9: School of Graduate Engineering and Applied Science

General Information | Degree Programs | Program Descriptions | Course Descriptions | Faculty

Aerospace Engineering | Applied Mathematics | Applied Mechanics | Biomedical Engineering
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Mechanical and Aerospace Engineering

Mechanical and Aerospace Engineering faculty

Listed prerequisites represent ordinary and reasonable preparation. Equivalent preparation is acceptable. Enrollment without prerequisites is allowed with permission of instructor.

Courses with asterisks will be offered subject to sufficient student interest; they may be taken on an independent-study basis by doctoral students.

Graduate students in Mechanical and Aerospace Engineering often take courses in applied mathematics and other engineering and science departments.

MAE 602 - (3) (Y)
Continuum Mechanics With Applications
Introduction to continuum mechanics and mechanics of deformable solids. Vectors and cartesian tensors, stress, strain, deformation, equations of motion, constitutive laws, introduction to elasticity, thermal elasticity, viscoelasticity, plasticity, and fluids. Cross-listed as AM 602, APMA 602, CE 602.

MAE 603 - (3) (Y)
Computational Solid Mechanics
Prerequisite: MAE 602
Variational and computational mechanics of solids, potential energy, complementary energy, virtual work, Reissner's principle, Ritz and Galerkin methods. Displacement, force and mixed methods of analysis. Finite element analysis, including shape functions, convergence and integration. Applications in solid mechanics. Cross-listed as AM 603, CE 603.

MAE 604 - (3) (E)
Plates and Shells
Prerequisites: APMA 541, AM 601 or AM 602
Classical analysis of plates and shells. Plates of various shapes (rectangular, skew) and shells of various shapes (cylindrical, conical, spherical, hyperbolic, paraboloid). Closed-form numerical and approximate methods of solution governing partial differential equations. Advanced topics (large deflection theory, thermal stresses, orthotropic plates). Cross-listed as AM 604, CE 604.

MAE 611 - (3) (O)
Heat Transfer
Prerequisite: Undergraduate fluid mechanics
Multi-dimensional heat conduction under steady and transient conditions. Heat, mass, and momentum transfer associated with laminar and turbulent fluid flow in free and forced convection. Heat transfer during phase changes. Radiation heat transfer analysis, including considerations of gray, diffuse, and specular surfaces. Gas radiation. Applications of theory to mechanical, chemical, and nuclear systems.

MAE 616 - (3) (Y)
Advanced Thermodynamics
Prerequisite: Undergraduate thermodynamics
Basic concepts, postulates, and relationships of classical thermodynamics. Thermodynamics potentials and derivatives. Energy minimum and entropy maximum principle. Generalized Maxwell relations. Stability considerations. Phase transitions. Application to perfect and imperfect systems. Extension to chemically reacting and solid systems.

MAE 617 - (3) (E)
Microscopic Thermodynamics
Prerequisite: Undergraduate thermodynamics
Thermodynamics of gases developed from a microscopic point of view. Kinetic theory derivation of equilibrium thermodynamic and transport properties of gases. Introduction to advanced non-equilibrium kinetic theory. Quantum mechanical treatment of atomic and molecular energy level structure. Statistical mechanics derivation of the thermodynamic properties of equilibrium gases. Chemical thermodynamics and chemical equilibrium of reacting gas mixtures. Applications of the theory of high temperature gas behavior, gas-phase combustion and equilibrium and non-equilibrium gas dynamics.

MAE 620 - (3) (Y)
Energy Principles in Mechanics
Prerequisite: Permission of instructor
Derivation, interpretation, and application to engineering problems of the principles of virtual work and complementary virtual work. Related theorems such as the principles of the stationary value of the total potential and complementary energy, Castigliano's Theorems, theorem of least work, and unit force and displacement theorems. Introduction to generalized, extended, mixed, and hybrid principles. Variational methods of approximation, Hamilton's principle, and Lagrange's equations of motion. Approximate solutions to problems in structural mechanics by use of variational theorems. Cross-listed as AM 620, CE 620.

