Those courses which carry graduate credit are listed below. A graduate student's program should be dominated by courses numbered 500 or above. Arabic numeral in parentheses indicates the number of credit hours; (arr) indicates the number of credit hours vary and are arranged with the instructor. Roman numerals indicate the term in which the course is offered (I=Fall, II=Winter, IIIa=Spring Half, IIIb=Summer Half, III=Spring-Summer Full). * Offerings still subject to College of Engineering approval.

NA 401. Small Craft Design

Prerequisite: preceded or accompanied by NA 321 and NA 340. I (4 credits)

NA 403. Sailing Craft Design Principles

Prerequisite: preceded or accompanied by NA 321. II (4 credits)

Forces and moments acting on a sailing yacht. Speed polar diagrams. Two- and three-dimensional airfoil theory. Application to keel and rudder design. Yacht model testing. Delft Standard Series for prediction of hydrodynamic performance. Aerodynamics of yacht sails. Sail force coefficients. Velocity Prediction Program. Rigging design and analysis. Yacht racing rules.

NA 410 (Mfg 410). Marine Structures II

Prerequisite: NA 310. I (4 credits)

Structural modeling and analysis techniques applied to ship and marine structure components. Equilibrium and energy methods applied to elastic beam theory; static bending, torsion and buckling. Shear flow and warping of multicell cross sections. Stiffened and composite plates. Plastic analysis of beams. Thick walled pressure vessels. Course project using finite element analysis.

NA 420 (AOSS 420). Environmental Ocean Dynamics

Prerequisites: NA 320 or AOSS 305 or CEE 325. I (4 credits)

Physical conditions and physical processes of the oceans; integration of observations into comprehensive descriptions and explanations of oceanic phenomena. Emphasis on wave and current prediction, optical and acoustical properties of sea water, currents, tides, waves and pollutant transport.

NA 421. Ship Model Testing

Prerequisite: undergraduates only and permission of instructor. I, II, IIIa (to be arranged)

Individual or team project, experimental work, research or directed study of selected advanced topics in ship model testing.

NA 431. Marine Engineering II

Prerequisite: NA 310, NA 331, NA 332, NA 340. II (3 credits)

Integrated treatment of the statics and dynamics of marine power transmission systems. Shafting design and alignment. Bearing selection and lubrication. Propeller excitation, added mass, and damping. Vibration modeling, analysis and evaluations of shafting systems: torsional, longitudinal, and lateral vibrations.

NA 440. Marine Dynamics II

Prerequisite: NA 321, NA 340. II (4 credits)

Dynamic analysis in a fluid environment. Rayleigh's principle for continuous systems. Equations of motion for ship rigid body dynamics. Wave excitation. Response Amplitude Operator (RAO). Random processes and probability. Motion in irregular seas. Introduction to time series analysis.

NA 455. Environmental Nearshore Dynamics

Prerequisite: NA 320. offered alternate years II (4 credits)

Shallow water waves and currents are investigated in nearshore processes including tides and longterm sea-level changes, longshore current and prediction of sediment and pollutant transport. Beach response to these processes is examined; coastal structures and effects on the nearshore environmentally conscious coastal design is emphasized. Interpretation of aerial photography is investigated.

NA 470 (Mfg 470). Foundations of Ship Design

Prerequisite: NA 321, NA 332, NA 340. Co-requisites: NA 310. I (4 credits)

Organization of ship design. Preliminary design methods for sizing and form; powering, maneuvering, and seakeeping estimation; arranging; propulsion; structural synthesis; and safety and environmental risk of ships. Extensive use of design computer environment. Given owner's requirements, students individually create and report the conceptual/preliminary design for a displacement ship.

NA 475. Marine Design Team Project

Prerequisite: NA 470. II (4 credits)

Small teams of up to 4 students create, develop, and document original marine designs to contract design level. Projects typically involve a ship, yacht, submersible, or offshore system. Involves extensive project planning and weekly progress reporting. Extensive written and oral presentation of the project. Significant design CAD effort.

