# Subject Areas

## 4.1 Fundamental Material

The material listed in this Section (Section 4.1) is undergraduate material that helps to build the foundation for graduate-level core courses described in Section 4.2 below. In the Preliminary Examination, students are examined on material from two graduate-level core course sequences (Section 4.2).

### 4.1.1 Mechanics Area

Major Topics

Statics (MEM202): Concurrent force systems; statics of particles; equivalent force/moment systems; distributed forces; centroids; equilibrium of rigid bodies; trusses, frames and machines; internal forces in structural members; friction; moments of inertia.

Dynamics (MEM238): Kinematics of particles (Newton's Second Law, energy and momentum methods); kinematics of rigid bodies; plane motion of rigid bodies.

Mechanics Of Materials (MEM230, MEM330): Tension, compression and shear; axially loaded members; torsion; shear forces and bending moments; stress in beams; analysis of stress and strain; deflections of beams; statically indeterminate beams; columns; energy principles.

Further Information: By request from Dr. T. Tan

### 4.1.2 Thermal Fluid Sciences Area

Major Topics

Fluid Mechanics (MEM220, MEM320): Fluid statics, conservation equations for fluid motion, applications of the Bernoulli equation, pipe flow, basic inviscid and potential flow, basic compressible flow, one-dimensional isentropic, normal shock, two-dimensional supersonic flow, oblique shocks and Prandtl-Meyer expansion, supersonic nozzles, diffusers

heat conduction, forced and free convection. Combined heat transfer problems in engineering systems.

Thermodynamics (MEM310, MEM410): Fluid properties, First and Second Law applications, thermal efficiencies, properties of real fluids, analysis of ideal and real gas mixtures; gas-phase reacting systems.

Further Information: By request from Dr. Y. Cho

### 4.1.3 Systems and Control Area

Major Topics

Introduction to Control (MEM255): Modeling of linear & nonlinear systems, linearization, transfer functions, poles and zeros, state-space models, eigenvalues, eigenvectors and transition matrices, block diagrams and signal flow graphs, frequency and time-domain analysis.

Control System Design (MEM355): Root-locus and Nyquist techniques, Compensator design, Stability, controllability, and observability, regulator, observer, and set-point controllers.

Microcomputer Based Control Systems (MEM458, MEM459): Discrete-time systems, z-transform, sampling theorem, the pulse transfer function, discrete state equations, stability, time-domain analysis, frequency-domain analysis, design of discrete-time controllers, digital simulation, microcomputer and microprocessor implementation of digital controllers.

Further Information: By request from Dr. B.C. Chang.

## 4.2 Core Course Sequences

The Preliminary Examination covers material from two of the nine core course sequences listed in Section I. The material covered in each of the core course sequence include but not limited to those topics listed below.

### 4.2.1 Theory of Elasticity

Major Topics

Review of Mechanics of Materials; vector and tensor analysis; indexical notation; integral theorem; analysis of stress; equilibrium equations; principal stresses and stress invariants; analysis of strain; displacements and small strains; principal strains and strain invariants; compatibility; generalized Hooke's law; engineering elastic constants; governing equations in linear elasticity; strain energy; uniqueness of solution; Saint-Venant's principle; elementary problems in three dimensions.

Two dimensional problems in Cartesian and polar coordinates; solution by polynomials and Fourier series; Airy's stress function; solution by means of complex variables; torsion problem; bending of bars.

Three-dimensional problems, elastic contact; energy principles and applications; Rayleigh-Ritz methods; advanced topics.

Reference Material

Timoshenko, S.P. and Goodier, J.M., Theory of Elasticity, McGraw-Hill, 3rd ed., 1970.

Chou, P.C. and Pagano, N.J., Elasticity, Dover, 1992.

