Fundamentals of Rail Vehicle Dynamics: Guidance and Stability (Advances in Engineering Series)

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Dynamic Stability of the Two-Axle Vehicle 6. The Bogie Vehicle 7. The Three-Axle Vehicle 8. Articulated Vehicles 9. Unsymmetric Vehicles. Notes Includes bibliographical references and index. View online Borrow Buy Freely available Show 0 more links Set up My libraries How do I set up "My libraries"? Monash University Library.

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Tags What are tags? Multiload bridges play significant roles in the entire transportation system, and thus it is critically important to protect such immense capital investments and ensure user comfort and bridge safety. However, the strength and integrity of these bridges will decrease during the serviceability stage due to the degradation mechanisms induced by traffic, wind, temperature, corrosion, and environmental deterioration.

In order to detect the abnormal changes through nondestructive testing NDT technology or periodical evaluation, a fundamental but critical step is to obtain dynamic responses at some critical bridge locations. The mostly concerned dynamic responses of a multiload bridge may include global response displacement, velocity, and acceleration and local response acceleration and stress , which are mainly induced by traditional live load such as highway, railway, and wind loading or accidental live load such as ship impact and earthquake.

Structural intrinsic characteristics could be extracted from these dynamic responses or vibration signals to develop all sorts of vibration-based damage detection techniques. A well-known family of them is based on structural dynamic characteristics such as frequencies, mode shapes, damping ratios, and strain mode shapes and their derivatives [ 1 — 3 ]. Some damage identification approaches were proposed based on the dynamic responses of bridge structures under moving vehicle loads [ 4 — 6 ].

The dynamic responses of long-span bridges also could be used for structural assessment, for example, fatigue assessment at the critical locations over the service history of the bridge [ 7 — 10 ] and assessment of extreme events such as complex traffic congestion coupled with moderate or even strong wind [ 11 ]. Over the past decades, on-structure long-term structural health monitoring systems SHMSs have been implemented on long-span bridges in Europe, the United States, Canada, Japan, Korea, China, and other countries [ 12 ].

They are installed in newly constructed bridges and existing bridges for monitoring structural behavior in real time, evaluating structural performance under various loads, and identifying structural damage or deterioration [ 13 ]. To comprehensively understand the bridge performance, dynamic bridge responses are important monitoring items of structural health monitoring. Although dynamic responses have been measured for those bridges installed with SHMSs, condition evaluation based on measurement still has some limitations: 1 it is difficult to identify all of the local critical locations, and even so, it is uneconomical to monitor all critical locations in long term; 2 not every fatigue-critical location is suitable for sensor installation; 3 it is difficult to obtain measurement data in the extreme events such as combination of traffic congestion and strong wind which rarely happen; 4 it is hard to exactly predict the influence of possible traffic growths based on field measurement only.

Integrating with numerical simulation technologies and field measurements is an alternative approach which is able to overcome the limitations of evaluation approaches only based on measurements. The information on the concerned dynamic loadings measured by the SHMS could be taken as inputs for the numerical simulation, and the computed dynamic responses could be compared with the measured ones in the validation [ 17 ]. However, numerical simulation of dynamic response of a long-span multiload bridge is not an easy job, because it requires a complex dynamic finite element model of the bridge including all important bridge components, various dynamic loading models for running trains, running road vehicles, and high winds, and interactive models between the bridge and wind, bridge and trains, and bridge and road vehicles [ 17 ].

This paper focuses on recent research and applications of numerical simulation technology for dynamic response of long-span multiload bridges. Firstly, key issues involved in dynamic response analysis of long-span multiload bridges based on numerical simulation technologies are reviewed in Section 2. The applications of newly developed numerical simulation technologies to safety assessment of long-span bridges are subsequently reviewed in Section 3.

Finally, the existing problems and promising research efforts for the numerical simulation technologies and their applications to assessment of long-span multiload bridges are explored in Section 4. For the most complex situation, a long-span multiload bridge which is located at a wind-prone region carries both railway and highway traffic, and thus the combined effect of running trains, running road vehicles, and wind is acting on the bridge. Several key issues are involved in this complicated situation, such as dynamic interaction between running trains and bridge, dynamic interaction between running road vehicles and bridge, and dynamic interaction between wind and bridge.