NA 477 (Eng 477). Principles of Virtual Reality

Prerequisite: Senior standing or permission of instructor. I (4 credits)

Enabling technologies (display systems, motion trackers, interactive devices, others), applications, human factors and perception, computer graphics and geometric modeling principles, creation of virtual environments, existing tools, special topics. Interdisciplinary group projects will develop VR applications using the facilities in the Media Union. http://wwwVRL.umich.edu/Eng477/

NA 490. Directed Study, Research and Special Problems

Prerequisite: undergraduate only and permission. I, II, IIIa (to be arranged)

Individual or team project, experimental work or study of selected topics in naval architecture or marine engineering. Intended primarily for students with senior standing.

NA 491. Marine Engineering Laboratory

Prerequisite: NA 310, NA 320, NA 321, NA 331, NA 332, NA 340. I (4 credits)

Instruction in laboratory techniques and instrumentation. Use of computers in data analysis. Technical report writing. Investigation of fluid concepts, hydro-elasticity, marine dynamics, propeller forces, wave mechanics, ship hydrodynamics, and extrapolation of model tests to full scale.

NA 510. Marine Structural Mechanics

Prerequisite: NA 500. II (4 credits)

Failure modes encountered in ship and offshore structures. Von Karman plate equations. Geometric and material nonlinear analyses of beams and stiffened plates. Calculus of variations. Effective width and breadth of stiffened plates. Introduction to structural reliability theory with applications to marine structural design.

NA 511. Special Topics in Ship Structure

Prerequisite: prior arrangement with instructor. (to be arranged)

Individual or team project, experimental work, research or directed study of selected advanced topics in ship structure. Primarily for graduate students.

NA 512 (CEE 510). Finite Element Methods in Solid and Structural Mechanics

Prerequisite: Graduate Standing. II (3 credits)

Basic equations of three dimensional elasticity. Derivation of relevant variational principles. Finite element approximation. Convergence requirements. Isoparametric elements in two and three dimensions. Implementational considerations. Locking phenomena. Problems involving non-linear material behavior.

NA 518. Strength Reliability of Ship and Offshore Structures

Prerequisite: NA 410, Aero 452. I (3 credits)

Stress versus strength analysis. Deterministic stress analysis, safety factor approach. Random nature of loads, geometry material and construction. Random variables and random functions. Reliability of structures described by one or more random variables. Introduction to random vibration of discrete and continuous structural systems.

NA 520. Wave Loads on Ships and Offshore Structures

Prerequisite: NA 500. II (4 credits)

Computation of wave loads on marine vehicles and offshore structures including resistance, diffraction, viscous and radiation forces. Linear theory using panel methods and Green functions. Forces on cylindrical bodies. Morison's Equation. Nonlinear computation using desingularized method for inviscid flow and Reynold's averaged Navier-Stokes equation (RANS) for viscous flow.

NA 521. Directed Study and Research in Marine Hydrodynamics

Prerequisite: permission of instructor. (to be arranged)

Individual or team project, experimental work, research or directed study of selected advanced topics in marine hydrodynamics. Primarily for graduate students.

NA 522. Experimental Marine Engineering

Prerequisite: NA 410 and NA 440 or third-term Graduate Standing. IIIa (3 credits)

Advanced experiments in mechanics, vibrations, dynamics, and hydro-dynamics illustrating concepts of 400 and introductory 500 level NA courses. Typical experiments include full scale experiments using Remote Operated Vehicle; vessel dynamic stability; offshore tower strength and vibrations; high speed planing; Tension Leg Platform hydrodynamic damping.

NA 528 (AOSS 528). Remote Sensing of Ocean Dynamics

Prerequisite: NA 420 (AOSS 420) or permission of instructor. II (3 credits)

The dynamics of ocean wave motion, both surface and internal waves, and ocean circulation are explored utilizing active and passive remote sensing techniques. Emphasis is placed upon the synoptic perspective of ocean dynamics provided by remote sensing which is not obtainable by conventional means.

NA 531. Adaptive Control

Prerequisite: Graduate standing or permission of instructor. I (3 credits)

Models of systems with unknown or time-varying parameters. Theory and algorithm for online parameter identification. Adaptive observers. Direct and indirect adaptive control. Model reference systems. Design and analysis of nonlinear adaptive control. Application and implementation of adaptive systems.