MAE 621 - (3) (Y)
Analytical Dynamics
Prerequisite: Differential equations
Kinematics of rigid body motion, Eulerian angles, Lagrangian equations of motion, inertia tensor, momental ellipsoid. Rigid body equations of motion, Euler's equations, force-free motion, polhode and herpolhode, theory of tops and gyroscopes, variational principles, Hamiltonian equations of motion, Poinsote representation. Cross-listed as AM 621.

MAE 623 - (3) (Y)
Prerequisite: Permission of instructor
Free and forced vibrations of undamped and damped single-degree-of-freedom systems and undamped multi-degree-of-freedom systems. Use of Lagrange's equations, Laplace transforms, matrix formulation, and other solution methods. Normal mode theory. Introduction to vibration of continuous systems. Cross-listed as AM 623, CE 623.

MAE 625 - (3) (Y)
Advanced Dynamics of Machinery I
Prerequisite: MAE 623
Advanced dynamical problems in reciprocating and rotating machinery. Vibration reduction techniques. Torsional and lateral critical frequencies for multi-mass systems. Dynamic vibration absorbers.

MAE 627 - (3) (IR)
Dynamic Stability of Aerospace Vehicles
Prerequisite: Permission of instructor
Development of vehicle equations of motion using state-space methods. Linearization and nondimensionalization of these equations. Aerodynamic coefficients and characteristics. Closed-form and computer solutions. Special configuration effects, ground effects. Topics of current interest.

MAE 631 - (3) (Y)
Fluid Mechanics I
Prerequisite: Permission of instructor
Hydrostatics, including surface tension. Kinematics. Non-inertial reference frames. Rigorous formulation of conservation equations for mass, momentum, and energy dimensional analysis. Euler and Bernoulli equations. Vorticity dynamics. Two-dimensional potential flow theory, complex potentials; applications to airfoils. The Navier-Stokes equations: selected exact and approximate solutions The laminar boundary layer equations, differential and integral. Elementary similar and integral solutions. Introduction to and modeling of turbulent flows. Cross-listed as AM 631.

MAE 632 - (3) (Y)
Fluid Mechanics II
Prerequisite: MAE 631
Hydrodynamic stability, surface waves, quasi-one-dimensional compressible, perfect gas dynamic analysis, creeping flows. Practical applications. Cross-listed as AM 632.

MAE 637 - (3) (O)
Singular Perturbation Theory
Prerequisites: APMA 315, APMA 513 or equivalent
Regular perturbations, roots of polynomials. Singular perturbations in ODE's, periodic solutions of simple nonlinear differential equations. Multiple-Scales method. WKBJ approximation. Turning-point problems. Langer's method of uniform approximation. Asymptotic behavior of integrals, Laplace Integrals, stationary phase, steepest descents. Examples drawn from Physical systems. Cross-listed with APMA 637.

MAE 641 - (3) (O)
Lubrication Theory and Design
Prerequisite: Permission of instructor
The hydrodynamic theory of lubrication for an incompressible fluid. Design principles of bearings: oil flow, load-carrying capacity, temperature rise, stiffness, damping properties. Influence of bearing design upon rotating machinery. Computer modeling methods. Applications to specific types.

MAE 644 - (3) (IR)
Theoretical Acoustics
Prerequisite: APMA 341
Theoretical description of sound-transmission processes. Derivation of basic gas dynamic equations, behavior of plane waves. The basic processes of transmission, reflection, and absorption. Transmission in non-uniform, shearing atmospheres. Sound waves in two and three dimensions; line sources, monopoles, dipoles, quadrupoles. Helmholtz integral equation. Sound transmission inducts and resonators. Cross-listed as AM 644.

MAE 651 - (3) (Y)
Linear Automatic Control Systems
Prerequisite: Permission of instructor
Dynamics of linear, closed-loop systems. Mechanical, electrical, hydraulic, and other servo systems. Analysis of transfer functions; stability theory. Compensation methods.