To give a comprehensive review, the above three key issues will be individually reviewed in Sections 2. In early research in this area, simplified bridge models were employed to study vehicle-bridge interactions. For example, a cable-stayed bridge was simulated as a beam resting on an elastic foundation by Meisenholder and Weidlinger [ 18 ] for the dynamic analysis of cable-stayed guideways subject to track-levitated vehicles moving at high speeds.

Mao [ 19 ] investigated the impact factor of a cable-stayed bridge, which was assumed to be formed of continuous elastic beams supported by intermediate elastic supports. More recently, with the development of finite element FE technology, it has become common practice to use a computer software package to establish a finite element model FEM of a cable-supported bridge. This technology establishes an accurate bridge model that takes into account the geometric nonlinear behavior of a cable-supported bridge.

To make the bridge model close to the realistic bridge in terms of its dynamic properties, the modal frequencies and shapes determined by dynamic tests are used for further model validation or updating. Many FEMs of cable-supported bridges have been established for the analysis of train-bridge interactions.

The Tsing Ma Suspension Bridge in Hong Kong can be used as an example to illustrate the various bridge models that have been established for analysis. The first generation of Tsing Ma Bridge model was a spinal beam model [ 20 ] in which the hybrid steel deck was represented by a single beam with equivalent cross-sectional properties, two bridge towers made of reinforced concrete that were modeled by three-dimensional Timoshenko beam elements, and cables and suspenders that were modeled by cable elements to account for geometric nonlinearity due to cable tension.

The model was validated by comparing it with measurements of the first 18 modal frequencies and shapes of the actual bridge. Using this model, Guo et al. However, they modeled the bridge deck as a simplified spine beam of equivalent sectional properties and were thus unable to capture the local stress and strain behavior of the bridge. A second-generation bridge model hybrid 3-dimensional model was established to overcome this weakness [ 22 ]. The modeling work is based on the previous model developed by Wong [ 23 ]. In this model, 15, beam elements were used to model the bridge deck to closely replicate the geometric details of the complicated deck in reality see Figure 2 a.

The railway beams and rails were modeled by beam elements to allow the accurate computation of the contact forces between the bridge and railway vehicle. The deck-plates carrying the road vehicles were modeled by plate elements to allow the accurate computation of the contact forces at the contact points between the road surface and the vehicle tires.

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The bridge deck was modeled to closely replicate the geometric details of the complicated deck which is required for calculation of the action of the wind forces. The bridge model was also updated using the first 18 measured natural frequencies and mode shapes. Based on this model, Xu et al. Finite element model of suspended deck module: a hybrid 3D bridge model [ 22 ]; b full 3D model [ 25 ].

For example, the orthotropic decks steel deck-plates supported by U-shape troughs were modeled by plate elements with equivalent depths so that the measured results from strain gauges at the surfaces of deck-plates or U-shape troughs had no counterparts in computation results. Therefore, Duan et al. In this model, the major structural components were modeled in detail and the connections and boundary conditions are modeled properly, which results in about half million elements for the complete bridge model. Although full 3D bridge model provides the possibility for exact stress analysis at the local components, large computational efforts are needed for the refined section model with complicated structural details.

Li et al. The global structural analysis was carried out using the beam element modeling method at the level of a meter. The local detailed hot-spot stress analysis was carried out using shell or solid elements at the level of a millimeter. Based on this model, the global dynamic response of the bridge and local damage accumulation of two typical weld details of the bridge under traffic loading were numerically analyzed.

Multiscale FE modeling scheme was also proposed by Zhang et al. Bridge details with multiple stiffeners were modeled with shell elements using equivalent orthotropic materials. Based on this model, Zhang et al.

Handbook of Railway Vehicle Dynamics_02 A History of Railway Vehicle Dynamics_百度文库

Previously, running vehicles were commonly modeled as a series of moving forces, either due to limits on computational capacity or because it is easier to find the analytical solutions in many cases [ 28 — 37 ]. This treatment neglects the effect of interactions between the bridge and running vehicles.

