Elastodynamic analysis of a cracked orthotropic half-plane

The solution of elastodynamic volterra-type dislocation in an orthotropic half-plane is obtained by means of the Fourier transforms. The distributed dislocation technique is used to construct integral equations for an orthotropic half-plane weakened by cracks where the domain is under time-harmonic anti plane traction. These equations are of Cauchy singular type at the location of dislocation which is solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determine stress intensity factors for multiple smooth cracks. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.     

Identification and orbit determination of a tethered satellite system

Orbital motion of a tethered satellite system, composed of two satellites and an inextensible tether, is considered by using a perturbed two-body model. This approach is adopted so that the determination of the orbit of one of the satellites can be attempted without using observations of the motion of the other satellite in the system. The identification of the tethered condition of the system using observations of only one of the satellites in the tethered satellite system is considered. The characteristics of the `tether perturbed' motion of the observed satellite are investigated. Estimation of the state of the system using near perfect data is also illustrated. Observations of one satellite provide the entire state of the system and a parameter involving the ratio of the masses of satellites and the tether length.     

Forced vibration of a bubble spring-mass system: Nonlinear analysis and experiment

In the present study, we investigate the nonlinear forced vibration of a bubble-mass system both theoretically and experimentally, where the bubble is viewed as a spring. The mathematical model on the excited vibration is developed by assuming the contour line of the bubble being a parabola curve. The incremental harmonic balance method is used to solve the ordinary differential equation, and the high speed video camera is utilized to take photographs. The effects of the bubble volume and radius of the plate on the static compression of the spring, the amplitude–frequency curves for the fundamental and second harmonic wave, and phase–frequency curve of the fundamental wave, are all demonstrated. The results show that the spring representing the bubble is always in compression in the process of vibration, and a greater bubble volume and a smaller plate radius make the system stiffness smaller. The second harmonic wave has some different characteristics from the counterparts of the fundamental wave. We also perform an experiment to validate these theoretical analyses. This study sheds new light on the nonlinear vibration of soft system, which may be beneficial to such areas as aerospace, microgravity, and soft robotics.     

On a closed orbit of some constrained system

We study on what one calls a constrained system of ODEs on It consists of two ordinary differential equations and an algebraic equation with respect to three unknown functions. We seek closed orbits of such a system. A necessary and sufficient condition for the system to have non-trivial closed orbits is given. Elementary tools such as Lyapunov functions and Poincaré’s index theory are used in the proof of the result. As an application we consider a constrained system associated with a non-constraint system of ODEs called the modified Bonhöffer-van der Pol system.     

Dynamic analysis, controlling chaos and chaotification of a SMIB power system

The dynamic behaviors of a SMIB power system are studied in this paper. A single modal equation is used to analyze the qualitative behaviors of the system. The famous equation of motion is called “swing equation”. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. The bifurcation of the parameter dependent system is studied numerically. Besides, the phase portraits, the Poincaré maps, and the Lyapunov exponents are presented to observe periodic and chaotic motions. Further, the addition of periodic force and the feedback control are used to control chaos effectively. Finally, the chaotification problem of the SMIB power system is also issued.     

动态特性稳健设计中的响应曲面分析

针对含有单个噪声因素的动态特性的稳健设计，建立了响应曲面模型，给出了模型的统计分析方法，得到了有关统计量的统计分布及效的估计。     

Mathematical analysis of a shuttle system based on two interdependent queues

This is an analysis of a multishuttle system, using a car ferry as the example, to develop mathematical models of shuttle systems. Poisson-exponential mathematical models for the single- and two-shuttle systems are formulated as interdependent queueing systems. The vector (X_A, X_B) representing the number of cars waiting at shore A and shore B respectively, at the end of an unloading at one of the shores is shown to form a bivariate Markov chain; thus the long run probability distributions of (X_A, X_B) can be evaluated using classical Markov chain theory.     

