Graduate Student Handbook
Chapter 7
Curricula and Course Information
The courses available within the Department of Aerospace Engineering are divided into four major areas - Aerodynamics, Structural Mechanics, Dynamics and Controls, and Experimental Methods in Aerodynamics, Structural Dynamics, and Applied Automatic Control. The 400-level courses are only available for undergraduate credit. The 500-level, 600-level, and 700-level courses are available for Master's degree credit. The 600-level and 800-level courses are available for Doctoral degree credit. A tentative course offering schedule (past and future) is given in Appendix A. The current course listing is summarized below:
Core
Core Curricula
AE 601 - Theoretical Continuum Mechanics (All areas)
AE 602 - Fundamentals of Fluid Dynamics (Aerodynamics)
AE 603 - Variational Methods in Structural Mechanics (Structural Mech.)
AE 604 - Analytical Dynamics of Aerospace Vehicles (Dynamics and Cont.)
AE 605 - Applied Engineering Analysis (MEXM program)
AE 606 - Applied Signal Processing (MEXM program)
Aerodynamics
Theoretical Aerodynamics
AE 406/506 Fluid Dynamics and Aerodynamics
AE 610 Subsonic Flow
AE 611 Supersonic Flow
AE 612 Boundary Layer Theory
AE 613 Fundamentals of Turbulence
AE 710/810 Transonic Flow
AE 711/811 Hypersonic Flow
AE 712/812 Unsteady Flow
AE 713/813 Turbulence Modeling
AE 714/814 Flow Stability, Transition, and Control
AE 715/815 Aerothermodynamics
Computational and Experimental Aerodynamics
AE 620 Computational Fluid Dynamics I
AE 621 Experimental Fluid Mechanics
AE 622 Aerospace Test Facilities
AE 623 Computational Fluid Dynamics Laboratory
AE 720/820 Computational Fluid Dynamics II
AE 721/821 Computational Fluid Dynamics Project
Structural Mechanics
Theoretical Structural Mechanics
AE 420/520 Aerospace Structures
AE 630 Theory of Elasticity
AE 631 Theory of Plates
AE 632 Theory of Shells
AE 633 Flight Vehicle Structural Analysis
AE 634 Structural Vibrations
AE 730/830 Stability of Structures
AE 731/831 Mechanics of Composite Structures
AE 732/832 Thermal Stress Analysis
AE 733/833 Nonlinear Aerospace Systems
AE 734/834 Random Vibrations of Structures
Computational and Experimental Structural Mechanics
AE 640 Finite Element Analysis I
AE 641 Experimental Structural Dynamics
AE 740/840 Finite Element Analysis II
AE 741/841 Finite Element Analysis II
I AE 743/843 Experimental Modal Analysis
Dynamics and Controls
Theoretical Dynamics and Controls
AE 438/538 Control System Design and Application
AE 650 Modern Control Theory
AE 651 Applied Real-time Control
AE 750/850 Robot Analysis and Control
Flight Dynamics and Controls
AE 403/503 Flight Mechanics
AE 660 Aerospace Vehicle Performance
AE 760/860 Atmospheric Flight Dynamics and Control
AE 761/861 Spacecraft Dynamics and Control
Other Courses
Thermal Sciences and Propulsion
AE 417/517 Propulsion Systems
AE 671 Aircraft Propulsion Systems
AE 770/870 Thermal Analysis of Aerospace Vehicles
Miscellaneous and Interdisciplinary Topics
AE 681 Theoretical Acoustics
AE 682 Introduction to Computational Mechanics
AE 683 Introduction to Rotorcraft Performance and Dynamics
AE 780/880 Perturbation Methods in Aerospace Engineering
AE 781/881 Multidisciplinary Problems in Aerospace Engineering
AE 782/882 Aeroelasticity
AE 783/883 Aeroacoustics
AE 784/884 Aerodynamic Design Optimization
Seminars, Thesis Courses etc.