For this reason, the moving load model is suitable only for the case in which the mass of the vehicle is small relative to that of the bridge or when the vehicle response is not of interest [ 38 ]. For cases in which the inertia of the vehicle cannot be regarded as small, a moving mass model should be adopted instead [ 39 — 42 ]. More recently, the emergence of high-performance computers and advances in computer technology has made it feasible to more realistically model the dynamic properties of the various components of moving vehicles [ 43 — 48 ].

In a more sophisticated railway vehicle model, the suspension mechanisms are modeled by springs, the damping effect of the suspension systems and air-cushion by dashpots, and the energy dissipating effect of the interleaf mechanism by frictional devices. Using this technique, a tractor-trailer is represented as two discrete masses, each of which is supported by two sets of springs and dashpots or frictional devices [ 38 ].

To represent the various dynamic properties of railway vehicles, vehicle models that contain dozens of degrees of freedom DOFs have been devised and used by [ 49 — 52 ]. To investigate the dynamic interaction between a long suspension bridge and running trains, Xia et al.

Fundamentals of Rail Vehicle Dynamics: Guidance and Stability (Advances in Engineering Series)

Each railway vehicle was assumed to consist of a rigid car body resting on front and rear bogies, with each bogie supported by two wheelsets see Figure 3. Five DOFs were assigned to the car body and to each bogie to account for vertical, lateral, rolling, yawing, and pitching motions.

In contrast, only three DOFs were assigned to each wheelset to account for vertical, lateral, and rolling motions. Dynamic model of a railway vehicle [ 51 ].

Many vehicle models have been established for vehicle-bridge interaction analysis. In most of these studies, the equations of motion of the vehicles were derived analytically. However, a great inconvenience of this method is that the equations of motion of the whole vehicle-bridge system must be rederived if the vehicle type is changed. Furthermore, it is very difficult to derive the equation of motion for a complex vehicle model containing a large number of DOFs, such as the articulated components of a TGV train with an DOF dynamic system [ 53 ].

General commercial FE software has recently been adopted to make vehicle modeling more easily applicable for different vehicle types [ 54 ]. Finite element model of a railway vehicle: a elevation view; b side view; c isometric view; d model details [ 52 ]. Track irregularities represent an important source of excitation for bridges during the passage of railway vehicles.

Track irregularities may occur as a result of initial installation errors, the degradation of support materials, or the dislocation of track joints. Four geometric parameters can be used to quantitatively describe rail irregularities: the vertical profile, cross level, alignment, and gauge [ 49 , 50 , 56 ]. Vertical profile and cross level irregularities chiefly influence the vertical vibrations of vehicles and of the bridge, whereas alignment, gauge, and cross level irregularities initiate horizontal transverse vibrations of vehicles and the bridge and also the torsional movement of the bridge [ 57 ].

Track irregularities may be periodic or random. Random irregularities are due to wear, clearance, subsidence, and insufficient maintenance. For engineering applications, random irregularities can be approximately regarded as stationary and ergodic processes that can be generated from measured results or simulated by numerical methods. Several numerical methods have been proposed for the simulation of random rail irregularities, such as the trigonometry series, white noise filtration, autoregressive AR , and power spectral density PSD sampling methods.

Among these methods, the PSD sampling method has been widely adopted due to its high computational accuracy. The lateral and vertical irregularities could be all assumed to be zero-mean stationary Gaussian random processes and expressed through the inverse Fourier transformation of a PSD function [ 58 ]:. Rail irregularity in railway engineering is commonly represented by a one-sided PSD function. The PSD functions of rail irregularities have been developed by different countries.

Based on the PSD functions of rail irregularities developed by the Research Institute of the China Railway Administration, Zhai [ 59 ] expressed all rail irregularities using the unified rational formula as follows:. The dynamic analysis of vehicle-bridge coupled system requires two sets of equations of motion for the bridge and vehicles, respectively. These describe the interaction or contact forces at the contact points of the two subsystems.