Static and dynamic analysis of cracked or weakened structures

Stiffness modifications in engineering structures, for example due to damage and cracking, will inevitably also lead to changes in deformations, internal forces, natural frequencies and mode shapes of the structures. In this paper, an efficient and simple method for sensitivity analysis of cracked or weakened structures under time-harmonic loading is presented. The method is based on a comparison between the strain energy and the kinetic energy of an uncracked structure and that of a cracked structure in conjunction with the application of exact or approximate Green's functions as described in [3] for the static case. The present analysis enables the prediction of any changes in the displacements and stresses and has a lower computational effort as compared to available classical methods, because only the damaged region has to be re-considered in the method. Green's functions are taken as a basis of the approach, which have the ability to weight the influence of the stiffness modifications in a region of a structure and show how sensitive other regions respond to the stiffness modifications. Based on linear elastic fracture mechanics, cracked or damaged regions are approximated by spring models in the analytical solution of some simple beam problems, while cracked finite elements are used for complicated cases where analytical solutions cannot be obtained. Sensitivity analysis with Green's functions (SAGF) approach is applied to static and dynamic analysis of cracked and weakened structures, which consist of homogeneous materials or fiber reinforced composites like reinforced concretes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic energy management for a novel hybrid electric system based on driving pattern recognition

This paper focuses on the dynamic energy management for Hybrid Electric Vehicles (HEV) based on driving pattern recognition. The hybrid electric system studied in this paper includes a one-way clutch, a multi-plate clutch and a planetary gear unit as the power coupling device in the architecture. The powertrain efficiency model is established by integrating the component level models for the engine, the battery and the Integrated Starter/Generator (ISG). The powertrain system efficiency has been analyzed at each operation mode, including electric driving mode, driving and charging mode, engine driving mode and hybrid driving mode. The mode switching schedule of HEV system has been designed based on static system efficiency. Adaptive control for hybrid electric vehicles under random driving cycles with battery life and fuel consumption as the main considerations has been optimized by particle swarm optimization algorithm (PSO). Furthermore, driving pattern recognition based on twenty typical reference cycles has been implemented using cluster analysis. Finally, the dynamic energy management strategy for the hybrid electric vehicle has been proposed based on driving pattern recognition. The simulation model of the HEV powertrain system has been established on Matlab/Simulink platform. Two energy management strategies under random driving condition have both been implemented in the study, one is knowledge-based and the other is based on driving pattern recognition. The model simulation results have validated the control strategy for the hybrid electric vehicle in this study in terms of drive pattern recognition and energy management optimization.     

Dynamic analysis for a stage-structure competitive system with mature population harvesting

In this paper, a stage-structured model of two-species competitive system with mature population harvesting is formulated. Mathematical analysis of the model equations with regard to invariance of positivity, boundedness of solutions and the conditions for the existence of equilibria is analyzed. The dynamical properties of equilibria are investigated, and conditions of globally asymptotically stable and absolutely stable for the equilibria are obtained.     

Singular fuel-optimal space trajectories based on linearization about a point in circular orbit

Singular solutions of a linearized problem of determining fuel-optimal trajectories of a spacecraft with bounded thrust near a satellite in circular orbit are investigated in detail. Mathematical results are presented which classify and discuss degeneracy of the singular solutions and which show that strictly singular and nonsingular solutions are mutually exclusive for fixed-end conditions. These results are consistent with those found using other approaches for other linear models, but they are not characteristic of the type of results obtained without linearization.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Steady-state response of a geared rotor system with slant cracked shaft and time-varying mesh stiffness

The dynamic behavior of geared rotor system with defects is helpful for the failure diagnosis and state detecting of the system. Extensive efforts have been devoted to study the dynamic behaviors of geared systems with tooth root cracks. When surface cracks (especially for slant cracks) appear on the transmission shaft, the dynamic characteristics of the system have not gained sufficient attentions. Due to the parametric excitations induced by slant crack breathing and time-varying mesh stiffness, the steady-state response of the cracked geared rotor system differs distinctly from that of the uncracked system. Thus, utilizing the direct spectral method (DSM), the forced response spectra of a geared rotor system with slant cracked shaft and time-varying mesh stiffness under transmission error, unbalance force and torsional excitations are, respectively, obtained and discussed in detail. The effects of crack types (straight or slant crack) and crack depth on the forced response spectra of the system without and with torsional excitation are considered in the analysis. In addition, how the frequency response characteristics change after considering the crack is also investigated. It is shown that the torsional excitations have significant influence on the forced response spectra of slant cracked system. Sub-critical resonances are also found in the frequency response curves. The results could be used for shaft crack detection in geared rotor system.     