AE 495 Topics in Aerospace Engineering and Engineering Mechanics
AE 497 Independent Study in Aerospace Engineering and Engineering Mechanics
AE 690 Aerospace Engineering Seminar
AE 691 Experimental Research Project
AE 695 Topics in Aerospace Engineering and Engineering Mechanics
AE 697 Independent Study in Aerospace Engineering and Engineering Mechanics
AE 698 Thesis Research in Aerospace Engineering and Engineering Mechanics
AE 795/895 Topics in Aerospace Engineering and Engineering Mechanics
AE 797/897 Independent Study in Aerospace Engineering and Engineering Mechanics
AE 898 Dissertation Research in Aerospace Engineering and Engineering Mechanics
7.1 Approved Courses for the Aerospace Engineering Degree Track
Today Aerospace Engineering involves the solution of complex multi disciplinary problems associated with aerospace vehicles and systems, high-speed trains, advance energy-efficient car designs, spacecraft systems, and many other problems in addition to the traditional areas of aeronautics and astronautics. The Aerospace Engineering Department provides an advanced, high-tech engineering program at ODU. The Department offers the Aerospace Option to Mechanical Engineering seniors as well as challenging Master's and Doctoral programs in Aerospace Engineering (aerodynamics and fluid dynamics, structures and structural dynamics, dynamics, guidance and controls). Our programs encompass theoretical formulations, computational simulations and experimental verification. Our programs emphasizes modern yet fundamental issues of mechanics, applied mathematics, and computational science to provide graduates with tools and incentives for life-long learning so important in today's changing technology.
Notable
All courses listed as AE-XXX are approved for fulfillment of the requirements for the Aerospace Engineering degree, subject to the other requirements mentioned, and approval of the advisor and guidance committee. In addition, MATH 691, 692, 693 are approved. Additional courses may be approved on a case-by-case basis.
7.2 Approved Courses for the Engineering Mechanics Degree Track
Engineering Mechanics involves the application of the fundamental principles of mechanics (solids, fluids, and motion) to the solution of engineering problems of current interest to industry, the government, and the scientific community. Engineering Mechanics provides the basic core set of courses in all undergraduate engineering programs (statics, dynamics, mechanics of materials, and mechanics of fluids). The Aerospace Engineering Department's Engineering Mechanics programs emphasize modern yet fundamental issues of mechanics, applied mathematics, and computational science to provide graduates with tools and incentives for life-long learning so important to today's changing technology.
Solutions are reached through the development of sound engineering models appropriate to specific situations, and the application of applied mathematics, computational science, and/or experimental methods. Our graduates have an increased understanding of fundamental mechanics issues, create efficient, accurate, and adaptable solution techniques, and develop methods for use in the design of new and innovative engineering products. The Department offers the Master's and Doctoral programs in Engineering Mechanics. Our programs encompass theoretical formulations, computational simulations and experimental verification. Engineering Mechanics (AE) program requirements parallel those of other national engineering mechanics graduate programs.
Only certain courses are approved for fulfillment of the core curricula requirements for the Engineering Mechanics degree track. These are:
Master of Science or Master of Engineering in Engineering Mechanics
Aerodynamics - AE 602, 610, 611, 612, 613, 620, 621, 710, 711, 712, 713, 714, 715, 720
Solids - AE 603, 630, 631, 632, 633, 640, 730, 731, 732, 740, 741
Motion - AE 604, 634, 641, 650, 651, 660, 681, 733, 734, 760, 761, 782
Computational Methods - AE 620, 623, 640, 682, 720, 721,740, 741
Math-oriented - MATH 6XX, AE 605, 606, 780
Doctor of Philosophy in Engineering Mechanics
Aerodynamics - AE 610, 611, 612, 613, 620, 621, 810, 811, 812, 813, 814, 815, 820
Solids - AE 630, 631, 632, 633, 640, 830, 831, 832, 840, 841
Motions - AE 634, 641, 650, 660, 681, 833, 834, 860, 861, 882
Computational Methods - AE 620, 623, 640, 682, 820, 821, 840, 841
It is assumed that doctoral students in the engineering mechanics program have a background equivalent to the AE core courses (AE 601, 602, 603, 604) in aerodynamics, structural mechanics, dynamics and controls, partial differential equations and applied numerical methods. These areas should be covered in the Preliminary Diagnostic Examination, or taken by the student in addition to the 8 courses of their program of study.
7.3 Approved Courses for Master of Engineering in Experimental Methods
There is a growing feeling that graduates from traditional Master's level programs lack the practical skills to be immediately productive in the real-world environment of research, development and testing. In addition, the sophistication of experimental test and measurement techniques continues to increase rapidly. The Aerospace Engineering Department has responded to these trends with the Master of Engineering in Experimental Methods (MEXM).
