Chaotic dynamic analysis of viscoelastic plates

The dynamic buckling of viscoelastic plates with large deflection is investigated in this paper by using chaotic and fractal theory. The material behavior is given in terms of the Boltzmann superposition principle. in order to obtain accurate computation results, the nonlinear integro-differential dynamic equation is changed into an autonomic four-dimensional dynamical system. The numerical time integrations of equations are performed by using the fourth-order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of geometry nonlinearity and viscoelastic parameter on the dynamic buckling of viscoelastic plates is discussed.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Fish inspired biomimetic ionic polymer metal composite pectoral fins using labriform propulsion

Ionic polymer metal composites (IPMC) are a new class of smart materials that have attractive characteristics such as muscle like softness, low voltage and power consumption, and good performance in aqueous environments. Thus, IPMC’s provide promising application for biomimetic fish like propulsion systems. In this paper, we design and analyze IPMC underwater propulsor inspired from swimming of Labriform fishes. Different fish species in nature are source of inspiration for different biomimetic flapping IPMC fin design. Here, three fish species with high performance flapping pectoral fin locomotion is chosen and performance analysis of each fin design is done to discover the better configurations for engineering applications. In order to describe the behavior of an active IPMC fin actuator in water, a complex hydrodynamic function is used and structural model of the IPMC fin is obtained by modifying the classical dynamic equation for a slender beam. A quasi-steady blade element model that accounts for unsteady phenomena such as added mass effects, dynamic stall, and the cumulative Wagner effect is used to estimate the hydrodynamic performance of the flapping rectangular shape fin. Dynamic characteristics of IPMC actuated flapping fins having the same size as the actual fins of three different fish species, Gomphosus varius, Scarus frenatus and Sthethojulis trilineata, are analyzed with numerical simulations. Finally, a comparative study is performed to analyze the performance of three different biomimetic IPMC flapping pectoral fins.

Nonequilibrium statistical mechanics of two-dimensional turbulence

The vorticity dynamics of two-dimensional turbulence are investigated analytically, applying the method of Qian (1983). The vorticity equation and its Fourier transform are presented; a set of modal parameters and a modal dynamic equation are derived; and the corresponding Liouville equation for the probability distribution in phase space is solved using a Langevin/Fokker-Planck approach to obtain integral equations for the enstrophy and for the dynamic damping coefficient eta. The equilibrium spectrum for inviscid flow is found to be a stationary solution of the enstrophy equation, and the inertial-range spectrum is determined by introducing a localization factor in the two integral equations and evaluating the localized versions numerically.

多目标追逐问题的一种混合整数线性规划解

研究多车辆多目标追逐的路径规划问题。提出两个基于混合整数线性规划(Mixed integer linear programming,MILP)的多目标追逐(Multi-target pursuit,MTP)模型:就近追逐和"一对一"使能追逐。在两个MIP追逐模型中,小车运动的状态方程考虑为具有线性阻尼的质点动力学方程。采用整数变量描述小车与障碍物的相对位置信息,提出"目标膨胀尺寸"的概念来描述对目标的追逐,定义小车的"追逐方向"。采用选取整变量的等高面法求解MILP追逐问题,并给出初始内点整变量的确定方法。最后给出仿真试验1对两个多目标追逐模型进行对比研究,仿真试验2证实了算法的效率。