Because the contact points move from time to time, the system matrices are generally time dependent and must be updated and factorized at each time step. The various solution methods can be generalized into two groups according to whether or not an iterative procedure is needed at each time step. The first group of methods solves the equations of motion of a coupled vehicle-bridge system at each time step without iteration.

This approach has been widely used in coupled vehicle-bridge analysis [ 51 , 53 , 60 — 69 ]. These methods have good computational stability and are convenient for dealing with vehicle-bridge interaction problems when the vehicle model is relatively simple. The main disadvantage is that the equations of motion of the coupled system are time dependent, and thus the characteristic matrices must be modified at each time step. In addition, the equations of motion of the coupled vehicle-bridge system become very difficult to determine if nonlinear wheel-rail contacts and nonlinear vehicle models are considered.

The second group of methods solves the equations for the vehicles and bridge separately and requires an iterative process to obtain convergence for the displacements of the vehicles and bridge at all contact points. Given that the conditions of wheel-rail contact geometry and contact forces are rather complex, a stable integration method adopting a small time interval is needed for obtaining the convergence of vehicle and bridge subsystems at the contact points in each time step.

Many studies have applied this type of method to investigate vehicle-bridge interactions [ 70 — 76 ]. The advantage of these methods is that the dynamic property matrices in the two sets of equations of motion remain constant, which is convenient for the consideration of nonlinear vehicle-bridge interactions and nonlinear vehicle models [ 55 ].

However, in engineering applications, the iterative convergence is a critical problem with this type of method. The low convergence rate and occasional divergence of the solution have also been noted [ 77 ]. Most of the above methods solved the equations of motion of a coupled vehicle-bridge system using the nonjump model, which assumes that the moving vehicle traveling along the bridge is always in contact with the rails, no matter what the sign is of the contact forces. This is not always true in view of the physics of the moving vehicle which simply sits on the upper surfaces of the rails.

The interaction forces between the moving vehicle and the bridge depend on the motions of the vehicle, the flexibility of the bridge, and the track irregularities. Antolin et al. Section 2. As there are some fundamental differences between trains and road vehicles, this section reviews the modeling of road vehicles, the simulation of road vehicle flow, and the modeling of road surface roughness. To analyze the dynamic interaction between a bridge and running road vehicles, a model of road vehicles must be established.

A sophisticated road vehicle model is required to make the simulation as realistic as possible.

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A road vehicle is modeled as a combination of several rigid bodies, each of which is connected by a set of springs and dashpots which model the elastic and damping effects of the tires and suspension systems, respectively. There are various configurations of road vehicles, such as a tractor and trailer with different axle spacing. Road vehicle models that contain several DOFs have been devised for vehicle-bridge interaction analysis.

For example, Guo and Xu [ 79 ] modeled a DOF four-axle heavy tractor-trailer vehicle see Figure 5 to investigate the interaction between vehicles and a cable-stayed bridge. A total of three DOFs were assigned to rigid bodies representing either the tractor or the trailer to account for vertical, rolling, and pitching motions. Only one DOF was assigned to the rigid body representing the axle set moving in the vertical direction. Different vehicle models are adopted in wind-vehicle-bridge interaction analyses. Xu and Guo [ 80 ] modeled a DOF two-axle road vehicle see Figure 6 for the dynamic analysis of a coupled road vehicle and bridge system under turbulent wind.

Five DOFs were assigned to the vehicle body with respect to its center of gravity to account for vertical, lateral, rolling, yawing, and pitching motions, and two DOFs were assigned to the front and rear axle sets to account for motions in the vertical and lateral direction. More DOFs are needed to account for lateral crosswinds. Dynamic model of a tractor-trailer [ 79 ]. Dynamic model of a high-sided road vehicle [ 80 ]. On long-span bridges there is a high probability of the simultaneous presence of multiple road vehicles, including heavy trucks.

This may lead to larger amplitude stress responses and greater fatigue damage of the local bridge components than would be the case with only one road vehicle. The simulation of road vehicle flow is thus important in the analysis of the dynamic interaction between road vehicles and bridges. Rather simple patterns of road vehicle flow have been assumed in most vehicle-bridge coupled dynamic analyses [ 79 , 81 , 82 ] in which either one or several vehicles are distributed on the bridge in an assumed usually uniform pattern.