MAE 662 - (3) (IR)
Mechanical Design Analysis
Prerequisite: Undergraduate mechanical design or permission of instructor
Design analysis of machine elements subject to complex loads and environments. Emphasis on modern materials and computer analysis. Theory of elasticity, energy methods. Failure theories, fracture, fatigue, creep. Contact, residual, and thermal stresses. Experimental stress analysis. Corrosion.

MAE 665 - (3) (Y)
Computer Aided Engineering and Design
Prerequisites: Permission of instructor; programming language (FORTRAN or PASCAL), matrix algebra
A comprehensive overview of computer graphics, geometric modeling, and computer aided design. Addresses theory and applications, reviewing both the mathematical and technological foundations of interactive computer graphics, selected CAD applications and examples. Currently available CAD/CAM hardware and software are covered, as is various analysis and optimization programs. Students address the problems and issues in constructing and using integrated CAD/CAM in a production environment. Students use the hardware and software available in the Center for Computer Aided Engineering and Design.

MAE 666 - (3) (O)
Manufacturing Processes and Materials
Prerequisite: Undergraduate courses in strength of materials and material science that match the course content in the University of Virginia courses ENGR 306 and ME 339
Metal fabrication processes. Analytical treatment of metal extrusion, rolling, forging of disks, flow through conical converging dies, wire and rod drawing and open die extrusion, tube shrinking and expanding, flow through inclined planes, and forging of strips. Typical material properties associated with these processes will be discussed.

MAE 667 - (3) (Y)
Introduction to Manufacturing Systems
Prerequisite: Permission of instructor
Systems approach to manufacturing. Tools and concepts necessary to integrate the computer into manufacturing: numerical control, programmable controllers, flexible manufacturing systems, group technology, process planning and control, modeling and simulation of factory operations. This course will include models of manufacturing processes and operations (ICAM, ECAM, National Bureau of Standards), and case histories of exemplary Computer Integrated Manufacturing (CIM) implementations (the John Deere Tractor Works, the Ingersoll Milling Machine Company, AT&T Technologies Richmond Works, and selected GE plants). Field trips to several advanced manufacturing facilities (AT&T, GE, NBS/AMRF) will be conducted.

MAE 668 - (3) (Y)
Advanced Manufacturing Technologies
Prerequisites: MAE 665 and 667
New technologies for factory automation, including intelligent machines, robotics, machine vision, image processing, artificial intelligence. Emphasis on control for automated manufacturing; computer control of machines and processes; automatic controls; distributed networks; monitoring, inspection, and quality control. The course will also focus on research problems in each of these areas.

MAE 671 - (3) (Y)
Applied Finite-Element Analysis
Prerequisite: Permission of instructor
Introduction to finite element methods for solving problems in heat transfer, fluid mechanics, solid mechanics, and electrical fields. Basics of one, two, and three-dimensional elements. Applications to bars, electrical networks, trusses, conduction and convection heat transfer, ideal and viscous flow, electrical current flow, plane stress, plane strain, and elasticity. Development of computer codes to implement finite element techniques. Cross-listed as AM 671.

MAE 672 - (3) (Y)
Computational Fluid Dynamics I
Prerequisite: MAE 631 or permission of instructor
Solution of flow and heat transfer problems involving steady and transient convective and diffusive transport. Superposition and panel methods for inviscid flow, finite-difference methods for elliptic, parabolic and hyperbolic partial differential equations, elementary grid generation for odd geometries, primitive variable and vorticity-steamfunction algorithms for incompressible, multidimensional flows. Extensive use of personal computers/workstations including interactive graphics. Cross-listed as APMA 672.

MAE 676 - (3) (IR)
Advanced Finite Element Analysis
Prerequisite: Permission of instructor
Two and three dimensional structural and elastic finite element models will be generated for the analysis of deformations, stress, three dimensional structural mode shapes, heat transfer properties using the latest state-of-the-art finite element programs for color graphics desktop workstations. Practice will be given in the proper application of boundary conditions, optimum finite element mesh generation and element usage. Classical solutions will be compared to FEA solutions to illustrate the rate of convergence.