NA 540. Marine Dynamics III

Prerequisite: NA 340 or equivalent, preceded or accompanied by NA 500. I (4 credits)

Fundamental analysis of marine dynamical systems. Normal mode analysis. Matrix representation of frequency domain seakeeping equations. Properties of linear gravity waves. Wave forces on marine structures. Linear and non-linear time domain seakeeping, and maneuvering simulations. Nonlinear stability and bifurcation theory applied to mooring and capsizing. Shock mitigation.

NA 550 (AOSS 550). Offshore Engineering Analysis II

Prerequisite: NA 420 (AOSS 420). II (3 credits)

Design and analysis requirements of off-shore facilities. Derivation of hydrodynamic loads on rigid bodies. Loads on long rigid and flexible cylinders. Viscous forces on cylinders, experimental data, Morison's equation, Stokes wave theories. Shallow water waves. Selection of appropriate wave theory. Diffraction of waves by currents. Hydrodynamic loads on risers, cables, pipelines and TLP's.

NA 561 (Mfg 573). Marine Product Modeling

Prerequisite: NA 570. II (3 credits)

Fundamental aspects of marine product modeling, data exchange, and visualization. Simulation Based Design. Introduction to activity modeling and information modeling. Overview of Object Oriented Programming. Geometric modeling of solids and surfaces. Simulation and visualization. Virtual prototyping.

NA 562 (Mfg 563). Marine Systems Production Business Strategy and Operations Management

Prerequisite: NA 260 or graduate standing. I (4 credits)

Examination of business strategy development, operations management principles and methods, and design-production integration methods applied to the production of complex marine systems such as ships, offshore structures, and yachts. Addresses shipyard and boat yard business and product strategy definition, operations planning and scheduling, performance measurement, process control and improvement.

NA 570 (Mfg 572). Advanced Marine Design

Prerequisite: Graduate Standing required. II (4 credits)

Organization of marine product development; concurrent marine design. Shipbuilding policy and build strategy development. Group behaviors; leadership and facilitation of design teams. General theories and approaches to design. Conceptual design of ships and offshore projects. Nonlinear programming, multicriteria optimization, and genetic algorithms applied to marine design. Graduate standing required.

NA 571 (Mfg 571). Ship Design Project

Prerequisite: prior arrangement with instructor. I, II, IIIa (to be arranged)

Individual (or team) project, experimental work, research or directed study of selected advanced topics in ship design. Primarily for graduate students.

NA 575 (Mfg 575). Computer-Aided Marine Design Project

I, II, IIIa, IIIb, III (2-6 credits), (to be arranged)

Development of computer-aided design tools. Projects consisting of formulation, design, programming, testing, and documentation of programs for marine design and constructional use.

NA 579. Concurrent Marine Design Team Project

Prerequisite: NA 460, NA 570, and NA 580. II, IIIa (2-4 credits)

Industrial related team project for Master's of Engineering Concurrent Marine Design degree program. Student teams will conduct concurrent design project for and in conjunction with industrial or government customer.

NA 580 (Mfg 578). Optimization, Market Forecast and Management of Marine Systems

Prerequisite: NA 500. I (4 credits)

Optimization methods (linear, integer, nonlinear, sequential) concepts and applications in the operations of marine systems. Forecasting methods (ARMA, Fuzzy sets, Neural nets) concepts and applications to shipping and shipbuilding decisions. Economics of merchant shipbuilding and ship scrapping. Elements of maritime management: risk and utility theory. Deployment optimization.

NA 582 (Mfg 579). Reliability and Safety of Marine Systems

Prerequisite: EECS 401 or Math 425 or Stat 412. II (3 credits)

Brief review of probability, statistics, trade-off analysis, and elements of financial management. Thorough presentation of the methods and techniques of reliability analysis. Marine reliability, availability, maintenance, replacement, and repair decisions. Safety and risk analysis. FMEA, faulttree and event-tree analysis. Marine applications.

NA 590. Reading and Seminar

Prerequisite: permission. I, II, IIIa, IIIb (to be arranged)

A graduate level individual study and seminar. Topic and scope to be arranged by discussion with instructor.