Obviously, such assumptions do not represent actual road traffic conditions. Recently, Chen and Wu [ 83 ] modeled the stochastic traffic load for a long-span bridge based on the cellular automaton CA traffic flow simulation technique. In this study, they simulated a complicated road vehicle flow on long-span bridges in terms of vehicle number, vehicle type combination, and driver operation characteristics, such as lane changing, acceleration, or deceleration.

Road surface roughness is an important factor that greatly affects vehicle-bridge interactions. Paultre et al. The roughness or surface profile depends primarily on the workmanship involved in the construction of the pavement or roadway and how it is maintained, which, although random in nature, may contain some inherent frequencies [ 38 ]. In most cases, surface roughness, which is three-dimensional in reality, is often approximated by a two-dimensional profile. To account for its random nature, the road profile can be modeled as a stationary Gaussian random process and derived using a certain power spectral density function.

Other methods similar to this have been widely adopted by researchers studying vehicle-induced bridge vibration [ 65 , 70 , 71 , 85 — 90 ]. Dodds and Robson [ 91 ] developed power spectral density functions that were later modified and used by Wang and Huang [ 87 ] and Huang et al. This approach was also adopted by literatures [ 79 , 81 ] in their dynamic analyses of coupled vehicle-bridge and wind-vehicle-bridge systems. When a long-span cable-supported bridge is immersed in a given flow field, the bridge will be subject to mean and fluctuating wind forces.

To simulate these forces, a linear approximation of the time-averaged static and time-varying buffeting and self-excited force components must be formulated [ 93 , 94 ]. As dynamic bridge responses are of concern in this study, only buffeting and self-excited forces are considered and reviewed in this section. Buffeting action is a random vibration caused by turbulent wind that excites certain modes of vibration across a bridge depending on the spectral distribution of the pressure vectors [ 95 ].

Although the buffeting response may not lead to catastrophic failure, it can lead to structural fatigue and affect the safety of passing vehicles [ 96 ]. Hence, buffeting analysis has received much attention in recent years in research into the structural safety of bridges under turbulent wind action [ 81 , 95 , 97 — ]. By assuming no interaction between buffeting forces and self-excited forces and using quasi-steady aerodynamic force coefficients, the buffeting forces per unit span F bf ei on the i th section of a bridge deck can be expressed as [ ].

To simulate the stochastic wind velocity field, the fast spectral representation method proposed by Cao et al. This method rests on the assumptions that 1 the bridge deck is horizontal at the same elevation, 2 the mean wind speed and wind spectra do not vary along the bridge deck, and 3 the distance between any two successive points where wind speeds are simulated is the same. The time histories of the along-wind component u t and the upward wind component w t at the j th point can be generated using the following equations [ ]:.

In reality, the equivalent buffeting forces in 3 are actually associated with the spatial distribution of the wind pressures on the surface of the bridge deck. Ignoring the spatial distribution or aerodynamic transfer function of the buffeting forces across the cross-section of the bridge deck may have a considerable impact on the accuracy of buffeting response predictions. Furthermore, the local structural behavior of the bridge deck associated with local stresses and strains, which are prone to causing local damage, cannot be predicted directly by the current approaches based on equivalent buffeting forces.

In this regard, Liu et al. Buffeting wind pressures and buffeting forces at nodes [ 22 ]. In addition to buffeting action, flutter instability caused by self-excited forces induced by wind-structure interactions is an important consideration in the design and construction of long-span suspension bridges [ 96 ], because the additional energy injected into the oscillating structure by the aerodynamic forces increases the magnitude of vibration, sometimes to catastrophic levels [ 95 ]. The self-excited forces on a bridge deck are attributable to the interactions between wind and the motion of the bridge.

When the energy of motion extracted from the flow exceeds the energy dissipated by the system through mechanical damping, the magnitude of vibration can reach catastrophic levels [ ]. Expressing self-excited forces in the form of indicial functions was first suggested by Scanlan [ 94 ].

