of single lap composite joints are studied. In the present paper we investigate for which level of loads or prescribed end displacements nonlinear effects become significant and how they appear. These aspects are studied by comparing finite element results obtained from geometric nonlinear models with the results from the linear ones. The well-known software package ANSYS is applied in the numerical analysis together with a self-implemented module in the C++ library Diffpack. Some of the results are also compared with classical analytical theories of idealized joints showing significant differences.The joints examined are made of cross-ply laminates having 0 or 90° surface layers. A combined cross-ply/steel joint and an isotropic joint made of steel are also studied. All the models except the all-steel one are assembled with adhesives, while the latter is welded.Through the investigation a considerable departure from linear behavior has been detected for a large regime of prescribed end displacements or external loads. Geometric nonlinear effects begin to develop for external loads that produces stresses which are far below ultimate strength limits and for average longitudinal strains that are less than 0.5%. It has also been detected that the distribution of materials within the joint has some influence on the nonlinear behavior. Thus, geometric nonlinear methods should always be applied when single lap (or other non-symmetric) composite joints are analyzed.     

Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models

Many dynamic models are used for risk assessment and decision support in ecology and crop science. Such models generate time-dependent model predictions, with time either discretised or continuous. Their global sensitivity analysis is usually applied separately on each time output, but Campbell et al. (2006 [1]) advocated global sensitivity analyses on the expansion of the dynamics in a well-chosen functional basis. This paper focuses on the particular case when principal components analysis is combined with analysis of variance. In addition to the indices associated with the principal components, generalised sensitivity indices are proposed to synthesize the influence of each parameter on the whole time series output. Index definitions are given when the uncertainty on the input factors is either discrete or continuous and when the dynamic model is either discrete or functional. A general estimation algorithm is proposed, based on classical methods of global sensitivity analysis.The method is applied to a dynamic wheat crop model with 13 uncertain parameters. Three methods of global sensitivity analysis are compared: the Sobol'-Saltelli method, the extended FAST method, and the fractional factorial design of resolution 6.     

Decision making in health care using robust parameter design with conditions‐based selection of regression estimators

Health care professionals often use regression methods to quantitatively describe the functional relationships between predictors and outcomes. However, little research investigates the appropriateness of tool application for response‐surface‐based design of experiments, the choice of regression estimators under different environments, and the impact of the determination of optimum conditions, or optimal factor‐level settings, to achieve desirable target outcomes. Robust parameter design (RPD) is an established methodology for determining optimum conditions for a process to achieve specified process targets while minimizing variability of the outcomes. Underlying assumptions for RPD modeling and process conditions should be taken into account when selecting a regression estimator for developing fitted models. If these assumptions are incorrect, then a direct use of estimates obtained has the potential to be problematic, and the results may be potentially catastrophic, particularly when applied to the health care field. Many approaches to RPD in existing literature use ordinary least squares to obtain response functions by assuming normality and moderate variability in the underlying process. Given that some biologic processes are often highly variable and inherently asymmetric, a conditions‐based approach for the selection of a regression estimate technique needs to be explored. This paper examines alternative approaches to regression estimation when the process data indicates that asymmetry or a high degree of process variability exists. The performance of select alternative regression methods is compared using Monte Carlo simulation and numerical analysis.     

Nonlinear Analysis of Woven Fabric-Reinforced Graphite/PMR-15 Composites under Shear-Dominated Biaxial Loads

An elastic-plastic, time-independent, macroscopic, homogenous model of an 8HS woven graphite/PMR-15 composite material has been developed that predicts the nonlinear response of the material subjected to shear-dominated biaxial loads. The model has been used to determine the response of woven composite off-axis and Iosipescu test specimens in nonlinear finite element analyses using a multilinear averaging technique. The numerically calculated response of the specimen was then compared to experimentally obtained data. It has been shown that the numerically calculated stress - strain diagrams of the off-axis specimens are very close to the experimentally obtained curves. It has also been shown that the numerically determined shear stress - strain and load-displacement curves of the woven Iosipescu specimens are close to the experimentally obtained curves up to the point of significant interlaminar damage initiation and propagation. The results obtained in this study clearly demonstrate that the nonlinear material behavior of the graphite/polyimide woven composites subjected to shear-dominated biaxial loading conditions cannot be ignored and should be considered in any stress analysis. The linear-elastic approach grossly overestimates the loads and stresses at failure of these materials in the off-axis and Iosipescu tests. It can be assumed that the same discrepancies will arise in the numerical analysis of the woven composites tested under other biaxial shear-dominated loading conditions using other biaxial test methods.     