NA 592. Master's Thesis

Prerequisite: Graduate Standing. I, II, III, IIIa, IIIb (1-6 credits)

To be elected by Naval Architecture and Marine Engineering students pursuing the master's thesis option. May be taken more than once up to a total of 6 credit hours.

NA 615. Special Topics in Ship Structure Analysis II

Prerequisite: NA 510, prior arrangement with instructor. I, II (to be arranged)

Advances in specific areas of ship structure analysis as revealed by recent research. Lectures, discussions, and assigned readings.

NA 620. Computational Fluid Dynamics for Ship Design

Prerequisite: NA 500. I alternate years (3 credits)

Development of the necessary skills for the hydrodynamic design of hull shapes based on available Computational Fluid Dynamic (CFD) tools. Topics: Potential Flows (Deeply submerged, Free-surface treatment, Status of CFD solvers), Viscous flows (Basics, Turbulence modeling, Grid generation, Discretization, Numerical techniques, Free-surface, Status of CFD solvers), Design methodologies (Strategies for Wave Resistance, Viscous flows, Total resistance and Optimization work).

NA 625. Special Topics in Marine Hydrodynamics

Prerequisite: permission. I, II (to be arranged)

Advances in specific areas of marine hydrodynamics as revealed by recent research.

NA 627 (ME 627). Wave Motion in Fluids

Prerequisite: ME 520 or NA 520 or equivalent. I (3 credits)

Surface waves in liquids; group velocity and dispersion; water waves created by and wave resistance to a moving body; Korteweg-deVries equation; conoidal and solitary waves in water; wave reflection and diffraction; shallow-water waves by the method of characteristics; statistical approach and spectral analysis; wave generation.

NA 635. Special Topics in Marine Engineering

Prerequisite: permission. I, II (to be arranged)

Advances in specific areas of marine engineering as revealed by recent research. Lectures, discussions, and assigned readings.

NA 644. Numerical Methods for Vibro-Acoustic Modeling of Complex Systems

Prerequisite: NA 340 or ME 440. II alternate years (3 credits)

Theoretical development, numerical formulation, and practical modeling aspects of the Statistical Energy Analysis (SEA) and the Energy Finite Element Analysis (EFEA). Numerical evaluation of vibration and acoustic characteristics of complex structural/acoustic systems, such as ship structure, airframe, or trimmed car body.

NA 650. Dynamics of Offshore Facilities

Prerequisite: NA 410, NA 440. II (3 credits)

Dynamics and stability of single point mooring systems. Marine cable statics and dynamics. Dynamics and stability of multilegged mooring systems. Dynamics and stability of towing systems. Dynamics of offshore towers. Structural redesign. Correlation of finite element model and physical structure. Dynamics and stability of marine risers; bundles of risers. Statics and dynamics of pipelines.

NA 655. Special Topics in Offshore Engineering

Prerequisite: NA 410, NA 440, NA 550 or NA 650. II (to be arranged)

Advances in specific areas of offshore engineering as revealed by recent research. Lectures by doctoral students. Projects and presentations by M.S. students. Discussion, assigned readings.

NA 685. Special Topics in Marine Systems

Prerequisite: permission of instructor; mandatory pass/fail. I, II (to be arranged)

Advances in specific areas of marine systems engineering as revealed by recent research. Lectures, discussions, and assigned readings.

NA 792. Professional Degree Thesis

I, II, III (2-8 credits); IIIa, IIIb (1-6 credits)

NA 990. Dissertation/Pre-Candidate

I, II, III (2-8 credits); IIIa, IIIb (1-4 credits)

Dissertation work by doctoral student not yet admitted to status as candidate. The defense of the dissertation, that is, the final oral examination, must be held under a full-term candidacy enrollment.

NA 995. Dissertation/Candidate

Prerequisite: Graduate School authorization for admission as a doctoral candidate. I, II, III (8

credits); IIIa, IIIb (4 credits)

Election for dissertation work by a doctoral student who has been admitted to candidate status. The defense of the dissertation, that is, the final oral examination, must be held under a full-term candidacy enrollment.