Test Specifications for ME PhD Qualifying Exams
Graduate Handbook: Appendix D
TEST SPECIFICATIONS FOR ME PH.D. QUALIFYING AREA EXAMS
Description of Standard Examination Areas
Georgia Tech courses that cover the equivalent preparatory subject matter in the Standard Examination Areas are summarized below.
Objective and Scope. The purpose of this examination is to evaluate the student's ability to solve engineering problems using mathematical models. Topics will be drawn from:
1. Vector Calculus
b. Divergence, Green's, and Stokes' theorems
2. Linear Algebra
a. Finite-dimensional vector spaces and subspaces
b. Linear independence
c. Orthogonality of vectors and subspaces
d. Properties of the determinant
e. Eigenvalues and eigenvectors
3. Linear Ordinary Differential Equations
a. Initial-value problems
b. Two-point boundary-value problems
c. Homogeneous and nonhomogeneous solutions
d. Solution techniques
e. Laplace transforms
f. Solution of systems of ODE's using matrix methods
4. Linear Partial Differential Equations
a. Classification of PDE's
b. Separation of variables
c. Laplace transforms
d. Fourier transforms
5. Elementary Numerical Analysis
a. Root-finding techniques, e.g. bisection, Newton-Raphson, secant, and fixed-point
b. Curve fitting by the method of least squares
c. Functional approximation using Fourier series or polynomial series
d. Numerical integration, e.g., trapezoidal rule and Simpson's rule
e. Integration of ODEs, e.g., Euler, Runge-Kutta, and predictor-corrector methods
Courses. The examination will be based on materials normally covered in the following courses: MATH 4305 (Topics in Linear Algebra), MATH 4581 (Classical Mathematical Methods in Engineering), and ME 2016 (Computer Applications).
1. Boyce, W. E. and R. C. DiPrima, Elementary Differential Equations
2. Chapra, S. C. and R. P. Canale, Numerical Methods for Engineers
3. Davis , H. F. and A. D. Snider, Introduction to Vector Analysis
4. Hildebrand, F. B. , Advanced Calculus for Applications
5. Powers, D. L., Boundary Value Problems
6. Strang, G ., Linear Algebra and Its Applications
Objective and Scope.
The purpose of this exam is to evaluate a student's ability to design engineering systems efficiently and effectively. The exam will cover the conception, planning, evaluation and implementation of engineering system designs. Emphasis is placed on engineering systems which are interdisciplinary and typically require the consideration and integration of several of the traditional engineering disciplines. Therefore, to a large extent, success in this examination will depend upon a student's ability to apply design methods and integrate basic knowledge of the engineering sciences. Specific areas which are emphasized in the examination are as follows:
1. Design Methods: Designers should use a systematic and methodical approach when designing engineering systems. Knowledge and understanding about design methods; the identification of design requirements; and continuous quality improvement are examples of the topics examined. A student may be given a statement describing the need for a particular functionality and then be asked to design an appropriate engineering system to satisfy this functionality. A student will be rewarded based on the ability to solve the problem in a sound and systematic way and to identify questions which are worthy of further research.
2. Physical Realizability: Insight into technical, economic, quality and environmental factors and their effect on the subsequent physical realizability of design concepts is required. Questions related to manufacturing, cost, quality, safety, sustainability, wear, etc., can be expected. What makes one implementation better than another? What are some existing components which could be utilized? Should they be utilized?
3. Analysis: The student should appreciate the role of analysis in engineering design and be capable of ascertaining the implications of analysis results during design. One aspect is the ability to use the appropriate engineering science knowledge to analyze a design with respect to the design requirements. For instance, will structural failure occur in the design? A more important aspect is the interpretation of the analysis and the identification of ways to improve the design with respect to the requirements. For instance, how can structural failure be avoided with a minimum of weight increase?
The examination will assume knowledge of material normally covered in the undergraduate core curriculum in mechanical engineering at Georgia Tech, but will presume the maturity and experience commensurate with a graduate student at the master's level. The primary courses to which this examination will relate are: ME 3180 (Machine Design); ME 2110 (Creative Decisions and Design); and ME 4182 (Capstone Design). In addition, ME 4210 (Manufacturing Process and Engineering) will be useful. At the graduate level, ME 6101 (Engineering Design) provides an introduction to a systematic design method and is recommended.