Recommended Courses

Theory of Elasticity I & II (MEM 660, MEM 661)

Further Information: By request from Dr. T. Tan

### 4.2.2 Solid Mechanics

Major Topics

The student is expected to have knowledge on the foundations of continuum mechanics. Major subjects include: Algebra and analysis of tensors. Kinematics of deformable bodies: material and spatial descriptions; material time derivative; measures of strain; rate of deformation and spin tensors. Balance principles: conservation of mass, linear and angular momentum, balance of energy; Cauchy and Piola-Kirchhoff stress tensors.

Constitutive equations: Introduction to phenomenological plasticity; strain-stress curves; ideal plastic models; crystal plasticity; fundamental one-dimensional problems; stress and strain deviatoric tensors; Von Mises and Tresca yield criteria; flow laws; isotropic and kinematic strain hardening. Nonlinear behavior of materials; kinematics of large deformations; Cauchy and Green elasticity; exact solutions for compressible and incompressible nonlinear elastic materials.

Reference Material

Chandrasekharaiah, D.S. and Debnath, L., Continuum Mechanics, Academic Press, 1994.

Fung, Y.C., Foundations of Solid Mechanics, Prentice Hall, 1965.

Gurtin, M., An Introduction to Continuum Mechanics, Academic Press, 1981.

Lublimer, J., Plasticity Theory, Mac Millan, 1990.

Malvern, L.E., Introduction to the Mechanics of a Continuous Medium, Prentice- Hall, 1969.

Recommended Courses

Continuum Mechanics (MEM 663)
Introduction to Plasticity (MEM 664)
Time– Dependent Solid Mechanics (MEM 665)

Further Information: By request from Dr. ????.

Major Topics

The student will be expected to show competence in Analytical Dynamics (Lagrangian) as well as Vector Dynamics in three dimensions (Eulerian). As a prerequisite, the student must have an undergraduate background in Statics and Dynamics at the level of the text by Beer & Johnston, as well as working knowledge of Vector Analysis and Matrix Algebra.

The topical coverage the student should be conversant with includes, but is not limited to: analytical statics, principle of virtual work, Lagrange's equations, generalized coordinates and forces, stability about dynamic equilibrium, conservation of generalized momentum constraints, Lagrange multipliers, generalized impulse and momentum, nonholonomic constraints, central forces, effect of rotation of the earth, three-dimensional vector dynamics applied to systems of particles and rigid bodies, linear vibration theory for systems with multiple degrees of freedom, normal coordinates, small oscillations about steady state.

Reference Material

Beer, F.P. and Johnston, E.R., Vector Mechanics for Engineers, 3rd ed., McGraw-Hill, 1977 (Elementary level).

Greenwood, D.T., Classical Dynamics, Prentice Hall, Inc., 1977 (Advanced level).

Recommended Courses

Advanced Dynamics I & II (MEM 666, MEM 667).

Further Information: By request from Dr. S. Siegler.

Major Topics

The student will be tested for competence in classical and statistical thermodynamics. The student is also expected to be able to demonstrate a reasonable background in undergraduate thermodynamics topics at the level of the texts by Van Wylen and Sonntag, Wark, or Black and Hartley.

The topical coverage includes, but is not limited to: first and second laws and properties of real and ideal substances, basic kinetic theory of gases, velocity and speed distributions, transport properties, elementary quantum mechanics, including energy level and degeneracy concepts, classical and quantum statistics, calculation of thermodynamic properties of ideal gases and gas mixtures, chemical equilibrium and thermochemistry, and real gas equations of state.

Reference Material

Wark, Thermodynamics, 5th ed., McGraw-Hill, 1988.

Van Wylen and Sonntag, Fundamentals of Classical Thermodynamics, 3rd ed., Wiley, 1986.

Callen, Thermodynamics and an Introduction to Thermostatics, 2nd ed., Wiley, 1985.

Incorpera, Introduction to Molecular Structure & Thermodynamics, Wiley, 1984.

Tien and Lienhard, Statistical Thermodynamics, Hemisphere, 1979.

Smith, Elementary Statistical Thermodynamics, Plenum, 1982.