All MEXM students take AE 605, 606 and 691. Students select two emphasis areas, with 3 courses in each area. One approved elective completes the 30-credit-hour requirement. The emphasis areas and required courses are:
Aerodynamics: AE 610 or 506 or 602, 621 and 622
Structural Dynamics: AE 634, 641 and 741
Applied Automatic Control: AE 650, 538 and 651
7.4 AE Course Descriptions
AE 300T Aerospace Technology and Its Impact. Lecture 3 hours; 3 credits. History of flight and evolution. Basic concepts and terminology of flight. Evaluation of flight vehicle configurations and missions. Space programs. Industry/government oversight. Safety and risk management. Current domestic and international aerospace programs. Impact of aviation and space programs on the global society and economy. Case studies in historical and contemporary topics and issues.
AE 403/503 Flight Mechanics. Lecture 3 hours; 3 credits. Prerequisites: AE 406, ME 436. Aircraft concepts including performance prediction and optimization, flight and maneuver envelopes, and steady flight performance. Additional topics: longitudinal static stability and trim; aircraft dynamics; development, separation and solution of aircraft equations of motion; natural modes; dynamic stability, sensors and actuators; design of stability augmentation and autopilot systems.
AE 406/506. Fluid Dynamics and Aerodynamics. Lecture 3 hours; 3 credits. Prerequisites: ME 303, 312, 340. Inviscid flow concepts including: Euler equations, stream function, velocity potential, singularities, vorticity and circulation laws. Viscous flow topics including boundary layers, separation, and turbulent flow. In addition, external flows, lift and drag, thin airfoil theory, finite wing theory and airfoil design will be discussed.
AE 417/517. Propulsion Systems. Lecture 3 hours; 3 credits. Prerequisites: ME 312 or 414. Basic principles of design, operation and performance of propulsion systems - including turbojet, turboprop, turbofan, and ramjet engines. Introduction to chemical rockets, ion and plasma thrusters.
AE 420/520. Aerospace Structures. Lecture 3 hours; 3 credits. Prerequisites: ME 332. Analysis of aircraft and space vehicle structural components. Effects of bending, torsion, and shear on typical aerospace structural components; statically indeterminate beams; shear center and shear flow. Introduction to typical aerospace structures. Introduction to composite structures.
AE 438/538. Control System Design and Application. Lecture 3 hours; 3 credits. Prerequisites: ME 436. Analysis, computer-aided design and implementation of practical control systems; introduction to state space and digital control; laboratory sessions on data acquisition, system identification, analog and digital controllers.
AE 495. Topics in Aerospace Engineering and Engineering Mechanics. Variable 1-3 credit hours. Prerequisite: Permission of the Chair. Special topics of interest with emphasis placed on recent developments in aerospace engineering or engineering mechanics.
AE 497. Independent Study in Aerospace Engineering and Engineering Mechanics. Variable 1-3 credit hours. Prerequisite: Permission of the Chair. Individual analytical computational and/or experimental study selected by student.
AE 601. Introduction to Continuum Mechanics. Lecture 3 hours, 3 credits. Indicial notations and tensor calculus; stress and strain tensors; rate of deformation tensor, Eulerian and Lagrangian descriptions, conservation principles, constitutive formulations for elastic solids and viscous fluids, formulations of fluid mechanics and solid mechanics problems. Simple applications. (cross-listed with ME 607)
AE 602. Fundamentals of Fluid Mechanics and Aerodynamics. Lecture 3 hours; 3 credits. Corequisite: MATH 691, Prerequisites: AE 601. Conservation laws for viscous and inviscid flows, formulation of fluid mechanics and aerodynamics problems. Analytical and numerical solutions of viscous flow problems. Two- and three-dimensional potential flows with applications to airfoils and wings. Introduction to hydrodynamic stability and turbulence.
AE 603. Energy and Variational Methods in Structural Mechanics. Lecture 3 hours; 3 credits. Corequisite: MATH 691. Concepts of energy and variational methods, calculus of variations, variational principles of structural mechanics, Castigliano's Theorems. Approximate methods of solution, applications to bars, beams, and plates. Linear Stress, buckling and vibration problems. (cross-listed with ME 606)
AE 604. Analytical Dynamics of Aerospace Vehicles. Lecture 3 hours; 3 Credits. Advanced kinematics with moving reference frames. Coordinate transformation matrices. Euler equations of motion. Gyroscopic systems and gyroscopic instrument theory. Elementary missile dynamics. Principle of virtual work, D'Alembert's principle, Hamilton's principle, Lagrange's Equations of Motion.
AE 605. Applied Engineering Analysis. Lecture 3 hours, 3 credits. Applications of linear algebra, ordinary and partial differential equations, and complex variables to engineering problems in structural dynamics, applied automatic control and aerodynamics.