1. Pahl, G., W. Beitz, K. Wallace, L. Blessing, and F. Bauert, Engineering Design Berlin Springer Verlag, 1996.
2. C. R. Mischke and R. Budynas, Shigley's Mechanical Engineering Design, 8th Edition. New York: McGraw-Hill, 2007.
Objectives and Scope.
The purpose of this examination is to evaluate the student's understanding of the principles governing the dynamics of rigid and elastic systems and to synthesize those principles to predict the response of mechanical systems. A key aspect of the required expertise is demonstrated by the ability to anticipate and explain response characteristics based on physical arguments. Topics will be drawn from the following:
1. Kinematics of particles and rigid bodies: Analysis of velocity and acceleration for curvilinear motion, motion relative to a moving reference frame, angular motion, linkages, rolling bodies.
2. Kinetics of particles and rigid bodies: Free-body diagrams, inertia properties, equations of motion for planar and spatial motion, static and dynamic balancing, gyroscopic effect, linear and angular impulse-momentum principles, work-energy principle.
3. Vibration of one-degree-of-freedom systems: Free response with damping, response to harmonic, periodic and transient vibration, vibration measurement and control.
4. Vibration of systems having several degrees of freedom: Evaluation of natural frequencies and modes, modal response to excitation, harmonic forced response, vibration absorbers, Raleigh ratio.
5. Vibration of simple continuous systems: Natural frequencies and modeshapes for simple structures such as strings, rods, and flexural beams. Estimation of natural frequencies using approximate techniques such as assumed modes, or Rayleigh-Ritz.
Courses The examination requires a thorough understanding of the material covered in ME 2202 (Dynamics of Rigid Bodies), and ME 4189 (Structural Vibrations). Many of these topics are covered in greater detail in ME 6441 (Dynamics of Mechanical Systems) and ME 6442 (Vibration of Mechanical Systems) , but the examination is set at the undergraduate level. In addition, the exam assumes a familiarity with many concepts from ME 3017 and 4452 (System Dynamics) including modeling of mechanical systems, transient/steady-state response, and stability.
1. Ginsberg, J. H., Mechanical and Structural Vibrations, Theory and Applications
2. Ginsberg, J. H., Advanced Engineering Dynamics
3. McGill, D. J. and W. W. King, An Introduction to Dynamics
4. Meirovitch, L., Elements of Vibration Analysis
5. Rao, V. V., Mechanical Vibrations
Objective and Scope.
The purpose of this examination is to evaluate the student's understanding of the fundamental principles of fluid mechanics. Topics will be drawn from the following:
1. Fundamentals: properties of fluids; Eulerian and Lagrangian descriptions; streamlines, streaklines, and pathlines; stress in fluids; boundary and initial conditions.
2. Fluid statics: forces on submerged and partially submerged objects; buoyancy.
3. Control-volume forms of basic principles: mass, momentum and energy balances; Bernoulli's equation.
4. Local forms of basic principles: continuity, and Navier-Stokes equations; irrotational motion; velocity potential and stream function; simplification of equations and solution of problems.
5. Dimensional analysis: Buckingham Pi theorem, similarity.
6. Viscous flow through pipes: laminar and turbulent flow; head loss; friction factor; major and minor losses; Moody chart (Colebrook formula) analysis.
7. Boundary-layer flows: scaling; boundary-layer equations; integral methods; similarity solutions; separation.
8. Turbulence: scaling arguments.
Courses. This examination will be based on material covered in ME 3340 (Fluid Mechanics)
1. Munson, B. R., D. F. Young, T. H. Okiishi, and W. W. Huebsch, Fundamentals of Fluid Mechanics, 6th edition.
2. Fox, R. W. P. J. Pritchard, and A. T. McDonald, Introduction to Fluid Mechanics. 7th edition.
Objective and Scope. The purpose of this examination is to determine if the student is adequately prepared to perform independent research in the heat transfer area. This requires fundamental knowledge in each of the classical mechanisms of heat transfer. The student must be able to classify particular applications according to regimes using nondimensional groups and other aids. In addition, the student should be able to formulate mathematical models for a variety of applications. The examination may include material from conductive, radiative and convective heat transfer areas and will be based on a minimum of undergraduate training.