Herzberg, Spectra of Diatomic Molecules, Van Nostrand & Reinhold, 2nd ed., 1950.

Sonntag and Van Wylen, Fundamentals of Statistical Thermodynamics, Krieger, 1985.

Bejan, Advanced Engineering Thermodynamics, Wiley, Interscience, 1988.

Lay, Statistical Mechanics and Thermodynamics of Matter: An Introductory Survey, Harper & Row, 1990.

Black and Hartley, Thermodynamics, Harper Collins, 1991.

Recommended Courses

Statistical Thermodynamics I & II (MEM 601, MEM 602).

Further Information: By request from Drs. N. Cernansky and D. Miller.

### 4.2.5 Heat Transfer

Major Topics

Basic concepts in heat transfer and fundamental mechanisms, the heat conduction equation and its boundary conditions, analytical solutions of steady state and transient heat conduction equation with and without heat generation, application of transform techniques, heat conduction with moving boundaries.

Heat transfer in free and forced convection, the equations of motion and energy, boundary layer analysis, determination of friction factor and heat transfer coefficients, fundamentals of boiling and condensation, basic thermal analysis of heat exchangers.

The concept of blackbody radiation, radiation heat transfer among surfaces separated by a nonparticipating medium, problems involving radiation combined with conduction and convection.

Reference Material

Eckert and Drake, Analysis of Heat and Mass Transfer, McGraw-Hill.

Arpaci, Conduction Heat Transfer, Addison-Wesley, 1966.

Kays and Crawford, Convective Heat and Mass Transfer, McGraw-Hill, 1993.

Siegel and Howell, Thermal Radiation Heat Transfer, McGraw-Hill, 1993.

Incorpera and Dewitt, Fundamentals of Heat and Mass Transfer, Wiley, 3rd ed., 1990.

Kakac and Yener, Heat Conduction, Hemisphere Publishing Co., 1985.

Bejan, Convection Heat Transfer, Wiley, 2nd edition, 1995.

In addition, it is recommended that the student be familiar with the materials covered in a typical undergraduate heat transfer text.

Recommended Courses

Conduction Heat Transfer (MEM 611).

Convection Heat Transfer (MEM 612).

Further Information: By request from Drs. B. Farouk and Y. Cho.

### 4.2.6 Fluid Mechanics

Major Topics

The student is expected to have a basic understanding of the principles of fluid mechanics and the methods for the analysis of 2-D ideal and viscous fluids. It is assumed that the student has the analytical background in vector and tensor analysis, complex variables and differential equations.

The topical coverage may include, but is not limited to: concept of fluid as a continuum, kinematics, conservation laws for fluids, vorticity and circulation, ideal inviscid 2-D flows, momentum integral equations, Navier-Stokes equations, exact solutions of the Navier-Stokes equations, viscous flows, laminar boundary layers including non-steady flows, similarity methods, asymptotic methods, introduction to stability, turbulence, shock waves, and compressible flows.

Reference Material

Schlichting, H., Boundary Layer Theory, 7th Ed., McGraw-Hill, 1979.

Currie, I.G., Fundamental Mechanics of Fluids, McGraw-Hill, 1974.

White, F., Fluid Mechanics, McGraw-Hill, 1986.

White, F., Viscous Fluid Flow, McGraw-Hill, 2nd Ed., 1991.

Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, 1973.

Recommended Courses

Foundation of Fluid Mechanics (MEM 621)

Boundary Layer Theory (MEM 622)

Further Information: By request from ????.

### 4.2.7 Robust Control Systems

Major Topics

Linear spaces and linear operators; internal stability, coprime factorization, matrix fraction description, irreducible MFD's, Smith-McMillan form; poles and zeros; canonical realizations of multivariable systems, minimal realizations; structure of stabilizing controllers; algebraic Riccati equation, state-space computation of coprime factorizations; YJB controller parametrization; linear fractional transformation; state-space structure of the proper stabilizing controllers; formulation of control problems; optimization problem, optimization problem, model matching problem, tracking problem, robust stabilization problem; inner-outer factorizations, spectral factorizations; Sarason's interpolation theory; Hankel-norm approximations, balanced realizations.