AE 606. Applied Signal Processing. Lecture 3 hours; 3 credits. Introduction to random processes, fast Fourier transforms, digital filters, digital signal processing methods, and sensors and transducers. Applications to experimental modal analysis, experimental aerodynamics, and real-time control of electro-mechanical systems.
AE 610. Subsonic Flow. Lecture 3 hours; 3 credits. Prerequisites: AE 406 or 602, MATH 691. Conservation laws, curvilinear coordinates; exact solutions to inviscid equations; Green's theorem; superposition of singularities; nonlifting bodies; vortex and circulation theorems; conformal mapping; thin airfoil theory; lifting line and lifting surface theories; panel techniques; introduction to unsteady flows.
AE 611. Supersonic Aerodynamics. Lecture 3 hours; 3 credits. Prerequisite: AE 602. Governing equation for supersonic flows, Crocco's Theorem, entropy production, Euler limit equations, full potential equation, classification of PDE's governing subsonic, supersonic and transonic flows, first and second-order small disturbance theory, airfoil flows, slender bodies of revolution flows, conical flows, wing flows.
AE 612. Boundary Layer Theory. Lecture 3 hours; 3 credits. Prerequisite: AE 602. Boundary layer equations; method of matched asymptotic expansions; body oriented coordinates, finite-difference solutions; separations, wake and jet flows; thermal and compressible boundary layers, transformations and finite-difference solutions, unsteady boundary layers.
AE 613. Fundamentals of Turbulence. Lecture 3 hours; 3 credits. Corequisite: AE 612. Prerequisite: AE 602. Introduction to the statistical behavior of turbulence. Spectral analysis. Two-point correlations. Reynold's and Favre averaging. Turbulence scales; Kolmogoroff scales. Isotropic and homogeneous turbulence. Mixing length theories. Introduction to turbulence modeling. Introduction to experimental measurements.
AE 620. Computational Fluid Dynamics I. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Classification of single PDE's; finite difference methods; stability analysis, convergence, consistency, efficiency; basics of finite volume methods; model equations of hyperbolic, parabolic and elliptic type; explicit and implicit schemes, central and upwind schemes, weak solutions of quasi-linear hyperbolic equations.
AE 621. Experimental Fluid Mechanics. Lecture 2 hours; Laboratory 2 hours; 3 credits. Prerequisite: AE 602 or 406; AE 611. Techniques for static and dynamic measurement of pressure, temperature, and velocity. Experiment control, statistical treatment of data. Probe methods, including multi-hole pressure probes and hot-wire anemometers. Non-intrusive methods, including Laser Doppler Velocimetry and other optical methods. Surface and stream flow visualization. Surface measurements.
AE 622. Aerospace Test Facilities. Lecture 3 hours; 3 credits. Prerequisite: Permission of the Instructor. Comprehensive examination of aerodynamic test facilities for use in subsonic, transonic, supersonic, and hypersonic flow regimes. Aspects of wind tunnel design and operation. Flow quality. Wall and support interferences. Advanced concepts, including cryogenic wind tunnels, adaptive wall test sections and magnetic suspension. Dynamic testing. Review of flight test methods, including extraction of aerodynamic parameters from flight test data. Review of engine test facilities. Review of ground test facilities for space structures and other space systems.
AE 623. Computational Fluids Dynamics Laboratory. Laboratory 4 hours; 2 credits. Prerequisite: Permission of the Instructor. Overview of fluids equations, discretization, algorithms, stability, grid generation, uncertainty; use of selected software commonly used by practitioners in industry, research labs and academia for grid generation, solutions and postprocessing.
AE 630. Theory of Elasticity. Lecture 3 hours; 3 credits. Prerequisites: MATH 691 and AE 601, or ME 607. Equations of equilibrium, strain-displacement, compatibility, and constitutive equations using Airy and complex potential stress functions; plane engineering boundary-value problems for beams, disks, thick-walled cylinders and various stress raiser problems. Torsion of thin-walled sections. General three-dimensional elasticity problems. (cross-listed with ME 609).
AE 631. Theory of Plates. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Classical and higher-order theories of plates. Navier and Levy solution procedures. Applications to isotropic and laminated plates. Buckling and vibration of plates.
AE 632. Theory of Shells. Lecture 3 hours; 3 credits. Prerequisite: MATH 691 and AE 603. Differential geometry and curvilinear coordinates. Membrane theory of shells. Shells of revolution. Applications to isotropic and laminated shells. Introduction to nonlinear theory.