Based on the assumption that self-excited forces are generated in a linear fashion, Lin and Yang [ ] simplified the self-excited forces acting on a bridge deck and expressed them in terms of convolution integrals between the bridge deck motion and the impulse response functions:.

The relationship between the aerodynamic impulse functions and flutter derivatives can be obtained by taking the Fourier transform of 7 [ 98 ]:. According to classical airfoil theory, the impulse functions can reasonably be approximated by a rational function [ ]:. These coefficients are determined by using the nonlinear least-squares method to fit the measured flutter derivatives at different reduced frequencies.

The expression of the aerodynamic impulse functions in the time domain can be obtained by taking the inverse Fourier transform of the impulse functions. By substituting the related impulse response functions into 5b , the self-excited lift force at the i th section of bridge deck can then be derived as. Similar formulations for self-excited drag and moment can be derived with analogous definitions. The self-excited forces at the i th node of the bridge deck can thus be expressed as. For example,.

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  5. The self-excited forces expressed by 9 relate to the center of elasticity of the i th deck section. A commercial, general-purpose finite element computer program is used to solve problems that are more complex. Projects are used to introduce the use of FEA in the iterative design process. II This course emphasizes the applications of fluid mechanics to biological problems. The course concentrates primarily on the human circulatory and respiratory systems. Topics covered include: blood flow in the heart, arteries, veins and microcirculation and air flow in the lungs and airways.

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    I This course covers topics on the design, fabrication and behavior of advanced materials used in structural and propulsion components of aerospace vehicles. The design, fabrication, and properties of polymer, metal and ceramic matrix composites used in aerospace structures are presented. The fabrication and behavior of aluminum and titanium alloys used in propulsion components as well as the processing and performance of Nickel-based superalloys are also presented.

    The fundamentals of coatings for high temperature oxidation, hot corrosion, and thermal protection are introduced. II This course focuses on materials used in the automotive industry. Students complete a term-long project that integrates design, materials selection and processing considerations. Activities include: problem definition, development of design specifications, development and analysis of alternative designs, conceptual designs and materials and process selection. Students will consider cost, and environmental impact of alternative material choices.

    Students will present their results in intermediate and final design reviews. Recommended background: materials science ES , stress analysis ES , or equivalent. II This course develops an understanding of the processing, structure, property, performance relationships in crystalline and vitreous ceramics. The topics covered include crystal structure, glassy structure, phase diagrams, microstructures, mechanical properties, optical properties, thermal properties, and materials selection for ceramic materials. In addition the methods for processing ceramics for a variety of products will be included.

    Recommended Background: ES or equivalent. I A course specializing in material selection and special problems associated with biomedical engineering. Topics covered include: fundamentals of metals, plastics, and ceramics and how they can be applied to biomedical applications. Case histories of successful and unsuccessful material selections. Current literature is the primary source of material. Recommended background: materials ES I This course introduces students to robotics within manufacturing systems.

    Topics include: classification of robots, robot kinematics, motion generation and transmission, end effectors, motion accuracy, sensors, robot control and automation. This course is a combination of lecture, laboratory and project work, and utilizes industrial robots. Through the laboratory work, students will become familiar with robotic programming using a robotic programming language VAL II and the robotic teaching mode. The experimental component of the laboratory exercise measures the motion and positioning capabilities of robots as a function of several robotic variables and levels, and it includes the use of experimental design techniques and analysis of variance.

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    Prerequisites: differential equations at the undergraduate level. Students cannot receive credit for this course if they have taken either the Special Topics ME A version of the same course or ME The course will include methods for solving linear and nonlinear equations, interpolation strategies, evaluating integrals, and solving ordinary and partial differential equations.

    Finite difference methods will be developed in full for the solution of partial differential equations. The course materials emphasize the systematic generation of numerical methods for elliptic, parabolic, and hyperbolic problems, and the analysis of their stability, accuracy, and convergence properties. The student will be required to write and run computer programs. Topics include computational models of objects and motion, the mechanics of robotic manipulators, the structure of manipulator control systems, planning and programming of robot actions.