Control of chaos in nonlinear systems with time-periodic coefficients

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is desired to be driven to a periodic orbit. This is achieved by employing either a linear or a nonlinear control technique. In the linear method, a linear full-state feedback controller is designed by symbolic computation. The nonlinear technique is based on the idea of feedback linearization. A set of coordinate transformation is introduced, which leads to an equivalent linear system that can be controlled by known methods. Our second idea is to delay the onset of chaos beyond a given parameter range by a purely nonlinear control strategy that employs local bifurcation analysis of time-periodic systems. In this method, nonlinear properties of post-bifurcation dynamics, such as stability or rate of growth of a limit set, are modified by a nonlinear state feedback control. The control strategies are illustrated through examples. All methods are general in the sense that they can be applied to systems with no restrictions on the size of the periodic terms.     

Chaos in dynamic atomic force microscopy

In tapping mode atomic force microscopy (AFM) the highly nonlinear tip-sample interaction gives rise to a complicated dynamics of the microcantilever. Apart from the well-known bistability under typical imaging conditions the system exhibits a complex dynamics at small average tip-sample distances, which are typical operation conditions for mechanical dynamic nanomanipulation. In order to investigate the dynamics at small average tip sample gaps experimental time series data are analysed employing nonlinear analysis tools and spectral analysis. The correlation dimension is computed together with a bifurcation diagram. By using statistical correlation measures such as the Kullback-Leibler distance, cross-correlation and mutual information the dataset can be segmented into different regimes. The analysis reveals period-3, period-2 and period-4 behaviour, as well as a weakly chaotic regime.     

Stability and bifurcation analysis of models for zebrafish somitogenesis

Notch-Delta signaling is indispensable for somitogenesis, which controls the vertebrate segmentation during embryonic development. Several theoretical models have been proposed to explain this interesting process. In zebrafish somitogenesis, genes her1, her7, delta, and their proteins plays the important roles. However, an auto-repression model with time delay involved only by her1/her7 is able to explain zebrafish somitogenesis. This paper will systematically study the dynamics of this model. Specifically we investigate its stability, bifurcation (oscillation), and stability of oscillation. First, the conditions for both stability and bifurcation are presented based on the linearized model. Then three indices for bifurcation of this nonlinear model are derived by using linear functional operator analysis. Finally, the numerical simulations are carried out to illustrate the theoretical results developed in this study.     

Parameter uncertainty effects on variance-based sensitivity analysis

In the past several years there has been considerable commercial and academic interest in methods for variance-based sensitivity analysis. The industrial focus is motivated by the importance of attributing variance contributions to input factors. A more complete understanding of these relationships enables companies to achieve goals related to quality, safety and asset utilization. In a number of applications, it is possible to distinguish between two types of input variables—regressive variables and model parameters. Regressive variables are those that can be influenced by process design or by a control strategy. With model parameters, there are typically no opportunities to directly influence their variability. In this paper, we propose a new method to perform sensitivity analysis through a partitioning of the input variables into these two groupings: regressive variables and model parameters. A sequential analysis is proposed, where first an sensitivity analysis is performed with respect to the regressive variables. In the second step, the uncertainty effects arising from the model parameters are included. This strategy can be quite useful in understanding process variability and in developing strategies to reduce overall variability. When this method is used for nonlinear models which are linear in the parameters, analytical solutions can be utilized. In the more general case of models that are nonlinear in both the regressive variables and the parameters, either first order approximations can be used, or numerically intensive methods must be used.     

Univariate and multivariate process yield indices based on location-scale family of distributions

Several measures of process yield, defined on univariate and multivariate normal process characteristics, have been introduced and studied by several authors. These measures supplement several well-known Process Capacity Indices (PCI) used widely in assessing the quality of products before being released into the marketplace. In this paper, we generalise these yield indices to the location-scale family of distributions which includes the normal distribution as one of its member. One of the key contributions of this paper is to demonstrate that under appropriate conditions, these indices converge in distribution to a normal distribution. Several numerical examples will be used to illustrate our procedures and show how they can be applied to perform statistical inferences on process capability.     

Materials Specification and Analytical Measurement Precision

Abstract

Chemical manufacturing processes are often sensitive to changes in conditions and minor components, for which there may be limited data and no simple relationships. The product specialist has the dilemma of basing raw materials and process specifications either on current practice or intuitive experience, without adequate knowledge that their attainment will ensure the product’s fitness for use.

However, a natural reaction is to demand increasingly tighter specifications and measures of the process capabilities involved. A judgement has to be made of the acceptable level of variability in the measuring process, in relation to the overall variability of the factor to be controlled. There is empirical evidence to suggest that there are limits on the precision to which analytical measurements can be taken and the application of process capability indices may be inappropriate when applied to chemical specifications.