复杂介质边界元法数值模拟研究

A major impetus to study the rough surface and complex structure in near surface model is because accuracy of seismic observation and geophysical prospecting can be improved. Wave theory study about fluid-satuated porous media has important significance for some scientific problems, such as explore underground resources, study of earth's internal structure, and structure response of multi-phase porous soil under dynamic and seismic effect. Seismic wave numerical modeling is one of the effective methods which understand seismic propagation rules in complex media. As a numerical simulation method, boundary element methods had been widely used in seismic wave field study. This paper mainly studies randomly rough surface scattering which used some approximation solutions based on boundary element method. In addition, I developed a boundary element solution for fluid saturated porous media. In this paper, we used boundary element methods which based on integral expression of wave equation to study the free rough surface scattering effects of Kirchhoff approximation method, Perturbation approximation method, Rytov approximation method and Born series approximation method. Gaussian spectrum model of randomly rough surfaces was chosen as the benchmark model. The approximation methods result were compared with exact results which obtained by boundary element methods, we study that the above approximation methods were applicable how rough surfaces and it is founded that this depends on and ( here is the wavenumber of the incident field, is the RMS height and is the surface correlation length ). In general, Kirchhoff approximation which ignores multiple scatterings between any two surface points has been considered valid for the large-scale roughness components. Perturbation theory based on Taylor series expansion is valid for the small-scale roughness components, as and are .Tests with the Gaussian topographies show that the Rytov approximation methods improves the Kirchhoff approximation in both amplitude and phase but at the cost of an extra treatment of transformation for the wave fields. The realistic methods for the multiscale surfaces come with the Born series approximation and the second-order Born series approximation might be sufficient to guarantee the accuracy of randomly rough surfaces. It could be an appropriate choice that a complex rough surface can be divided into large-, medium-, and small-scale roughness components with their scattering features be studied by the Kirchhoff or Rytov phase approximations, the Born series approximation, and the perturbation theory, respectively. For this purpose, it is important to select appropriate parameters that separate these different scale roughness components to guarantee the divided surfaces satisfy the physical assumptions of the used approximations, respectively. In addition, in this paper, the boundary element methods are used for solving the porous elastic wave propagation and carry out the numerical simulation. Based on the fluid-saturated porous model, this paper analyses and presents the dynamic equation of elastic wave propagation and boundary integral equation formulation of fluid saturated porous media in frequency domain. The fundamental solutions of the elastic wave equations are obtained according to the similarity between thermoelasticity and poroelasticity. At last, the numerical simulation of the elastic wave propagation in the two-phase isotropic media is carried out by using the boundary element method. The results show that a slow quasi P-wave can be seen in both solid and fluid wave-field synthetic seismograms. The boundary element method is effective and feasible.

Existência de soluções de inclusões diferenciais em escalas temporais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bare-tape scaling laws for de-orbit missions in a space debris environment