Reference Material

Francis, B. A., A Course in Control Theory, Springer-Verlag, 1987.

Vidyasagar, M., Control System Synthesis - A Factorization Approach, The MIT Press, 1985.

Chen, C-T, Linear Systems Theory and Design, CBS College Publishing, HRW, 1984.

Kailath, T., Linear Systems, Prentice-Hall, Inc., 1980.

Kwakernaak, H., and Sivan, R., Linear Optimal Control Systems, John Wiley & Sons, Inc., 1972.

Zhou, K., Doyle, J. C. and Glover, K., Robust and Optimal Control, Prentice Hall, 1996.

Recommended Courses

Robust Control Systems I & II (MEM 633, MEM 634)

Further Information: By request from Dr. A. Yousuff.

### 4.2.8 Nonlinear Control Theory

Major Topics

The student will be expected to demonstrate a broad knowledge in the qualitative behavior of nonlinear dynamical systems as well a facility in methods of nonlinear systems analysis and control system design. As a prerequisite to study in this field, the student should have a solid background in linear systems analysis and control systems design and background first year graduate mathematics including linear algebra and ordinary differential equations. The student should also be comfortable with the use of the computer in engineering analysis.

The topical coverage will include, but is not limited to: geometric theory of nonlinear dynamics; stability, controllability and observability of nonlinear systems; exact linearization, decoupling and stabilization by smooth feedback; systems with parameters: bifurcation and stability; regulator design; tracking and regulation; discontinuous feedback control.

Reference Material

Isidori, A., Nonlinear Control Systems: An Introduction, Springer-Verlag, 1989.

Beltrami, E., Mathematics for Dynamic Modeling, Academic Press, 1987.

Gelb, A. and Vander Velde, W. E., Multiple-Input Describing Functions and Nonlinear System Design, McGraw-Hill: New York, 1968.

Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag: New York, 1983.

Hagedorn, P., Non-Linear Oscillations, Oxford University Press: New York, 1981.

La Salle, J. and Lefschetz, S., Stability by Liapunov's Direct Method, Academic Press, New York, 1961.

Utkin, V. I., Sliding Modes and Their Application in Variable Structure Systems, MIR: Moscow, 1978.

Recommended Courses

Nonlinear Control Theory I & II (MEM 636, MEM 637)

Further Information: By request from Dr. H.G. Kwatny.

### 4.2.9 Real Time Microcomputer Control

Major Topics

Discrete-time systems and the z-transform; sampling and data reconstruction; the pulse transfer function; discrete state equations; time-domain analysis; digital simulation; stability; frequency-domain analysis; introduction to LabVIEW programming; data acquisition and processing.

Design of discrete-time controllers; sampled-data transformation of analog filter; digital filters; microcomputer implementation of digital filters; LabVIEW programming techniques; using the DAQ library; writing a data acquisition program; LabVIEW implementation of PID controllers.

Reference Material

Phillips, C. L. and Nagle, H. T., Digital Control System Analysis and Design, 3rd Edition, Prentice-Hall, 1995.

National Instruments, LabVIEW Student Edition, Prentice-Hall, 1995.

The MATH Works Inc., The Student Edition of MATLAB for Macintosh Computers, Version 4, Prentice Hall, 1995. (1992 Edition is also acceptable.)

Johnson, G.W., LabVIEW Graphical Programming: Practical Applications in Instrumentation and Control, McGraw-Hill, 1994.

Franklin, G. F., Powell, J. D., and Workman, M. L., Digital Control of Dynamic Systems, Addison-Wesley, 1990.

Astrom, K. J., Wittenmark, B., Computer Control Systems, Prentice-Hall, 1984.

Recommended Courses

Real Time Microcomputer Control I & II (MEM 639, MEM 640)

Further Information: By request from Dr. B.C. Chang.