MAE 685 - (3) (Y)
Measurement Theory and Advanced Instrumentation
Prerequisite: Undergraduate electrical science
Theory and practice of modern measurement and measurement instrumentation. Statistical analysis of data; estimation of errors and uncertainties. Operating principles and characteristics of fundamental transducers and sensors; common electrical circuits and instruments. Signal processing methods.

MAE 687 - (3) (IR)
Applied Engineering Optics
Prerequisite: PHYS 241E
Modern engineering optics and methods. Fundamentals of coherence, diffraction interference, polarization, and lasing processes. Fluid mechanics, heat transfer, stress/strain, vibrations, and manufacturing applications. Laboratory practice: interferometry, schlieren/shadowgraph, and laser velocimetry.

MAE 692 - (3) (Y)
Special Topics in Mechanical and Aerospace Science:
Intermediate Level
Prerequisites: As specified for each offering by title
Study of a specialized, advanced, or exploratory topic relating to mechanical or aerospace engineering science, at the first-graduate-course level. May be offered on a seminar or a team-taught basis. Subjects selected according to faculty interest. New graduate courses are usually introduced in this form. Exact subject indicated in the seasonal Course Offering Directory.

MAE 693 - (3) (Y)
Independent Study in Mechanical or Aerospace Science:
Intermediate Level
Prerequisite: As listed for the specific course involved
Independent study of first-year graduate level material under the supervision of a faculty member.

MAE 694 - (Credit as arranged) (Y)
Special Graduate Project in Mechanical or Aerospace
Engineering: First-Year Level
A design or research project for a first-year graduate student under the supervision of a faculty member. A written report must be submitted and an oral report presented. Up to three credit hours from either this course or MAE 794 may be applied toward the master's degree.

MAE 703 - (3) (IR)
Thermal Structures
Prerequisite: MAE 602 or permission of instructor
Fundamentals of thermal structural analysis. Mechanical and thermodynamic foundations. Formulation of heat transfer and thermal-structural problems. Heat transfer in structures. Thermal stresses in rods, beams, and plates. Thermally induced vibrations. Thermoelastic stability. Computational methods.

MAE 712 - (3) (E)
Convective Heat Transfer
Prerequisites: MAE 631 or CHE 625
Forced and free convective heat transfer in boundary layers, closed channels, and other geometries. Liquid-metal heat transfer. Two-phase flow. Condensation and boiling. Simultaneous heat and mass transfer.

MAE 713 - (3) (IR)
Radiative Heat Transfer
Prerequisite: Introductory heat transfer
Fundamental principles of radiant energy exchange, Kirchoff's laws. Characteristics of real vs. ideal systems, monochromatic vs. total energy exchange, configuration factors. Computational techniques. Analysis of non-gray and non-diffuse systems. Radiant energy transfer through absorbing, emitting, and scattering media. Practical examples.

MAE 715 - (3) (E)
Prerequisite: Undergraduate thermodynamics and MAE 631, or permission of instructor
Review of chemical thermodynamics, including conservation laws, perfect gas mixtures, combustion chemistry and chemical equilibrium. Finite-rate chemical kinetics. Conservation equations for multicomponent reacting systems. Detonation and deflagration waves in premixed gases. Premixed laminar flames. Gaseous diffusion flames and droplet evaporation. Introduction to turbulent flames. Chemically-reacting boundary-layer flows. Ignition. Applications to practical problems in energy systems, aircraft propulsion systems and internal combustion engines. Student projects selected from topics of interest to the class.

MAE 722 - (3) (O)
Analytical Dynamics II
Prerequisite: MAE 621
Formulation and application of the generalized principles of classical particle and continuum mechanics. Lagrangian mechanics: Hamiltonian mechanics. Canonical transformation theory. Dynamics of variable-mass systems. Dynamics of connected, rigid-body systems. Stability analysis of dynamical systems. Analysis of nonlinear systems by perturbation methods. Applications to space and machine dynamics. Cross-listed as AM 722.

