Engineering Mechanics (E M)

(Administered by the Department of Aerospace Engineering and Engineering Mechanics)
Thomas J. Rudolphi, Chair of Department
Distinguished Professors: R. B. Thompson
Professors: Chimenti, Greer, Holger, Inger, McDaniel, Munson, Pierson, Rogge, Rohach, Rothmayer, Rudolphi, Schmerr, Tannehill, Tsai, Zachary
Professors (Adjunct): Hsu
Distinguished Professors (Emeritus):
D. Thompson, Young
Professors (Emeritus): Akers, Iversen, Jenison, McConnell, Rizzo, Weiss, Wilson
Associate Professors: Dayal, Flatau, Hilliard, Hindman, Lu, Mann, Mitra, Rajagopalan, Sarkar, Sherman, Sturges, Trulin, Vogel
Associate Professors (Adjunct): Roberts
Associate Professors (Emeritus): Hermann, Seversike
Assistant Professors: Bastawros, Chavez, Jacobson
Assistant Professors (Adjunct): Gray, Legg

Undergraduate Study

The courses in mechanics are intermediate between those in physics and mathematics and the professional and design courses of the several engineering curricula. In the work of this department the student is expected to acquire an understanding of the principles underlying the technique of analysis and a knowledge of those properties of materials which influence the manner and extent of their use for engineering purposes. Physical properties of engineering materials are studied in the classroom and are evaluated in the laboratory. General laws, such as those of Newton, are given mathematical expression and are made suitable for use in the solution of specific problems in machine and structural design, and in the flow and measurement of fluids.

Graduate Study

The department offers work for the degrees master of science, master of engineering, and doctor of philosophy with major in engineering mechanics, and minor work to students taking major work in other departments.

The master of science degree requires a thesis and a minimum of 8 research credits. It has strong research emphasis and is recommended for students who anticipate entering a doctoral program later. At least 30 credits of acceptable graduate work are required for the degree.

The master of engineering degree does not require either research credits or a thesis. However, at least two credits of acceptable creative component and at least 26 credits of acceptable graduate coursework are required. A minimum of 30 credits of acceptable graduate work is required for the degree. The program is intended to give students additional instruction at the graduate level to better qualify them for advanced professional engineering work. By careful selection of electives and perhaps additional courses during the senior undergraduate year, students should be able to qualify for the master of engineering degree with an additional year of full-time study after receiving their baccalaureate degree in one of the several engineering curricula.

Credits for creative component will be obtained by registering for E M 599. A written report and an oral presentation will be given to the student's graduate committee.

The normal prerequisite to major graduate work is the completion of a curriculum substantially equivalent to that required of undergraduate students in engineering at this university. However, because of the diversity of interests in graduate work in engineering mechanics, it is possible for a student to qualify for graduate study even though undergraduate or prior graduate training has been in a discipline other than engineering-e.g., physics or mathematics.

Cooperative programs between Engineering Mechanics and Biomedical Engineering are provided jointly under the sponsorship of the Colleges of Engineering and Veterinary Medicine. Laboratory facilities are available both in the veterinary medicine complex and on the main campus. See Biomedical Engineering for requirements.

Courses open for nonmajor graduate credit: All 300- and 400-level courses except 301, 307 and 490.

Courses Primarily for Undergraduate Students

E M 274. Statics of Engineering
(3-0) Cr. 3. F.S.SS. Prereq: Credit or enrollment in Math 166; credit or enrollment in Phys 111 or 221. Vector and scalar treatment of coplanar and noncoplanar force systems. Resultants, equilibrium, friction, centroids, second moments of areas, principal second moments of area, radius of gyration, internal forces, shear and bending moment diagrams. Credit for only one of 274, 301, 306, 307 may be allowed for graduation.