Courses. The examination will be based on material normally covered in the following undergraduate courses offered in mechanical engineering at Georgia Tech: ME 3345 (Heat Transfer), and ME 4315 (Energy Systems Analysis and Design).
1. Moran and Shapiro, Fundamentals of EngineeringThermodynamics .
2. Incropera and DeWitt, Fundamentals of Heat & Mass Transfer .
3. Munson, Young and Okiishi, Fundamentals of Fluid Mechanics .
Objective and Scope. The purpose of this examination is to evaluate a student's ability to synthesize and analyze manufacturing processes for various materials. Emphasis will be placed on materials processing techniques, thus typically requiring consideration of several of the traditional engineering disciplines. To a large extent, success in this examination will depend on the ability to integrate and bring to bear upon the problem at hand basic knowledge of the engineering sciences such as mechanics and material properties and, to a lesser extent, design and fluid and thermal sciences. Knowledge of major material processing techniques is expected. Several of the specific areas which may be emphasized in the examination include the following:
1. Ingenuity and Judgment: Success as a manufacturing engineer depends strongly on one's ability to generate numerous alternative process designs and judiciously select the ones which warrant further consideration. The focus will be on defining the geometric and behavior modifications required of raw materials to produce finished products and on determining the appropriate manufacturing process(es) required to affect these changes. Tolerances on the product in terms of the geometry and behavior also need to be considered when defining a manufacturing process. Monolithic examination of a single idea will not be richly rewarded.
2. Analysis: The ability to apply appropriate physical principles and analytical techniques to draw conclusions regarding the feasibility of proposed processes will be emphasized. Typical questions are as follows: How is a product made? What clues does an artifact give you on the way it was made? What are the appropriate material models and what are their limitations? What are the mechanics (stresses, forces) of the process? What are the thermal and fluid considerations? How does the material react to the physical, thermal and fluid forces generated in the process?
3. Optimization: What are meaningful measures of merit and of performance for the proposed processes? How can process parameters be adjusted to achieve optimum performance?
4. Physical Realizability: Can the proposed process be implemented with available equipment? Is the process economically viable? How will manufacturing tolerances affect the end product's performance? What are the safety considerations?
Courses. The examination will assume knowledge of material normally covered in the undergraduate core curriculum in Mechanical Engineering at Georgia Tech, but will presume the maturity and experience commensurate with a graduate student at the Master's level. The primary subjects to which this examination will relate to are: MSE 2001 (Principles and Applications of Engineering Materials); ME 4210 (Manufacturing Processes); and ME 4214 (Mechanical Behavior of Materials). The following courses in the areas of design and fluid and thermal science also will be pertinent: ME 3180 (Machine Design); ME 3322 (Thermodynamics); ME 3340 (Fluid Mechanics), and ME 3345 (Heat Transfer). Further, ME 6222 (Manufacturing Engineering and Systems) provides in-depth knowledge of the material at a graduate level, and is suggested for students taking the exam, especially those who did not take ME 4210 as undergraduates.
1. Ashby, M. F. and D. R. H. Jones, Engineering Materials I and II . Oxford: Pergammon Press 1988.
2. Kalpakjian, S. and S. R. Schmid, Manufacturing Processes for Engineering Materials , 5th Edition. Prentice Hall, Pearson Education Inc., Upper Saddle River, NJ, 2008.3. Tlusty, G., Manufacturing Processes and Equipment, Prentice-Hall, Upper Saddle River, NJ, 2000.
Objective and Scope.
The purpose of this examination is to evaluate the student's capacity for logical reasoning, problem definition, problem solving, and knowledge of basic engineering skills in mechanics of materials in order to establish the qualifications of the student to pursue a Ph.D. program of study.
The student must demonstrate basic concepts in solid mechanics and mechanical behavior of engineering materials. Focus is on material from undergraduate courses, including: basic statics; mechanics of deformable bodies; and mechanical behavior of polymers, metals, ceramics and composites. Basic assumptions and limitations of simple classical beam and torsion theories are stressed, along with fundamental concepts of stress-strain relations, strain-displacement relations, boundary conditions, and simple theories for deformation and failure of engineering materials.
Courses. As each university offers a different curriculum, Georgia Tech courses are specified below which cover the equivalent preparatory subject matter. Although the subject matter on the test is at the undergraduate level, the students are expected to possess a graduate level understanding of the material. Precisely, this means they should thoroughly understand the assumptions and limitations of simple theories. Moreover, they are expected to understand the basic elements of the field equations necessary to solve general boundary value problems (e.g., stress-strain, strain-displacement, equilibrium and appropriate boundary conditions).
The following are equivalent undergraduate courses to which this examination will relate:
COE 2001 Statics
COE 3001 Mechanics of Deformable Bodies
ME 4214 Mechanical Behavior of Materials
1. Dowling, Mechanical Behavior of Materials.
2. Gere James M., Goodno Barry: Mechanics of Materials,Cengage Learning, 2009
Objective and Scope.
The purpose of this examination is to evaluate the student's understanding of the fundamental principles of interacting multidomain (such as mechanical, electrical, fluid, and thermal) dynamic systems and ability to apply these principles to modeling and control of physical systems. Emphasis will be placed on the formulation of mathematical models of physical systems, prediction and interpretation of system behavior, and the improvement of system performance through feedback. Topics will be drawn from the following:
1. Physical system modeling: Representation of a real physical system by an analytical lumped-parameter model (both linear and nonlinear); linearization; derivation of transfer function; state-space and block diagram representation and reduction technique.
2. Dynamic behavior of linear systems; concepts of poles and zeros, transient, steady-state, and frequency response, and dynamic stability.
3. Improvement of dynamic response through feedback: classical analysis and design of continuous-time, linear feedback control systems including root locus and frequency response techniques.
Courses. The examination will be based on materials normally covered in the undergraduate core curriculum in mechanical engineering at Georgia Tech. The primary core subjects to which this examination will relate are ME 3017 (System Dynamics). Candidates will also find the material covered in ME 6401 (Linear Control Systems) and ME 6403 (Digital Control Systems) will strengthen their position relative to the examination. However, no questions will be asked that require specialized techniques or advanced concepts which normally would be covered at the graduate level.
1. Franklin , Powell, and Emami-Naeini, Feedback Control of Dynamic Systems , 5th edition. Addison-Wesley, 2005.
2. Golnaraghi and Kuo , Automatic Control Systems , 9th edition. Prentice-Hall, 2009.
3. Ogata, Modern Control Engineering, 5th edition. Prentice-Hall, 2009.
4. Ogata, System Dynamics , 4th edition. Prentice Hall, 2003.
5. Shearer, Murphy and Richardson , Introduction to System Dynamics . Addison-Wesley, 1967.
Objective and Scope. Candidates should be familiar with the basic principles of thermodynamics and their application to evaluating the properties of simple substances and ideal mixtures and to analyzing representative engineering systems at an academic level of complexity. Expected familiarity and possible and exemplary topics follow:
1. Basic Principles: Includes the Zeroth law and the energy and entropy principles, heat and various common forms of work, and the properties of pure substances, ideal gases, and ideal gas mixtures. Students should be familiar with these elementary principles and capable of applying these principles to engineering systems.
2. Thermodynamics of Systems, Processes, and Cycles: Includes consideration of open and closed systems in transient and steady-state processes including energy and entropy analysis. Such systems may include multiple-port systems such as heat exchangers and mixers and two-port steady-flow steady-state systems including important components such as pumps, nozzles, turbines, and diffusers. Such analysis may include basic applications of exergy as the measure of potential work.
3. Thermodynamics of Properties: Covers the nature of extensive and intensive properties and understanding and application of the state postulate and the phase rule, the T ds equations, the detailed properties of ideal gases, the general and typical properties of real fluids, and use of tabulated properties and proper use of SI units. No conventional units will be used in the exam. Ideal gas mixtures may be considered, but detailed psychrometrics will not be addressed on the exam. Exam problems often involve ideal gases with constant specific heats as well as contrasting situations where the temperature variation must be considered.
4. Engineering Applications: Students should be very familiar with the common power and refrigeration cycles including the well established gas and vapor cycles. Nevertheless, exams typically challenge the student to analyze sometimes subtle or sometimes disparate variations on these cycles, so students should have developed an independent capacity to analyze representative engineering systems. Basic familiarity must include the following: (1) Common gas cycles such as the Carnot and Stirling cycles and the air standard Otto and Diesel and similar cycles, (2) Vapor Cycles to understand include the basic steam cycle and the steam cycle with superheat, reheat, and extraction and similar vapor power cycles (3) Refrigeration Cycles to include the Carnot and vapor compression cycles for refrigeration and heat pumping. Students should be familiar with the classical systems and cycles studied in undergraduate courses but should also be capable of analyzing and discussing both typical enhancements and novel or unusual variations. Students are usually not tested on applications far removed from main-stream applications in thermal and fluid power, thermal processing, refrigeration, heat pumps, and the thermodynamics of fluid and heat transfer machinery.
5. Second Law Analysis: Includes the calculation of entropy generation and irreversibility and related issues. Some related issues are (1) Principles and applications of stream and system exergy (This terminology is preferred to equivalent concepts such as "thermodynamic availability"), and (2) The limiting performance of systems including the evaluation of performance indices such as the so-called "Second Law Effectiveness" or "Combined Laws Efficiency" ratios. When addressed, such figures of merit will typically be defined for the student. Students are expected to apply the general principles and thermodynamic property relations in entropy analysis and related second-law analysis.
Courses. The exam will be based on materials covered in ME 3322 (Thermodynamics) and ME 4315 (Energy Systems Analysis and Design).
1. Moran and Shapiro, Thermodynamics.
Objective and Scope. The purpose of this examination is to evaluate the student's understanding of the fundamental principles of bioengineering. The emphasis will be placed on the modeling analysis and measurement of the mechanics of the biological systems including cellular biomechanics, biofluid dynamics, and biosolid mechanics. The examination may include material from the following:
1. Mechanical properties of cells
2. Cell adhesion
3. Cell locomotion
4. Analysis of unsteady flows in elastic tubes
5. Flow patterns in curved and branched tubes
6. Techniques of velocity and shear stress measurement.
7. Fluid mechanics of the carotid artery, the coronary artery, and the abdominal aorta.
9. Biological responses to mechanical stimuli
10. General laws for constitutive equations
11. Soft tissue biomechanics
12. Blood vessel mechanics
Courses. Examination will be based on undergraduate biomechanics material.This material is reviewed in ME 4758 (Biosolid Mechanics)/ ME 6743 (Tissue Mechanics), ME 6782 (Cellular Engineering), and ME4757 (Biofluid Mechanics) /ME 6720 (BioTransport).
1. Caro, C. G., Pedley, T. J., Schroter, R. C., Seed, W. A. The Mechanics of the Circulation. Oxford Medical Publications, Oxford, 1978.
2. Fung, Y. C. Biodynamics, Circulation. Springer-Verlag, New York, 1984.
3. Fung, Y. C., Biomechanics: Motion, Flow, Stress, & Growth. Springer-Verlag, New York, 1990.
4. Fung, Y. C., Biomechanics: Mechanical Properties of Living Tissue, 2 nd edition. Springer-Verlag, New York, 1993.
Special Examination Areas
The Special Exam Areas include materials at an advanced undergraduate level and/or at a graduate level. The equivalent preparatory courses for the Special Examination Areas offered at Georgia Tech are summarized as follows:
Each Special Exam Area is described below.
Objective and Scope. The purpose of this examination is to evaluate the student's understanding of the fundamental principles of acoustics. The student must demonstrate the ability to attack problems with a correct approach and show the ability to analyze problems and results with critical judgment in a manner compatible with doctoral level expectations. Topics will be drawn from the following:
1. Equations of continuity, momentum, and state; linear acoustic wave equation in fluids; pressure-density relations; speed of sound; plane waves, spherical waves, energy, intensity, directivity, power.
2. Frequency band analysis, Fourier series, and Fourier transforms; frequency weighting; coherent and incoherent sound; combining levels; power spectral density.
3. Reflection, transmission, specific acoustic impedance, standing waves, radiation from traveling flexural waves, critical frequency multilayer transmission and reflection, transmission of transients, transmission through solid slabs, plates, and blankets.
4. Radially and transversely oscillating spheres, monopoles, Green's function, dipoles, quadrupoles; Kirchhoff-Helmholtz integral theorem; Rayleigh integral; radiation from a baffled piston.
Courses. The examination will be based on materials covered in ME 6760-ME 6761.
(Acoustics I and II).
1. Pierce, A.D., Acoustics : An Introduction to Its Physical Principles and Applications . Reprinted by the Acoustical Society of America , 1988.
2. For a complement, see also Kinsler, Frey, Coppens, and Sanders, Fundamentals of Acoustics, 3rd edition. J. Wiley, New York , 1982.Computer-Aided Engineering (CAE)
Objective and Scope. The purpose of this exam is to evaluate a student's ability to apply the fundamental principles underlying computer-aided engineering to design and analysis problems in mechanical engineering. Emphasis will be placed on real systems which are subject to more than one physical phenomena (compressive and transverse loading, mechanical and thermal loading, etc.). The student should appreciate the role of computer-aided analysis in engineering design and be capable of ascertaining the implications of analysis results. To a large extent, success in this examination will depend upon the student's ability to integrate and apply basic knowledge of the engineering sciences to the formulation and solution of problems using numerical and computational methods. Specific topics emphasized in the examination include the following:
-Numerical Methods: Formulation and solution of engineering analysis problems using various numerical methods, including methods for numerical differentiation and integration, solving of ordinary differential equations, linear regression, root finding, optimization, eigenvalue, and boundary value problems. The student should understand sources of error and their implications for practical implementations of typical numerical methods. After finding the solution to an analysis problem, the students should be able to interpret the results: What does this imply for an engineering problem? How sensitive is the solution to changes in loading and boundary conditions? Or to changes in parameter values?
-Finite Element Analysis: Formulation and solution of finite element models. Given a "real-world" analysis problem, you may have to select appropriate element types and identify appropriate boundary and loading conditions. Insight into identifying the governing physical phenomena for engineering systems will also be important. The student should understand the governing principles and assumptions underlying the finite element technique.
-Geometric Modeling: Curve and surface modeling techniques. Given an engineering design problem, which curve/surface modeling technique would be appropriate, based on an understanding of fundamental technique properties and analysis of problem requirements? Why are components shaped the way they are and how would their shape be described (using CAD systems)? Other topics include the limitations of curve and surface models and the application of geometric modeling to shape design and component analysis, with analysis related to the formulation of finite element and other types of models.
Courses. The examination will assume knowledge of material normally covered in the undergraduate core and elective courses in mechanical engineering at Georgia Tech, but will presume the maturity and experience commensurate with a graduate student at the master's level. The undergraduate courses to which this examination will relate are ME 2016 (Computing Techniques), and ME 4041 (Interactive Computer Graphics and Computer-Aided Design). At the graduate level, the following courses are recommended: ME 6104 (Computer-Aided Design); ME 6124 (Finite Element Method: Theory and Practice).
1. Cook, R. D, D. S. Malkus , and M. E. Plesha, Concepts and Applications of Finite Element Analysis , . John Wiley and Sons, New York , Latest Edition.
2. Loga, D. L., A First Course in the Finite-Element Method, Thompson, Latest Edition.
3 . Hoffman, J. D., Numerical Methods for Engineers and Scientists . McGraw-Hill , New York, Latest Edition.
4. Chapra, S. C. and Canale, R. P., Numerical Methods for Engineers, McGraw-Hill, NY, Latest Edition.5. Zeid, I., Mastering CAD/CAM, McGraw-Hill, Latest Edition.
Objective and Scope. The purpose of this examination is to evaluate the student's understanding of the fundamental principles of tribology. Topics will be drawn from the following:
1. Surface roughness
2 Hertzian contact
3. Rough surface contact
5. Time varying phenomena
7. Lubrication regimes: full film, mixed and boundary
8. Hydrostatic lubrication
9. Hydrodynamic lubrication
10. Elasto-hydrodynamic lubrication
12. Liquid lubricants
13. Solid lubricants
14. Surface modification
Courses. The course covered in the examination is: ME 4193, ME 6243
1. Williams, J. A., Engineering Tribology, Cambridge University Press, 2005.
2. Hutchings, I. M., Tribology: Friction and Wear of Engineering Materials, CRC Press, 1992.
3. Hamrock, B.J., Schmid, S.R. and Jacobson, B.O., Fundamentals of Fluid Film Lubrication, 2nd Ed., Marcel Dekker, 2004.