AE 633. Flight Vehicle Structural Analysis. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Aircraft loads estimation. Review of basic elasticity. Stress functions Prandtl stress function, St. Venant warping, membrane analogy. Bending, shear, and torsion of open and closed, thin-walled cross sections. Analysis of tapered beams with application to fuselages and wings, cutouts and constraints. Introduction to composite materials
AE 634. Structural Vibrations. Lecture 3 hours; 3 credits. Prerequisites ME 404 and MATH 691. Natural modes of discrete and continuous systems, closed form and approximate methods; free and forced responses. Theory of modal analysis and approximate methods for undamped and damped systems; transform and wave solutions. Finite element methods. Structural vibrations under combined loading. Introduction to non-linear vibrations. Applications to rods, beams, plates, and shells.
AE 640. Finite Element Analysis I. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Mathematical concepts of finite element analysis. Variational approach based on weak-form solutions to partial differential equations. Basic concepts of interpolation functions, continuity, discretization, and assembly. Applications to 1-D and 2-D problems of engineering.
AE 641. Experimental Structural Dynamics. Lecture 1 hour; Laboratory 4 hours; 3 credits. Prerequisite: AE 634. Experimental techniques and methods for structural dynamics and vibrating systems. Instrumentation selection and utilization including electrodynamic shakers, impact hammers, accelerometers, laser vibrometers, signal analyzers, signal filters, and force transducers. Time and frequency domain data acquisition, assessment and post processing. Demonstration of correlation and theoretical vibration topics for lumped and distributed systems undergoing free and forced motion.
AE 650. Modern Control Theory. Lecture 3 hours; 3 credits. Prerequisite ME 436 or equivalent. Formulation of state space equations governing dynamics and stability of linear systems. Controllability; observability. State feedback control design. Optimal control methods. State observers and estimators. (cross-listed with ME 636).
AE 651. Applied Real-Time Control. Lecture 2 hours; laboratory 2 hours; 3 credits. Corequisite AE 438/538. Real-time computer programming methods for control of electromechanical systems. Synchronous programming, timing and time interrupts, asynchronous signal processing, data structures for real-time control, control of multiple independent processes, operator interfaces, event driven scheduling, interaction of digital computers with controlled processes. The course includes laboratory experience using micro-computers to control electro-mechanical systems.
AE 660. Aerospace Vehicle Performance. Lecture 3 hours; 3 credits. Prerequisites: AE406 or 602, ME 414 or AE 611. A study of the flight performance of aerospace vehicles. Review of aerodynamic, and propulsion characteristics. Range, flight and maneuver envelopes for vehicles in atmospheric flight. Introduction to methods of design and trajectory optimization. Design and performance of launch vehicles. Open-ended, design-oriented project work.
AE 667. Cooperative Education. 1-3 credits.
AE 671. Aircraft Propulsion Systems. Lecture 3 hours; 3 credits. Prerequisite: AE 417. Thermodynamic cycles of aerospace propulsion systems. Fluid flow in turbo machinery; rotor/fluid interaction. Design and performance of air intakes; axial compressors; combustion chambers; axial turbines; propelling nozzles. Special topics include transonic stages, centrifugal compressors and turbines, variable geometry nozzles.
AE 681. Theoretical Acoustics. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Introduction to the linear theory of acoustics. Waves on flexible strings, bars, membranes, plates and shells. Acoustic wave motion in fluids. Radiation, scattering and absorption of sound. Coupling of acoustical systems. Acoustics in moving media. Nonlinear oscillations and waves.
AE 682. Introduction to Computational Mechanics. Lecture 3 hours; 3 credits. Prerequisite: FORTRAN or C experience. Matrix and symbolic computing systems, use of computational and visualization techniques for solving linear and nonlinear algebraic systems, eigensolvers, minimization methods, integration, regression analysis, data reduction, ODE systems, performance metrics for algorithms, applications to aerospace engineering and engineering mechanics.
AE 683. Introduction to Rotorcraft Performance and Dynamics. Lecture 3 hours; 3 credits. Prerequisite: MATH 691. Introduction to rotorcraft; Hover aerodynamics performance; Auto rotation; Blade motion & rotor control; Forward flight aerodynamics & performance; Rotor dynamics & stability.
AE 690. Aerospace Engineering Seminar. Lecture 1 hour; 1 credit. Regular tutorials on recent topics of interest in Aerospace Engineering and Engineering Mechanics.