E M 301. Fundamentals of Mechanics
(4-0) Cr. 4. S. Prereq: Phys 221, Math 166. Newton's laws, equilibrium of rigid and deformable bodies, stress. Kinematics and dynamics of particles and rigid bodies. Deformation and strain of solids and fluids, constitutive equations for solids and Newtonian fluids. Applications to tension, torsion, flexure of solid bars and vibrations. Credit for only one of 274, 301, 306, 307 may be allowed for graduation.

E M 306. Static and Mechanics of Materials
(5-0) Cr. 5. F.S.SS. Prereq: Credit or enrollment in Math 166; credit or enrollment in Phys 111 or 221. Resultants, equilibrium of rigid and deformable bodies, centroids, second moments of area. Stress-strain relationships and deformation, Castigliano's Theorems. Analysis of axial, torsion, beam bending, buckling, and combined loading. Theories of failure and stress concentration factors. Credit for only one of 274, 301, 306, 307 may be allowed for graduation. No more than six credits from 306, 324 may be used for graduation. Nonmajor graduate credit.

E M 307. Statics and Dynamics
(5-0) Cr. 5. F. Prereq: Credit or enrollment in Math 166, credit or enrollment in Phys 221. Principles of static equilibrium. Forces and moments for planar systems. Applications to planar problems in trusses, beams, and machines, centroids, second moments of areas, and friction. Dynamics of particles and rigid bodies in planar motion. Kinematics of a particle in rectilinear and curvilinear motion. Equations of motion, energy, and momentum methods for a particle. Kinematics of rigid bodies. Moments of inertia. Equations of motion, energy, and momentum methods for rigid bodies. Vibrations. Credit for only one of 274, 301, 306, 307 may be allowed for graduation. No more than six credits from 307, 345, may be used for graduation.

E M 324. Mechanics of Materials
(3-0) Cr. 3. F.S.SS. Prereq: 274 or 307. Plane stress, plane strain, stress-strain relationships, and elements of material behavior. Application of stress and deformation analysis to members subject to centric, torsional, flexural, and combined loadings. Elementary considerations of theories of failure, buckling. No more than six credits from 306, 324 may be used for graduation.Nonmajor graduate credit.

E M 327. Mechanics of Materials Laboratory
(0-3) Cr. 1. F.S.SS. Prereq: 301 or 306 or credit or enrollment in 324. Experimental determination of mechanical properties of selected engineering materials. Experimental verification of assumptions made in 301 and 324. Use of strain measuring devices. Preparation of reports. Students who are not present for the first laboratory meeting of their own sections may qualify for continuation in the course only by attending the first laboratory meeting of some other section of the course. Nonmajor graduate credit.

E M 336. Engineering Materials
(2-0) Cr. 2. F.S. Prereq: 301 or 306 or credit or enrollment in 324. Structure, properties, and uses of engineering materials, with emphasis on construction materials. Nonmajor graduate credit.

E M 345. Dynamics
(3-0) Cr. 3. F.S.SS. Prereq: 274 or 301 or 306, credit or enrollment in Math 266 or 267. Particle and rigid body kinematics, Newton's laws of motion, kinetics of plane motion, rigid body problems using work-energy, linear, and angular impulse-momentum principles, vibrations. Nonmajor graduate credit. No more than six credits from 307, 345, may be used for graduation.

E M 350. Introduction to Nondestructive Evaluation Engineering
(3-0) Cr. 3. S. Prereq: 301 or 306 or 324, Math 266, Phys 222. Introduction to the fundamentals of ultrasonic, eddy current, and x-ray testing. The generation, transmission, scattering, and reception of ultrasonic waves and x-rays in an NDE inspection. Safety issues. The connection between NDE, fracture mechanics, and reliability. Probability of detection and its impact on failure. The use of NDE in design. Nonmajor graduate credit.

E M 362. Principles of Nondestructive Testing (Same as Mat E 362.)
See Materials Engineering. Nonmajor graduate credit.

E M 362L. Nondestructive Testing Laboratory (Same as Mat E 362L.)
See Materials Engineering. Nonmajor graduate credit.