Reliability analysis of a consecutive r-out-of-n: F system based on neural networks

In this paper, we present a generalized Markov reliability and fault-tolerant model, which includes the effects of permanent fault and intermittent fault for reliability evaluations based on neural network techniques. The reliability of a consecutive r-out-of-n: F system was obtained with a three-layer connected neural network represents a discrete time state reliability Markov model of the system. Such that we fed the neural network with the desired reliability of the system under design. Then we extracted the parameters of the system from the neural weights at the convergence of the neural network to the desired reliability. Finally, we obtain simulation results.     

Dynamic modeling of the power market and analysis of its complex behavior based on a nonlinear complementarity function

In order to accurately simulate the dynamic decision-making behaviors of market participants, a new dynamic model of power markets that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of market clearing. Compared with existing dynamic models, the remarkable characteristic of the proposed model is twofold: it accurately reflects the process of market clearing by the Independent System Operator (ISO) while considering the inherent physical characteristics of power networks, i.e., the complex network constraints; and it describes the market condition that the generation and demand sides bid simultaneously. Using a nonlinear complementary function, the complex discrete difference dynamic model is transformed into a set of familiar discrete difference algebraic equations. Then, the complex dynamic behaviors of power markets are quantitatively analyzed. Corresponding to different operating conditions of power network, such as congestion or non-congestion, the Nash equilibrium of power markets and its stability are calculated, and the periodic and even chaotic dynamic behaviors are exhibited when the market parameters are beyond the stability region of the Nash equilibrium.     

Topological sensitivity analysis of a multi‐scale constitutive model considering a cracked microstructure

This paper deals with the sensitivity analysis of the macroscopic elasticity tensor to topological microstructural changes of the underlying material. In particular, the microstucture is topologicaly perturbed by the nucleation of a small circular inclusion. The derivation of the proposed sensitivity relies on the concept of topological derivative, applied within a variational multi‐scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are defined as volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. We consider that the RVE can contain a number of voids, inclusions and/or cracks. It is assumed that non‐penetration conditions are imposed at the crack faces, which do not allow the opposite crack faces to penetrate each other. The derived sensitivity leads to a symmetric fourth‐order tensor field over the unperturbed RVE domain, which measures how the macroscopic elasticity parameters estimated within the multi‐scale framework changes when a small circular inclusion is introduced at the micro‐scale level. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical eigenmode analysis of an acoustic-duct system by CFD-OLTF and comparison against experiment

In this contribution, a novel approach to determine acoustic eigenmodes in duct systems is presented. The approach combines C omputational fluid dynamics, classical N etwork models of duct acoustics and the N yquist criterion known from control theory, and is therefore called CNN-method. The method has been applied to a geometrically simple, but aero-acoustically non-trivial configuration – i.e. a sudden change in cross-sectional area connecting two ducts with non-zero mean flow – and validated against experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic PET Reconstruction based on a Reaction-Diffusion Model

Positron-Emission Tomography (PET) is an imaging technique in nuclear medicine used to image physiological processes. A major obstacle is the need for dynamic image reconstruction from low quality PET-data, which applies in particular for tracers (radioactive water) with fast decay like H₂¹⁵O when looking for improved spatial resolution. Here we present a model-based approach to overcome those difficulties. We derive a set of differential equations able to represent the kinetic behavior of H₂¹⁵O PET tracers during cardiac perfusion. In this model one takes into account the exchange of materials between artery, tissue and vein, which predicts the tracer activity if the reaction rates, velocities, and diffusion coefficients are known. One then interprets the computation of these distributed parameters (spatially dependent only) as a nonlinear inverse problem, which we solve using variational regularization approaches. For the minimization we use the gradient-based methods and Forward-Backward Splitting. The main advantage is the reduction of the degrees of freedom, which makes the problem overdetermined and thus allows to proceed to low quality data. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)