To avoid the false security of over-tight specification limits, which cannot be meaningfully monitored, it is suggested that the specification process should start from the best practical estimate of the test capability for the measurement of the parameter or component being considered. From this, the raw material or process parameter specifications can be calculated, taking account of the balance of risk between the supplier and user.

Departure from specification would then have a basis of veracity and be less likely the subject of the random combination of chance effects. It would highlight areas in which there was a need for a real breakthrough in analytical technique or more robust product design.     

金属橡胶非线性隔振器试验研究与参数分析

研究了变激励条件下金属橡胶非线性隔振器的参数变化。以某型隔振器为研究对象,对其进行了静态试验及不同正弦激励条件下动态试验。借助双折线泛函本构关系的本构模型,利用粒子群优化算法对不同激励条件下的隔振器模型参数进行了识别,通过识别参数的对比得到了隔振器各参数在不同激励情况下的变化趋势。结果显示对金属橡胶非线性隔振系统进行动力学分析时,必须首先对实际工况下隔振器进行动态试验。再通过参数识别获取隔振器准确的数学模型,才能对金属橡胶隔振系统进行准确的动力学分析。为金属橡胶隔振系统的动力学分析提供了一般方法。     

Element-free Galerkin method using directed graph and its application to creep problems

The element-free Galerkin method (EFGM) is one of the meshless methods proposed by Belytschko et al. Since node-element connectivities used in the finite element method (FEM) are not needed in the EFGM, the EFGM is expected to be applied to many problems of the continuum mechanics and to be utilized for a tool in a CAE system instead of the FEM. However the EFGM requires more CPU time to search nodes of the MLSM than the FEM. In this paper, the method of the directed graph and the Delaunay triangulation are respectively used for searching nodes and the division of the integral domain respectively. These techniques are useful for saving the CPU time and the simplification of the analysis for the EFGM. Furthermore, the EFGM has not been applied to nonlinear problems such as creep problems under elevated temperature. In this paper, the EFGM using the method of the directed graph and the Delaunay triangulation is applied to several creep problems. The CPU times for the analyses are reduced by the proposed EFGM. The results obtained from the EFGM analyses agree well with those of the FEM.     

Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer's disease

The aim of the present study is to show the usefulness of nonlinear methods to analyse the electroencephalogram (EEG) and magnetoencephalogram (MEG) in patients with Alzheimer's disease (AD). The following nonlinear methods have been applied to study the EEG and MEG background activity in AD patients and control subjects: approximate entropy, sample entropy, multiscale entropy, auto-mutual information and Lempel-Ziv complexity. We discuss why these nonlinear methods are appropriate to analyse the EEG and MEG. Furthermore, the performance of all these methods has been compared when applied to the same databases of EEG and MEG recordings. Our results show that EEG and MEG background activities in AD patients are less complex and more regular than in healthy control subjects. In line with previous studies, our work suggests that nonlinear analysis techniques could be useful in AD diagnosis.     

Dynamics and Ground State Properties of Two-component Bose-Einstein Condensate in Different Hyperfine States

The dynamics of the Josephson effects for a homogeneous two-component Bose-Einstein condensate in different hyperfine states is studied by two coupled nonlinear equations, which are obtained by mean field approximation. We have shown the nonlinear Josephson effects, including Plasmon and macroscopic self-trapping. We have also studied the relaxation dynamics and the system under damping will evolve into a stationary state of two equivalent components. For the equivalent two-component condensate, Green’s function method is applied to find the excitation spectrum. We found that the excitation spectrum has two branched, of which one is the phonon excitation and one is of the single-particle form in the long wave-length limit. We have also studied the depletion of the condensate in the ground state.     

ISovector fields and self-similar solutions for power law creep

Isovector methods are a recently developed technique for systematically investigating properties of the solutions of systems of differential equations. These methods are applied to the nonlinear equations of power law creep with elastic strains under conditions of plane and antiplane strain. Among the results are a family of self-similar solutions which are shown to be the only ones extant for the cases investigated. Some light is also shed upon the existence of conservation laws for these equations, and upon the existence of mappings which transform the governing equations into a set of equivalent linear equations.     

An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization

Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment () have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivative-based ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loading—Part 2: Modelling

A model has been developed for the modulus reduction of cross-ply Kevlar laminates under static loading as a function of applied strain. The effects of strain-rate and temperature have also been considered. The ‘stiffening’ of Kevlar fibres and Kevlar fibre-epoxy (KFRP) laminates under creep or fatigue conditions has been modelled using a kinetic approach. This has enabled stiffening effects to be subtracted out of the residual modulus-with-cycles behaviour of cross-ply KFRP laminates under fatigue loading, leaving a modulus-reduction-with-cycles curve which reflects the damage due to matrix cracking. The analyses compare well with experimental data reported in Part 1.