E M 378. Mechanics of Fluids
(2-2) Cr. 3. F.S.SS. Prereq: 274 or 301 or 306 or 307. Properties of fluids. Fluid statics. Kinematics and kinetics of fluid flow. Mass, momentum, and energy conservation laws; dimensional analysis; flow in pipes and channels. Selected laboratory experiments. Nonmajor graduate credit.

E M 417. Experimental Mechanics
(2-2) Cr. 3. F. Prereq: 301 or 306 or 324. The use of strain gages and brittle coating with applications to practical engineering problems. Strain gage based transducers, recording and output devices. Selected laboratory experiments. Nonmajor graduate credit.

E M 424. Intermediate Mechanics of Materials
(3-0) Cr. 3. F.S. Prereq: 306 or 324. Stresses, strains, deflections and angular twist of symmetrical and unsymmetrical members subjected to combined loading. Analysis of contact stress problems and shrink fit problems. Dynamic load effects, fatigue and fracture mechanics introduction. Stress analysis of connections. Nonmajor graduate credit.

E M 425. Introduction to the Finite Element Method
(3-0) Cr. 3. F.S. Prereq: 301 or 306 or 324, Math 266 or Math 267. Introduction of finite element analysis through applications to one-dimensional, steady-state problems such as elastic deformation, heat and fluid flow, consolidation, beam bending, and mass transport. Transient heat conduction and wave propagation. Two-dimensional triangular and quadrilateral elements. Plane problems of torsion, thermal and potential flow, stress analysis. Simple computer programs for one- and two-dimensional problems. Nonmajor graduate credit.

E M 444. Mechanical Vibrations
(2-2) Cr. 3. F. Prereq: 306 or 324, 345. Elementary vibration analysis, single and multiple degrees of freedom, energy methods, free and forced vibrations, viscous damping, transmissibility, matrix methods, modal analysis. Selected laboratory experiments. Numerical methods of solution. Nonmajor graduate credit.

E M 451. Engineering Acoustics (Same as M E 451.)
(2-2) Cr. 3. S. Prereq: Phys 221 and Math 266 or 267. Sound sources and propagation. Noise standards and effects of noise on people. Principles of noise and vibration control used in architectural and engineering design. Characteristics of basic noise measurement equipment. Experience in use of noise measuring equipment, sound power measurements, techniques for performing noise surveys, evaluation of various noise abatement techniques applied to common noise sources. Selected laboratory experiments. Nonmajor graduate credit.

E M 490. Independent Study
Cr. arr. Prereq: Permission of instructor.

                H. Honors.

Courses Primarily for Graduate Students, Open to Qualified Undergraduate Students

E M 504. Analytical Methods in Mechanics
(3-0) Cr. 3. Prereq: Math 385. Applications of the equations of heat conduction, potential theory, and wave propagation to problems in mechanics. Methods of solution.

E M 505. Analytical Methods in Mechanics
(3-0) Cr. 3. Prereq: 504. Applications of the equations of heat conduction, potential theory, and wave propagation to problems in mechanics. Methods of solution.

E M 510. Continuum Mechanics
(3-0) Cr. 3. Alt. S., offered 2002. Prereq: Math 385. Presentation of the basic equations of engineering mechanics: conservation of mass, conservation of momentum, conservation of energy; principles of selection of constitutive equations; constitutive relations for classical elastic materials and classical fluids; simple rheological models for viscoelastic materials; introduction to Cartesion tensors.

E M 514. Advanced Mechanics of Materials (Same as Aer E 514.)
(3-0) Cr. 3. F. Prereq: 306 or 324. Theory of stress and strain, stress-strain relationships. Limitations of flexure and torsion formulas, unsymmetrical bending, curved beams, cross-shear, shear center. Torsion of thin-walled noncircular sections. Theories of failure, membrane stresses in shells, thick-walled cylinders.

E M 515. Buckling
(3-0) Cr. 3. Alt. S., offered 2002. Prereq: 514. Stability of columns, beam-columns, bars and frames. Inelastic buckling, torsional buckling, bending and buckling of thin plates and shells.

E M 516. Applied Elasticity
(3-0) Cr. 3. S. Prereq: Math 385. Fundamentals of linear continuum elasticity theory, formulation and solutions of simple elastostatic boundary value problems. Vector and tensor analysis. Kinematics of small deformations, constitutive laws for isotropic and anisotropic media. Field equations for one-, two-, and three-dimensional solids. Formulation of plane strain/plane stress problems by stress function methods. Corresponding solutions to a variety of classic canonical problems, such as those of Bickley, Boussinesq, Hertz, Kirsch, Lamé, Melan, and Mitchell.

E M 517. Experimental Stress Analysis (Same as Aer E 517.)
(3-2) Cr. 4. Alt. S., offered 2003. Prereq: 306 or 324. Fundamental concepts of stress and strain measurement, strain gage characteristics, strain gage circuits and instrumentation, strain gage based transducers, transmission and reflection photoelasticity, two- and three-dimensional photoelasticity, Moire interferometry methods of measuring displacement and strains.

E M 518. Wave Propagation in Elastic Solids
(3-0) Cr. 3. Alt. F., offered 2001. Prereq: Math 385. Elastic waves are treated from both an analytical and phenomenological standpoint, with an introduction to continuum mechanics. Reflection, transmission at planar interfaces lead to study of guided waves, primarily Rayleigh, Lamb, SH, and Stoneley waves, also with fluid loading. Waves in anisotropic elastic media are covered. Acoustic source radiation, reciprocity, and diffraction and material damping are covered.

E M 519. Experimental Methods of Motion Measurement
(2-2) Cr. 3. Alt. S., offered 2002. Prereq: 417, 444. Description, specifications, limitations, and applications of mechanical, electrical, and optical transducers used in motion measurements applied to steady state, transient, and shock motions. Calibration, signal conditioning, and transducer systems used to obtain reliable and reproducible experimental data. Seismic and absolute references for motion measurement.

E M 521. Biomechanics (Same as B M E 521, I E 521.)
(3-0) Cr. 3. Alt. F., offered 2001. Prereq: Phys 111 or 221, Math 265. For students with interests in the life sciences ergonomics, or rehabilitation engineering. Topics include motion, energy, equilibrium, stress and deformation, material properties, flow of fluids, dimensional analysis and modeling of biological systems. Illustrative examples taken from biology and medicine.

E M 522. Energy Methods in Applied Mechanics
(3-0) Cr. 3. Alt. F., offered 2002. Prereq: 514 or 516 and Math 385. Introduction to variational principles and energy methods in applied mechanics. Applications in solid mechanics, dynamics, and elasticity-bars, beams, torsion, and plane elasticity. Variational methods of approximation-Ritz's method, weighted residuals, finite elements. Applications in plates, shells, and components.

E M 524. Numerical Mesh Generation (Same as Aer E 524, M E 524.)
(3-0) Cr. 3. Alt. S., offered 2003. Prereq: Math 385. Introduction to modern mesh generation techniques. Structured and unstructured mesh methods, algebraic and PDE methods, elliptic and hyperbolic methods, variational methods, error analysis, Delaunay triangulation, data structures, geometric modeling with B-spline and NURBS surfaces, surface meshing.

E M 525. Finite Element Analysis (Same as Aer E 525.)
(3-0) Cr. 3. S. Prereq: 425, Math 385. Variational and weighted residual approach to finite element equations. Emphasis on two- and three-dimensional problems in solid mechanics. Isoparametric element formulation, higher order elements, numerical integration, imposition of constraints and penalty, convergence, and other more advanced topics. Use of two- and three-dimensional computer programs. Dynamic and vibrational problems, eigenvalues, and time integration. Introduction to geometric and material nonlinearities.

E M 526. Boundary Element Methods in Engineering
(3-0) Cr. 3. Alt. S., offered 2002. Prereq: 514 or 516. Introductory boundary element methods through plane problems. Singular integrals, Cauchy principal values, integral representations and boundary integrals in one dimension. Direct and indirect formulations. Plane potential and elastostatic problems. Higher order elements, numerical integration. Regularizations. Body forces and infinite regions. Specialized fundamental solutions, half-plane and axisymmetric problems. Diffusion and wave problems. Coupling with finite elements.

E M 544. Mechanical Vibrations
(2-2) Cr. 3. F. Prereq: 324, 345. Elements of lumped parameter linear systems, kinematics of vibrations, equations of motion for free and forced vibrations, energy methods, resonance, damping, multiple degrees of freedom, mechanical impedance, isolation and absorption of vibrations with impulsive and arbitrary excitation of linear systems, primary and residual shock spectra. Vibration of continuous systems.

E M 545. Vibration Testing
(2-2) Cr. 3. S. Prereq: 444 or 544. Theory of signal analysis, review of vibration concepts central to vibration testing, instrumentation considerations of force and acceleration measurements, digital frequency analyzer characteristics, and vibration exciter characteristics; application to overall test system-test structure interaction; requirements of transferring field data to laboratory simulation; standard test specifications. Term laboratory project.

E M 546. Introduction to Random Vibrations
(3-0) Cr. 3. Alt. S., offered 2003. Prereq: 544. Modal analysis, nonlinear vibration phenomena. Characteristics of random vibrations; random processes, probability distributions, spectral density and its significance, the normal or Gaussian random process. Transmission of random vibration, response of simple single and two-degree-of-freedom systems to stationary random excitation. Fatigue failure due to random excitation.

E M 548. Advanced Engineering Dynamics
(3-0) Cr. 3. F. Prereq: 345, Math 266 or 267. Dynamics of particles and rigid bodies. Generalized coordinates. Lagrangian equations of motion. Equations of motion in terms of Eulerian angles, motion of a gyroscope.

E M 550. Fundamentals of Nondestructive Evaluation (Same as M S E 550.)
(3-2) Cr. 4. S. Prereq: 301 or 306 or 324, Math 385. Basic physics of ultrasonic, radiographic, and electromagnetic NDE measurements. Principles and uses of other quantitative techniques in nondestructive evaluation. Signal processing and evaluation methods. Laboratory experiments in ultrasonics, eddy current, and x-ray radiography methods of NDE.

E M 551. Signal Processing in Mechanics (Same as M E 551.)
(2-2) Cr. 3. S. Prereq: 444 or 451, Math 385. Classification and measurement of time dependent phenomena in mechanics. Correlation, spectral and probabilistic techniques for the analysis of acoustical, vibrational, and unsteady fluid dynamic phenomena. Selected laboratory experiments emphasizing dual channel FFT analyzer applications in mechanics.

E M 552. Advanced Acoustics
(3-0) Cr. 3. Alt. F., offered 2001. Prereq: 444 or 451. Theoretical acoustics: wave propagation in fluids; acoustic radiation, diffraction and scattering; and architectural acoustics. Applications of basic acoustic theory in noise control and acoustic radiation. Introduction to selected numerical methods in acoustics.

E M 560. Scanning Electron Microscopy Characterization of Materials
(2-2) Cr. 3. F. Prereq: Mat E 272. Principles of scanning electron microscopy and energy dispersive X-ray microanalysis. Laboratory microstructural-microchemical analyses of materials.

E M 564. Fracture and Fatigue (Same as M S E 564 and M E 564.)
(3-0) Cr. 3. F. Prereq: 306 or 324 and any one of 336, E Sci 352, Mat E 211 or 272. Materials and mechanics approach to fracture and fatigue. Fracture mechanics, brittle and ductile fracture, fracture and fatigue characteristics. Fracture and fatigue tests, thermal fracture, mechanics and materials designed to avoid fracture or fatigue.

E M 568. Plasticity and Creep of Materials (Same as M S E 568.)
(3-0) Cr. 3. Alt. F., offered 2001. Prereq: 306 or 324. Mechanics and materials approach to plasticity and creep, stress and strain tensors, yield criteria, flow rules, slip-line theory, and work hardening. Axially symmetric problems, bending, thermal load, torsion. Introduction to creep deformation, stress relaxation, and recovery problems.

E M 569. Mechanics of Composite and Combined Materials (Same as M S E 569 and Aer E 569.)
(3-0) Cr. 3. Alt. S., offered 2003. Prereq: 306 or 324. Mechanics of fiber-reinforced materials. Macromechanical behavior of lamina and laminates. Strength and interlaminar stresses of laminates. Failure criteria. Micromechanics of lamina. Stress analysis of laminates. Thermal and moisture stresses and residual stresses.

E M 571. Advanced Fluid Mechanics
(3-0) Cr. 3. F. Prereq: 378 or M E 335. Mass, momentum, and energy conservation laws of fluid dynamics; control volume and differential forms of governing equations; real and ideal fluids; concepts of stress, strain-rate, and vorticity; exact solutions of Navier-Stokes equations for steady and unsteady flows; low Reynolds number flows; boundary layer approximation; laminar and turbulent boundary layers; two-dimensional and axisymmetric potential flow problems; elements of compressible flow; engineering applications.

E M 574. Ultrasonic Nondestructive Measurement Principles (Same as M S E 574.)
(3-0) Cr. 3. F. Prereq: 370, 516, Math 385. Ultrasonic inspection techniques, underlying theory of elastic wave propagation and scattering. Transducer modeling and the development of a complete ultrasonic measurement model. Fundamental aspects of linear system theory. Application to flaw detection and sizing.

E M 580. Biomaterials (Same as B M E 580 and M S E 580.)
(3-0) Cr. 3. S. Prereq: Mat E 211 or 272. Presentation of the basic chemical and physical properties of biomaterials as they are related to their manipulation by the engineer for incorporation into living systems. Role of microstructure properties in the choice of biomaterials and design of artificial organs, implants, and prostheses.

E M 590. Special Topics
Cr. 1 to 4 each time taken. Prereq: Permission of instructor.

                A. Advanced Engineering Acoustics

                C. Thermal Stresses in Design

                D. Linear Viscoelasticity

                E. Biomechanics

                F. Other Topics

E M 599. Creative Component
Cr. arr.

Courses for Graduate Students

E M 645. Advanced Vibration Analysis
(3-0) Cr. 3. Alt. F., offered 2002. Prereq: 544, Math 385. Multiple degrees of freedom, inertia and stiffness matrices, transfer matrices, numerical methods. Vibration of continuous systems, limitations, and comparison of lumped approximations of continuous systems. Engineering applications.

E M 648. Advanced Topics in Dynamics
(3-0) Cr. 3. Alt. S., offered 2002. Prereq: 548, Math 385. Topics of current interest in dynamics such as vehicle stability, modeling multicomponent dynamical systems, and nonrigid body dynamics.

E M 651. Advanced Topics in Fluid Mechanics (Same as M E 651.)
(3-0) Cr. 3. Alt. S., offered 2002. Prereq: 571. Topics of current interest in fluid mechanics such as separation phenomena, three-dimensional boundary layers, unsteady flow phenomena, asymptotic methods in viscous flows, stability, theory of homogeneous isotropic turbulence, and turbulence models.

E M 690. Special Topics
Credit 1 to 6 each time taken. Prereq: Permission of instructor.

                A. Advanced Experimental Mechanics

                B. Nonlinear Wave Propagation

                C. Nonlinear Material Behavior

                D. Composite Materials

                E. Holography in Mechanics

                F. Finite Elements of Nonlinear Continua

                G. Fracture Mechanics

                H. Atmospheric Fluid Mechanics

                I. Viscous Flow Theory

                J. Advanced Similitude Analysis

                K. Advanced Analytic Methods in Mechanics

                L. Rheology

                M. Other Topics