MAE 724 - (3) (Y)
Advanced Vibrations
Prerequisite: MAE 623
Study of the motion of large scale systems including model synthesis, model testing and reanalysis theory. Shock wave analysis. Shock and vibration isolation. Integration of linear and nonlinear governing equations. Use of general purpose analysis systems. Cross-listed as AM 724.

MAE 726 - (3) (E)
Advanced Dynamics of Machinery II
Prerequisite: MAE 625
Stability of high-speed rotating machinery. Equations of motion for a rotor, including gyroscopic effects. Instabilities due to internal shaft hysteresis and hydrodynamic bearings. Nonlinear systems. Secondary critical frequencies and subharmonic resonances.

MAE 729 - (3) (IR)
Mechanics of Space Flight
Prerequisite: MAE 621
Astrodynamics. Fundamental geometric, kinematic, and physical concepts involved in representing space-vehicle motion and modeling space-flight motion. Analytical and numerical methods employed in satellite position prediction, orbit determination, navigation, guidance, trajectory optimization, and mission analysis.

MAE 734 - (3) (E)
Turbulent Flow
Prerequisite: MAE 631
Mathematical representation of turbulent flows. Kinematics of homogeneous turbulence; linear problems. Decay dynamics, universal equilibrium theory. Recent theoretical and experimental work.

MAE 736 - (3) (O)
Gas Dynamics
Prerequisite: MAE 632
Theory and solution methods applicable to multi-dimensional compressible, inviscid gas flows at both supersonic and subsonic speeds. Similarity and scaling rules from small-perturbation theory. Introduction to transonic and hypersonic flows. Method-of-characteristics applications to nozzle flows, jet expansions, and flows over bodies. Properties of gases in thermodynamic equilibrium, including kinetic-theory, chemical-thermodynamics, and statistical-mechanics considerations. Dissociation and ionization processes. Quasi-equilibrium flows. Introduction to non-equilibrium flows.

MAE 738 - (3) (IR)
Nonlinear Dynamics and Waves
Prerequisites: APMA/MAE 637 or permission of instructor
Application of phase plane methods, singular perturbation theory, inverse scattering, and related techniques to the study of free and forced nonlinear vibrations, nonlinear stability and bifurcations, and nonlinear wave motions. Examples are drawn from mechanics and fluid dynamics. Cross-listed as APMA 738.

MAE 742 - (3) (IR)
Lubrication Theory and Design II
Prerequisite: MAE 641
General hydrodynamic theory of lubrication for multi-dimensional incompressible and compressible fluids. Thermal effects, in both laminar and turbulent films. Analytical and numerical solution techniques for two-dimensional bearings. Applications to journal, squeeze-film, thrust, and hydrostatic bearings. Applications to liquid annular seals.

MAE 752 - (3) (Y)
State-Space Methods for Linear Control Systems
Prerequisites: APMA 615, MAE 651, or permission of instructor
State-space representation of continuous and discrete linear dynamical systems, emphasizing decomposition, observability, controllability, and normal systems. Both analysis and design aspects. Pole placement, decoupling techniques, and design by quadratic performance measure treated by examples. State reconstruction via observers. State estimation in the presence of noise. Cross-listed as EE 724.

MAE 756 - (3) (E)
Nonlinear Control Systems
Prerequisite: EE 621 or permission of instructor
Dynamic response of nonlinear systems. Approximate analytical and graphical analysis methods. Stability analysis using the second method of Liapunov, describing functions, and other methods. Adaptive, learning, and switched systems. Examples from current literature. Cross-listed as EE 726.

MAE 761 - (3) (IR)
Mechanical Design Synthesis
Prerequisite: Permission of instructor
Rational design of mechanical elements and machine systems. Iterative and non-iterative solutions of constrained, nonlinear optimization problems. Mathematical modeling, nonlinear programming algorithms, methods for dealing with constraints, and ad hoc methods for special problems. Practical applications, industrial examples.