    The focus of this class is on the kinematics and programming of robotic mechanisms. Important topics also include the dynamics, control, sensor and effector design, and automatic planning methods for robots. The fundamental techniques apply to arms, mobile robots, active sensor platforms, and all other computer-controlled kinematic linkages. The primary applications include robotic arms and mobile robots and lab projects would involve programming of representative robots. An end of term team project would allow students to program robots to participate in challenges or competitions.

    Prerequisite: RBE or equivalent. FLUID DYNAMICS This course presents the following fundamental topics in fluid dynamics: concept of continuum in fluids; kinematics and deformation for Newtonian fluids; the mass conservation equation for material volumes and control volumes; the differential form of mass conservation, momentum and energy equations. This course covers applied topics chosen from: unidirectional steady incompressible viscous flows; unidirectional transient incompressible viscous flows; lubrication flows similarity and dimensional analysis.

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    Parallel computing. Prerequisite: Fluid dynamics and introductory course in numerical methods. Axial and centrifugal compressors will be discussed as well as axial and radial flow turbines. Analysis of the mean line flow in compressor and turbine blade rows and stages will be discussed. The blade-to- blade flow model will be presented and axisymmetric flow theory introduced. Three-dimensional flow, i. Students cannot receive credit for this course if they have taken the Special Topics ME H version of the same course. Pre-requisites; ES , ES or equivalents.

    Students cannot receive credit for this course if they have taken the Special Topics ME R version of the same course. Topics covered include: classification of partial differential equations PDEs in fluid dynamics and characteristics; finite difference schemes on structured grids; temporal discretization schemes; consistency, stability and error analysis of finite difference schemes; explicit and implicit finite differencing schemes for 2D and 3D linear hyperbolic, parabolic, elliptic, and non-linear PDEs in fluid dynamics; direct and iterative solution methods for algebraic systems.

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    The course will cover the development of the field and provide an overview on different control architectures deliberative, reactive, behavior-based and hybrid control , control topologies, and system configurations cellular automata, modular robotic systems, mobile sensor networks, swarms, heterogeneous systems. Topics may include, but are not limited to, multi-robot control and connectivity, path planning and localization, sensor fusion and robot informatics, task-level control, and robot software system design and implementation.

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    These topics will be pursued through independent reading, class discussion, and a course project. The project may be completed through simulation or hands-on experience with available robotic platforms. Groups will present their work and complete two professional-quality papers in IEEE format. Prerequisites: Linear algebra, differential equations, linear systems, controls, and mature programming skills, or consent of the instructor. Students cannot receive credit for this course if they have taken the Special Topics ME S version of the same course. Applications covered include: image-guided surgery, percutaneous therapy, localization, robot-assisted surgery, simulation and augmented reality, laboratory and operating room automation, robotic rehabilitation, and socially assistive robots.

    Specific subject matter includes: medical imaging, coordinate systems and representations in 3D space, robot kinematics and control, validation, haptics, teleoperation, registration, calibration, image processing, tracking, and human-robot interaction. Topics will be discussed in lecture format followed by interactive discussion of related literature. The course will culminate in a team project covering one or more of the primary course focus areas. Students cannot receive credit for this course if they have taken the Special Topics ME U version of the same course.

    Fundamental concepts including canonical representations, the state transition matrix, and the properties of controllability and observability will be discussed. The existence and synthesis of stabilizing feedback control laws using pole placement and linear quadratic optimal control will be discussed. The design of Luenberger observers and Kalman filters will be introduced. Examples pertaining to aerospace engineering, such as stability analysis and augmentation of longitudinal and lateral aircraft dynamics, will be considered.

    Assignments and term project if any will focus on the design, analysis, and implementation of linear control for current engineering problems. Recommended background: Familiarity with ordinary differential equations,introductory control theory, fundamentals of linear algebra, and the analysis of signals and systems is recommended. Familiarity with Matlab is strongly recommended. Introduction to various design methods based on linearization, sliding modes, adaptive control, and feedback linearization.

    Demonstration and performance analysis on engineering systems such as flexible robotic manipulators, mobile robots, spacecraft attitude control and aircraft control systems. Prerequisites: Familiarity with ordinary differential equations, introductory control theory at the undergraduate level, fundamentals of linear algebra.