AE 691. Experimental Research Project. Laboratory 6 hours; 3 credits. Prerequisite: permission of the instructor. An independent laboratory experience in the area of either aerodynamics, structural dynamics or applied automatic control. Results will be reported in a format and quality similar to a technical conference paper.
AE 695. Topics in Aerospace Engineering and Engineering Mechanics. Lecture 3 hours; 3 credits. Prerequisite: permission of the instructor. Special topics of interest with emphasis placed on recent developments in aerospace engineering or engineering mechanics.
AE 697. Independent Study in Aerospace Engineering and Engineering Mechanics. Lecture 3 hours; 3 credits. Prerequisite: Permission of the instructor. Individual analytical and/or experimental study selected by the student. Supervised and approved by the advisor.
AE 698. Thesis Research in Aerospace Engineering and Engineering Mechanics. Credit hours: Variable 1-3. Prerequisite: Permission of the instructor. Research leading to the Master of Science thesis.
AE 710/810. Transonic Flow. Lecture 3 hours; 3 credits. Prerequisite: AE 611. Singular surfaces under the Euler limit; transonic breakdown of linearized theory; transonic expansion procedures; transonic small disturbance theory; transonic slender bodies; similarity rules; hodograph equation; transonic far fields; relaxation schemes; unsteady transonic flows; three-dimensional wings; finite difference methods.
AE 711/811. Hypersonic Flow. Lecture 3 hours; 3 credits. Prerequisite: AE 611. General considerations of hypersonic flow and similarity principles; hypersonic flow past slender bodies with sharp and blunt leading edges. Hypersonic blunt-body flows. Real gas, viscous, and low density effects, and consideration of nonequilibrium phenomena in hypersonic flows.
AE 712/812. Unsteady Flow. Lecture 3 hours; 3 credits. Prerequisites: AE 610, 611, 612. Review of the basic laws; oscillating airfoils in incompressible, subsonic, and supersonic flows; arbitrary airfoil motion, oscillating finite wings; unsteady motion of finite wings; unsteady motion of nonlifting bodies; unsteady boundary layer flow in two-dimensional and axisymmetric flows, periodic boundary layer flows, unsteady separation; oscillating flow in a pipe, unsteady compressible boundary layers.
AE 713/813. Turbulence Modeling. Lecture 3 hours; 3 credits. Prerequisite: AE 613. Equilibrium turbulence models. Two-equations models (k-epsilon). Large-Eddy simulation. Reynold's stress transport models. Numerical simulations. Compressible and non-equilibrium turbulence effects.
AE 714/814. Flow Stability, Transition, and Control. Lecture 3 hours; 3 credits. Prerequisites: AE 612. Basic concepts of hydrodynamic stability; linear stability analysis; stability of parallel flows; Orr-Sommerfeld equations; inviscid and viscous instability; thermal instability; centrifugal instability; non-linear stability analysis; transition to turbulence, boundary layer control.
AE 715/815. Aerothermodynamics. Lecture 3 hours; 3 credits. Prerequisite: AE 611, 711. Thermal environment of high performance vehicles. Elements of supersonic combustion. Multiple temperature and relaxation models. Kinetics of chemical reactions in homogeneous and surface processes. Modifications to governing equations. Dimensionless forms and limiting cases.
AE 720/820. Computational Fluid Dynamics II. Lecture 3 hours; 3 credits. Corequisite: AE 602. Prerequisite: AE 620. Classification of systems of PDE's; mathematical nature of Euler equations; conservative form of the Navier-Stokes equations; grid generation; central difference schemes; finite volume schemes; upwind flux-vector, flux-difference, and TVD schemes; boundary conditions.
AE 721/821. Computational Fluid Dynamics Project. Laboratory 4 hours; 2 credits. Prerequisite: AE 720/820. Develop CFD codes for algebraic grid generation, inviscid flow using a central and upwind algorithm, viscous flow using an upwind-biased/central algorithm, applications to aerospace vehicles.
AE 730/830. Stability of Structures. Lecture 3 hours; 3 credits. Prerequisite: AE 601, 603, 631. Buckling of bars, plates, and shells. Energy, adjacent equilibrium, and small oscillations criteria for instability of equilibrium are applied to continuous and discrete systems. Finite element analysis and composite structures.
AE 731/831. Mechanics of Composite Structures. Lecture 3 hours; 3 credits. Prerequisite: AE 601. Stress-strain relations for a lamina; failure theories. Micro-mechanical behavior of a lamina. Constitutive relations of a laminate. Bending, buckling, and vibration of laminated plates. Approximate and finite element methods of solution.