El entorno espacial actual hay un gran numero de micro-meteoritos y basura espacial generada por el hombre, lo cual plantea un riesgo para la seguridad de las operaciones en el espacio. La situación se agrava continuamente a causa de las colisiones de basura espacial en órbita, y los nuevos lanzamientos de satélites. Una parte significativa de esta basura son satélites muertos, y fragmentos de satélites resultantes de explosiones y colisiones de objetos en órbita. La mitigación de este problema se ha convertido en un tema de preocupación prioritario para todas las instituciones que participan en operaciones espaciales. Entre las soluciones existentes, las amarras electrodinámicas (EDT) proporcionan un eficiente dispositivo para el rápido de-orbitado de los satélites en órbita terrestre baja (LEO), al final de su vida útil. El campo de investigación de las amarras electrodinámicas (EDT) ha sido muy fructífero desde los años 70. Gracias a estudios teóricos, y a misiones para la demostración del funcionamiento de las amarras en órbita, esta tecnología se ha desarrollado muy rápidamente en las últimas décadas. Durante este período de investigación, se han identificado y superado múltiples problemas técnicos de diversa índole. Gran parte del funcionamiento básico del sistema EDT depende de su capacidad de supervivencia ante los micro-meteoritos y la basura espacial. Una amarra puede ser cortada completamente por una partícula cuando ésta tiene un diámetro mínimo. En caso de corte debido al impacto de partículas, una amarra en sí misma, podría ser un riesgo para otros satélites en funcionamiento. Por desgracia, tras varias demostraciones en órbita, no se ha podido concluir que este problema sea importante para el funcionamiento del sistema. En esta tesis, se presenta un análisis teórico de la capacidad de supervivencia de las amarras en el espacio. Este estudio demuestra las ventajas de las amarras de sección rectangular (cinta), en cuanto a la probabilidad de supervivencia durante la misión, frente a las amarras convencionales (cables de sección circular). Debido a su particular geometría (longitud mucho mayor que la sección transversal), una amarra puede tener un riesgo relativamente alto de ser cortado por un único impacto con una partícula de pequeñas dimensiones. Un cálculo analítico de la tasa de impactos fatales para una amarra cilindrica y de tipo cinta de igual longitud y masa, considerando el flujo de partículas de basura espacial del modelo ORDEM2000 de la NASA, muestra mayor probabilidad de supervivencia para las cintas. Dicho análisis ha sido comparado con un cálculo numérico empleando los modelos de flujo el ORDEM2000 y el MASTER2005 de ESA. Además se muestra que, para igual tiempo en órbita, una cinta tiene una probabilidad de supervivencia un orden y medio de magnitud mayor que una amarra cilindrica con igual masa y longitud. Por otra parte, de-orbitar una cinta desde una cierta altitud, es mucho más rápido, debido a su mayor perímetro que le permite capturar más corriente. Este es un factor adicional que incrementa la probabilidad de supervivencia de la cinta, al estar menos tiempo expuesta a los posibles impactos de basura espacial. Por este motivo, se puede afirmar finalmente y en sentido práctico, que la capacidad de supervivencia de la cinta es bastante alta, en comparación con la de la amarra cilindrica. El segundo objetivo de este trabajo, consiste en la elaboración de un modelo analítico, mejorando la aproximación del flujo de ORDEM2000 y MASTER2009, que permite calcular con precisión, la tasa de impacto fatal al año para una cinta en un rango de altitudes e inclinaciones, en lugar de unas condiciones particulares. Se obtiene el numero de corte por un cierto tiempo en función de la geometría de la cinta y propiedades de la órbita. Para las mismas condiciones, el modelo analítico, se compara con los resultados obtenidos del análisis numérico. Este modelo escalable ha sido esencial para la optimización del diseño de la amarra para las misiones de de-orbitado de los satélites, variando la masa del satélite y la altitud inicial de la órbita. El modelo de supervivencia se ha utilizado para construir una función objetivo con el fin de optimizar el diseño de amarras. La función objectivo es el producto del cociente entre la masa de la amarra y la del satélite y el numero de corte por un cierto tiempo. Combinando el modelo de supervivencia con una ecuación dinámica de la amarra donde aparece la fuerza de Lorentz, se elimina el tiempo y se escribe la función objetivo como función de la geometría de la cinta y las propietades de la órbita. Este modelo de optimización, condujo al desarrollo de un software, que esta en proceso de registro por parte de la UPM. La etapa final de este estudio, consiste en la estimación del número de impactos fatales, en una cinta, utilizando por primera vez una ecuación de límite balístico experimental. Esta ecuación ha sido desarollada para cintas, y permite representar los efectos tanto de la velocidad de impacto como el ángulo de impacto. Los resultados obtenidos demuestran que la cinta es altamente resistente a los impactos de basura espacial, y para una cinta con una sección transversal definida, el número de impactos críticos debidos a partículas no rastreables es significativamente menor. ABSTRACT The current space environment, consisting of man-made debris and tiny meteoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris collisions and to new satellite launches. Among these debris a significant portion is due to dead satellites and fragments of satellites resulted from explosions and in-orbit collisions. Mitigation of space debris has become an issue of first concern for all the institutions involved in space operations. Bare electrodynamic tethers (EDT) can provide an efficient mechanism for rapid de-orbiting of defunct satellites from low Earth orbit (LEO) at end of life. The research on EDT has been a fruitful field since the 70’s. Thanks to both theoretical studies and in orbit demonstration missions, this technology has been developed very fast in the following decades. During this period, several technical issues were identified and overcome. The core functionality of EDT system greatly depends on their survivability to the micrometeoroids and orbital debris, and a tether can become itself a kind of debris for other operating satellites in case of cutoff due to particle impact; however, this very issue is still inconclusive and conflicting after having a number of space demonstrations. A tether can be completely cut by debris having some minimal diameter. This thesis presents a theoretical analysis of the survivability of tethers in space. The study demonstrates the advantages of tape tethers over conventional round wires particularly on the survivability during the mission. Because of its particular geometry (length very much larger than cross-sectional dimensions), a tether may have a relatively high risk of being severed by the single impact of small debris. As a first approach to the problem, survival probability has been compared for a round and a tape tether of equal mass and length. The rates of fatal impact of orbital debris on round and tape tether, evaluated with an analytical approximation to debris flux modeled by NASA’s ORDEM2000, shows much higher survival probability for tapes. A comparative numerical analysis using debris flux model ORDEM2000 and ESA’s MASTER2005 shows good agreement with the analytical result. It also shows that, for a given time in orbit, a tape has a probability of survival of about one and a half orders of magnitude higher than a round tether of equal mass and length. Because de-orbiting from a given altitude is much faster for the tape due to its larger perimeter, its probability of survival in a practical sense is quite high. As the next step, an analytical model derived in this work allows to calculate accurately the fatal impact rate per year for a tape tether. The model uses power laws for debris-size ranges, in both ORDEM2000 and MASTER2009 debris flux models, to calculate tape tether survivability at different LEO altitudes. The analytical model, which depends on tape dimensions (width, thickness) and orbital parameters (inclinations, altitudes) is then compared with fully numerical results for different orbit inclinations, altitudes and tape width for both ORDEM2000 and MASTER2009 flux data. This scalable model not only estimates the fatal impact count but has proved essential in optimizing tether design for satellite de-orbit missions varying satellite mass and initial orbital altitude and inclination. Within the frame of this dissertation, a simple analysis has been finally presented, showing the scalable property of tape tether, thanks to the survivability model developed, that allows analyze and compare de-orbit performance for a large range of satellite mass and orbit properties. The work explicitly shows the product of tether-to-satellite mass-ratio and fatal impact count as a function of tether geometry and orbital parameters. Combining the tether dynamic equation involving Lorentz drag with space debris impact survivability model, eliminates time from the expression. Hence the product, is independent of tether de-orbit history and just depends on mission constraints and tether length, width and thickness. This optimization model finally led to the development of a friendly software tool named BETsMA, currently in process of registration by UPM. For the final step, an estimation of fatal impact rate on a tape tether has been done, using for the first time an experimental ballistic limit equation that was derived for tapes and accounts for the effects of both the impact velocity and impact angle. It is shown that tape tethers are highly resistant to space debris impacts and considering a tape tether with a defined cross section, the number of critical events due to impact with non-trackable debris is always significantly low.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Design, development and control of a new generation high performance linear actuator for parallel robots and other applications