MAE 772 - (3) (O)
Computational Fluid Dynamics II
Prerequisite: MAE 672 or permission of instructor
A continuation of MAE 672. More advanced methods for grid generation, transformation of governing equations for odd geometries, methods for compressible flows, methods for parabolic flows, calculations using vector and parallel computers. Use of personal computers/workstations/supercomputer including graphics. Cross-listed as APMA 772.

MAE 773 - (3) (IR)
Finite Element Thermal-Fluid Analysis
Prerequisite: MAE 671 or permission of instructor
Method of weighted residuals. Solution of general field problems for elliptic parabolic and hyperbolic partial differential equations. Steady, unsteady, and eigenvalue problems. Transient solution algorithms. Nonlinear conduction heat transfer. Forced and free convection heat transfer. Finite element formulations for incompressible and compressible flows.

MAE 791 - (0-1) (S)
Research Seminar, Mechanical, Aerospace and Nuclear Engineering: Masters' Students
Required one-hour weekly seminar for masters' students in Mechanical and Aerospace and Nuclear Engineering. Students enrolled in MAE 898 or MAE 694/794 make formal presentations of their work.

MAE 792 - (3) (Y)
Special Topics in Mechanical or Aerospace Engineering
Science: Advanced Level
Prerequisites: As specified for each offering
Study of a specialized, advanced, or exploratory topic relating to mechanical or aerospace engineering science, at the second-year or higher graduate level. May be offered on a seminar or team-taught basis. Subjects selected according to faculty interest. New graduate courses are usually introduced in this form. Exact subject indicated in the seasonal Course Offering Directory.

MAE 793 - (Usually three credits) (Y)
Independent Study in Mechanical or Aerospace Engineering Science: Advanced Level
Independent study of advanced graduate material under the supervision of a faculty member.

MAE 794 - (Credit as arranged) (Y)
Special Graduate Project in Mechanical or Aerospace Engineering: Advanced Level
A design or research project for an advanced graduate student under the supervision of a faculty member. A written report must be submitted and an oral report must be presented. Up to three credits of either this course or MAE 694 may be applied toward the master's degree.

MAE 853 - (3) (SI)
Optimal Control Systems
Prerequisite: EE 724 or permission of instructor
Pontryagin's maximum principle, calculus of variations, Hamilton-Jacobi theory, and dynamic programming applied to the design of optimal control systems. Performance criteria include time, fuel, and energy. Optimal regulators and trackers for quadratic cost index designed via the Ricatti equation. Introduction to numerical optimization techniques. Cross-listed as EE 823.

MAE 854 - (3) (E)
Digital Control Systems
Prerequisite: MAE 752 or permission of instructor
Sampling processes and theorems, z-transforms, modified transforms, transfer functions, stability criteria. Analysis in both frequency and time domains. Discrete-state models for systems containing digital computers. Applications using small computers to control dynamic processes. Cross-listed as EE 728.

MAE 897 - (Credit as arranged) (S)
Graduate Teaching Instruction
For master's students.

MAE 898 - (see below regarding credit) (Y)
Master's Thesis Research, Mechanical and Aerospace Engineering
Formal documentation of faculty supervision of thesis research. Each full-time, resident Master of Science student in Mechanical and Aerospace Engineering is required to register for this course for the number of credits equal to the difference between his or her regular course load (not counting the one-hour MAE 791 seminar) and 12.

MAE 991 - (0-1) (S)
Research Seminar, Mechanical, Aerospace and Nuclear Engineering: Doctoral Students
Required one-hour weekly seminar for doctoral students in Mechanical, Aerospace and Nuclear Engineering. Students enrolled in MAE 999 may make formal presentations of their work.

MAE 997 - (Credit as arranged) (S)
Graduate Teaching Instruction
For doctoral students.

MAE 999 - (see below regarding credit) (Y)
Dissertation Research, Mechanical and Aerospace Engineering
Formal documentation of faculty supervision of dissertation research. Each full-time resident doctoral student in Mechanical and Aerospace Engineering is required to register for this course for the number of semester-hours equal to the difference between his or her regular course load (not counting the one-hour MAE 991 seminar) and 12.

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