AE 732/832. Thermal Stress Analysis. Lecture 3 hours; 3 credits. Prerequisite: AE 601. Formulation of thermoelasticity problems for elastic materials. Solution methods for two- and three-dimensional thermoelastic problems. Computational and finite element methods.
AE 733/833. Nonlinear Systems in Aerospace Engineering. Lecture 3 hours; 3 credits. Prerequisites: AE 634. Conservative and nonconservative non-linear systems. Qualitative analysis; methods of multiple scales and averaging. Super- and subharmonic resonances. Self-sustained oscillations. Parametrically excited systems; effects of nonlinearities. Multiple degree-of-freedom systems; continuous systems. Application to beams, strings and plates.
AE 734/834. Structural Vibrations II. Lecture 3 hours; 3 credits. Prerequisite: AE 634. Stationary random processes; autocorrelation and spectral density; ergodic processes and temporal statistics. Structures with single degree -of-freedom. Response of multi-degree-of-freedom and continuous systems. Estimating service life. Introduction to nonlinear vibrations of structures.
AE 740/840. Finite Element Analysis II. Lecture 3 hours; 3 credits. Prerequisite: AE 640. Application of variational methods to structural mechanics. General finite element development procedures including symbolic computations. Finite element formulations based on alternate variational principles. Applications to plate bending, buckling, and vibration. Introduction to non-linear problems.
AE 741/841. Finite Element Analysis III. Lecture 3 hours; 3 credits. Prerequisites: AE 601, 603 and 740/840. Introduction to nonlinear continuum mechanics. Nonlinear formulations and solution strategies for static and transient problems. Advanced computational procedures; introduction to multidisciplinary analysis.
AE 743/843. Experimental Modal Analysis. Lecture 2 hours; Laboratory 2 hours; 3 credits. Prerequisite: AE 641. Techniques of experimental modal analysis will be investigated including the application of Fast Fourier Transform methods to the structural dynamic measurement and mathematical modeling process, measurement and excitation methods, proper experimental procedure for collection of quality data, and development of mathematical models from experimental data. Laboratory demonstrations and student experiments will be performed using state-of-the-art equipment.
AE 750/850. Robot Analysis and Control. Lecture 3 hours; 3 credits. Prerequisite: AE 650. Kinematic and dynamic analysis of robotic servo mechanisms including drive and actuator dynamics. Introduction to non-linear control. Key state-of-the-art motion and force control techniques.
AE 760/860. Atmospheric Flight Dynamics and Control. Lecture 3 hours; 3 credits. Prerequisite: AE 403, 650. Principles governing the dynamics and control of vehicles in atmospheric flight. Equations of motion development and solution including inertia/gravitational/aerodynamic/propulsive loads, linear longitudinal and lateral-directional motions, and nonlinear trim and simulation. Flight control system design and analysis incorporating flying quality requirements, linear conventional/contemporary and frequency/time-domain techniques for control and guidance functions, validation with nonlinear simulation, gain scheduling.
AE 761/861. Space Flight Dynamics and Control. Lecture 3 hours; 3 credits. Prerequisites: AE 604, 650. Principles governing the dynamics and control of vehicles in space flight. Equations of motion development and solution including inertial/gravitational/propulsive loads, decoupled transnational and attitude motions. Orbital mechanics including elements, initial-value propagation, adjustments/transfers, Lambert boundary-value problem, perturbations, and nonlinear simulation. Attitude dynamics including torque free, gravity moment, axisymmetric/unsymmetric vehicles, and dual spinners. Flight control system design and analysis including impulsive velocities, finite burns, Lambert targeting, linear design using momentum wheels, and nonlinear phase-plane design using thrusters.
AE 770/870. Thermal Analysis of Aerospace Vehicles. Lecture 3 hours; 3 credits. Finite element formulation of heat conduction problems in aerospace structures. Development of thermal analysis techniques for extracting heat flux estimates from tunnel data. Application of boundary-layer techniques in estimating convective heat transfer for external, compressible flows. Overview of radiation heat transfer considerations.
AE 780/880. Perturbation Methods in Aerospace Engineering. Lecture 3 hours; 3 credits. Method of multiple scales, derivative expansion, two scales method, generalized method; solvability conditions, acoustic waves in ducts, vibrations of nearly circular membranes, general fourth-order P.D.E.; Methods of averaging, KB and KBM methods; canonical variables, Lagrangian and Hamiltonian, applications in vibrations and wave motion.