The main focus of this research is to design and develop a high performance linear actuator based on a four bar mechanism. The present work includes the detailed analysis (kinematics and dynamics), design, implementation and experimental validation of the newly designed actuator. High performance is characterized by the acceleration of the actuator end effector. The principle of the newly designed actuator is to network the four bar rhombus configuration (where some bars are extended to form an X shape) to attain high acceleration. Firstly, a detailed kinematic analysis of the actuator is presented and kinematic performance is evaluated through MATLAB simulations. A dynamic equation of the actuator is achieved by using the Lagrangian dynamic formulation. A SIMULINK control model of the actuator is developed using the dynamic equation. In addition, Bond Graph methodology is presented for the dynamic simulation. The Bond Graph model comprises individual component modeling of the actuator along with control. Required torque was simulated using the Bond Graph model. Results indicate that, high acceleration (around 20g) can be achieved with modest (3 N-m or less) torque input. A practical prototype of the actuator is designed using SOLIDWORKS and then produced to verify the proof of concept. The design goal was to achieve the peak acceleration of more than 10g at the middle point of the travel length, when the end effector travels the stroke length (around 1 m). The actuator is primarily designed to operate in standalone condition and later to use it in the 3RPR parallel robot. A DC motor is used to operate the actuator. A quadrature encoder is attached with the DC motor to control the end effector. The associated control scheme of the actuator is analyzed and integrated with the physical prototype. From standalone experimentation of the actuator, around 17g acceleration was achieved by the end effector (stroke length was 0.2m to 0.78m). Results indicate that the developed dynamic model results are in good agreement. Finally, a Design of Experiment (DOE) based statistical approach is also introduced to identify the parametric combination that yields the greatest performance. Data are collected by using the Bond Graph model. This approach is helpful in designing the actuator without much complexity.

Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd