# Test Specifications for ME PhD Qualifying Exams

Graduate Handbook: Appendix D

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Georgia Tech courses that cover the equivalent preparatory subject matter in the Standard Examination Areas are summarized below.
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
1. Boyce, W. E. and R. C. DiPrima, 2. Chapra, S. C. and R. P. Canale, 3. Davis , H. F. and A. D. Snider, 4. Hildebrand, F. B. 5. Powers, D. L., 6. Strang, G
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. 2. 3.
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)
1. Pahl, G., W. Beitz, K. Wallace, L. Blessing, and F. Bauert, 2. C. R. Mischke and R. Budynas,
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.
3. Tlusty, G., Manufacturing Processes and Equipment, Prentice-Hall, Upper Saddle River, NJ, 2000.
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. 8. Viscoelasticity 9. Biological responses to mechanical stimuli 10. General laws for constitutive equations 11. Soft tissue biomechanics 12. Blood vessel mechanics
1. Caro, C. G., Pedley, T. J., Schroter, R. C., Seed, W. A. 2. Fung, Y. C. Biodynamics, 3. Fung, Y. C., Biomechanics: 4. Fung, Y. C., Biomechanics:
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.
(Acoustics I and II).
1. Pierce, A.D., 2. For a complement, see also Kinsler, Frey, Coppens, and Sanders, Computer-Aided Engineering (CAE)
-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.
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.
1. Surface roughness 2 Hertzian contact 3. Rough surface contact 4. Friction 5. Time varying phenomena 6. Wear 7. Lubrication regimes: full film, mixed and boundary 8. Hydrostatic lubrication 9. Hydrodynamic lubrication 10. Elasto-hydrodynamic lubrication 11. Seals 12. Liquid lubricants 13. Solid lubricants 14. Surface modification
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. |