AE 781/881. Multidisciplinary Problems in Aerospace Engineering. Lecture 3 hours; 3 credits. Prerequisites: AE 630, 720/820, 760/860. Formulation of fluids/dynamics interaction. Initial and boundary conditions, frames of reference, moving grids, methods of solution, formulation of fluid/structure interaction, initial and boundary conditions, frame of reference, deforming grids, methods of solution; formulations of fluid/dynamics/control interaction, sequential versus simultaneous solutions; generalized interaction problems, sensitivity analysis, and optimization.
AE 782/882. Aeroelasticity. Lecture 3 hours; 3 credits. Prerequisite: AE 634. Introduction to aeroelasticity, Static and dynamic loads, energy methods eigenvalue problems, natural frequencies and modeshapes. Unsteady aerodynamics, 2-D incompressible flow, 2-D subsonic and supersonic compressible flow. Aeroelastic phenomena, divergence, control reversal, flutter, dynamic response. Aeroelastic models and testing, scaling laws, model design, testing techniques.
AE 783/883. Aeroacoustics. Lecture 3 hours; 3 credits. Prerequisite AE 611, 681. Equations of aeroacoustic wave propagation, aerodynamics sources, acoustic analogy, effects of uniform and nonuniform flow, duct acoustics, linearization, introduction to numerical simulation, boundary conditions and time-series analysis.
AE 784/884. Aerodynamic Design Optimization. Lecture 3 hours; 3 credits. Prerequisite AE 720/820 or 740/840. Review of aerodynamic analysis, surface and shape parameterization, unconstrained minimization, constraints, discrete sensitivities, control theory and variational sensitivities, stochastic search methods, inverse methods, analysis-optimization coupling, decomposition.
AE 795/895. Topics in Aerospace Engineering and Engineering Mechanics. Lecture 3 hours; 3 credits. Prerequisite: Permission of the Instructor. Special topics of interest with emphasis placed on recent developments in aerospace engineering or engineering mechanics.
AE 797/897. Independent Study in Aerospace Engineering and Engineering Mechanics. Lecture 3 hours; 3 credits. Prerequisite: Permission of the Instructor. Individual analytical, computational and/or experimental study selected by the student. Supervised and approved by the advisor.
AE 898. Dissertation Research in Aerospace Engineering and Engineering Mechanics. Credit hours: Variable 1-9. Prerequisite: Permission of the Instructor. Dissertation research in aerospace engineering or engineering mechanics.
7.5 MATH Course Descriptions
For completeness, the approved 600-level MATH course descriptions from the University catalog are included here:
MATH 621. Advanced Numerical Analysis I. Lecture 3 hours; 3 credits. Prerequisite: MATH 518. This course will deal with the analysis of interpolation approximation of functions, numerical integration and numerical matrix computations that include decomposition theory, orthogonalization methods, least square methods eigenvalue problems and the QR method.
MATH 622. Advanced Numerical Analysis II. Lecture 3 hours; 3 credits. Prerequisite: MATH 621. An introduction to the numerical solution of ordinary and partial differential equations. Topis include linear multistep methods, strong and weak stability analysis. Runge-Kutta methods, stiff differential equations, finite difference methods for parabolic, elliptic and hyperbolic partial differential equations, stability and convergence analysis.
MATH 691. Engineering Analysis I. Lecture 3 hours; 3 credits. Not available to students with credit in MATH 401 of 501. Prerequisites: MATH 307U and 312. Separation of variable techniques, Strum-Liouville Systems, generalized Fourier series, orthogonal functions of the trigonometric, Legendre and Bessel type boundary value problems associated with the wave equation and the heat conduction equation in various coordinate systems, applications to physics and engineering.
MATH 692. Engineering Analysis II. Lecture 3 hours; 3 credits. Not available to students with credit in MATH 422 or 522. Prerequisite: MATH 312. Topics include complex numbers, analytic functions and their properties, derivatives, integrals series representations, residues and conformal mappings. Applications of the calculus of residues and mapping techniques to the solution of boundary value problems in physics and engineering.
MATH 693. Methods of Applied Mathematics. Lecture 3 hours; 3 credits. Prerequisite: MATH 501 or 691. Advanced topics in the theory and application of ordinary differential equations, distributions, Green's functions, classification of partial differential equations, initial-value problems, eigenfunction expansions for boundary-value problems, selected special function, singular perturbation theory for differential equations.