Engineering Science and Mechanics
http://www2.esm.vt.edu
Ishwar K. Puri, Head
Scott W. Case, Associate Head
University Distinguished Professor: A. H. Nayfeh
Clifton C. Garvin Professor: R. C. Batra
Francis J. Maher Professor: D. P. Telionis
Preston Wade Professor: M. P. Singh
Reynolds Metals Professor: H. Aref
Professors: H. Aref; R. W. Barnwell; M. S. Cramer; D. A. Dillard; N. E. Dowling; J. C. Duke;
J. W. Grant; Z. Gurdal; M. R. Hajj; E. G. Henneke; M. W. Hyer; L. G. Kraige; L. Librescu;
D. H. Morris; I.K. Puri; S. A. Ragab
Associate Professors: S. W. Case; H. Dankowicz; K. Granata; S. L. Hendricks; R. D. Kriz;
J. J. Lesko; S. Thangjitham
Assistant Professors: J. Cotton; M. L. Madigan; Z. N. Masoud
Adjunct Professors: F. dell'Isola; J. S. Wayne
Professors Emeritus: D. Frederick; R. A. Heller; R. M. Jones; L. Meirovitch; A. A. Pap; D. Post; K.L. Reifsnider; D. J. Schneck; C. W. Smith; H. W. Tielman
Affiliate Faculty: D. Gao; C. Hall; D. Inmann; R. Kapania; M. Paul; R. Plaut; P. Vlachos
Career Advisor: M. R. Hajj
ESM Engineering Communications Program Director: M. C. Paretti
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Overview
Mechanics is a fundamental area of science and engineering. It is an exciting, expanding field of learning with its roots grounded in the laws of motion formulated by Newton and the principles governing the behavior of solids and fluids, branching out in modern times into interdisciplinary fields such as new engineering materials (adhesives, composites, polymers, light metals), biomechanics, transportation, wind engineering, and vehicular structures. Although the problems to which they are applied may change, the basic principles of mechanics remain current and relevant. The Department of Engineering Science and Mechanics at Virginia Tech has a rich tradition for providing a strong interdisciplinary engineering education. The undergraduate program educational objectives are:
- To produce graduates with a broad educational background in engineering science and mechanics.
- To produce graduates with an interdisciplinary background with a strong base of fundamental knowledge of the engineering sciences, physical sciences, applied mathematics, capable of discovering solutions to engineering problems appropriate to the needs of society and technology.
- To produce graduates employable in a modern engineering environment with a commitment to lifelong learning and achievement.
- A strong foundation in the basic and engineering sciences, mathematics, and fundamentals of engineering.
- An understanding of first principles in the traditional areas of mechanics: solid mechanics and materials, fluid mechanics, and dynamics.
- A capacity to apply engineering fundamentals and first principles of mechanics to a wide variety of engineering problems.
- Knowledge and experience in analytical, computational, and experimental methods, and an ability to critically evaluate these approaches for use in a given situation.
- The ability to combine various areas of mechanics and other disciplines.
- Exposure to the design process throughout the undergraduate curriculum, including capstone design exercises in which both group and individual efforts are involved.
- Exposure to a curriculum that possesses flexibility to the degree that the student might concentrate in one of the traditional areas of mechanics, in a discipline such as biomechanics, in a discipline centered outside the ESM department; or the student might opt to gain a more comprehensive general background in engineering science and mechanics.
- Effective written and oral communication skills.
- A sense of social, ethical, and human responsibilities, including a historical perspective of the impact of technology.
- The recognition that engineering is a lifelong combination of education and achievement.
A total of 12 credit hours of technical electives, 6 credit hours of senior design and project and 8 credit hours of free electives give the student freedom to develop individually tailored programs of concentrated study. Students take courses in basic engineering sciences such as statics, dynamics, deformable bodies, and fluid mechanics, followed by applications oriented courses in solids, fluids, dynamics, and experimental and computational methods. Exposure to the design process exists throughout the curriculum, culminating in a senior level capstone design course. Undergraduate courses in engineering science and mechanics are taught on a service basis for all engineering curricula. A minor in mechanics is available for engineering students. The department offers graduate programs leading to M.S. (thesis and non-thesis option), M.Eng., and Ph.D. The department also participates in the Five Year Bachelor's/Master's Program.
Biomechanics Option: An option in Biomechanics is available for students in engineering. Specific details of course requirements for this option may be obtained by contacting the department.
The Cooperative Education Program is available to qualified candidates at undergraduate and graduate levels.
Students majoring in Engineering Science and Mechanics who are residents of Delaware, Maryland, South Carolina, West Virginia, and Kentucky may be eligible for the Academic Common Market, a program whereby residents of these states are eligible for Virginia in-state tuition. Contact the Office of Undergraduate Admissions for information.
A total of 136 credits are required for the ESM degree.
Areas of Concentration
The student may use the technical electives, free electives, and the senior design and project to develop individually tailored programs of concentrated study in one of the following areas: Biomechanics, Fluid mechanics, Motion, Solid mechanics/materials.
In cases where a student plans to go on to medical school, entrance requirements can be satisfied. Students who do not wish to complete the entire biomechanics sequence (BIOL 2405-2406, 4105-4106, 4204, 4574, 5405-5406) may study a smaller number of courses in this field.
Engineering Science and Mechanics Program
| Second Year |
| First Semester |
| ESM 2104: Statics |
3
|
| ISE 2014: Engineering Economy |
2
|
| MATH 2224: Multivariable Calculus |
3
|
| PHYS 2306: Foundations of Physics |
4
|
| Aesthetics Elective (Area 6) |
1
|
| University Core (Area 2 or 3) |
3
|
|
ESM 2014: Professional Dev. Seminar
|
1
|
|
Credits
|
17
|
| Second Semester |
| ESM 2204: Mech of Deform Bodies |
3 |
| ESM 2074: Computational Methods |
3 |
| ESM 2304: Dynamics |
3 |
| MATH 2214: Intro. to Differential Equations |
3 |
| MSE 2044: Elements of Materials Engineering |
3 |
| University Core (Area 2 or 3) |
3 |
|
Credits
|
18
|
| Third Year |
| First Semester |
| ECE 3054: Electrical Theory |
3 |
| ESM 3015: Fluid Mechanics I |
2 |
| ESM 3054: Mech Behavior of Matls |
2 |
| ESM 3064: Mech Behavior of Mat Lab |
1 |
| MATH 4574: Vector and Complex Analysis |
3 |
| ME 3134: Thermodynamics |
3 |
| University Core (Area 2 or 3) |
3 |
|
Credits
|
17
|
| Second Semester |
| ESM 3016: Fluid Mechanics II |
3 |
| ESM 3034: Fluid Mechanics Lab |
3 |
| ESM 3124: Intermediate Dynamics |
3 |
| ESM 3154: Solid Mechanics |
3 |
| MATH 4564: Operational Methods for Engineers |
3 |
| ESM 4004: Inst. and Exp. Mech. |
3 |
|
Credits
|
16
|
| Fourth Year |
| First Semester |
| ESM 4014: Appl Fluid Mech |
3 |
| ESM 4015: Creative Design I |
3 |
| ESM 4074: Vibration and Control |
3 |
| ESM 4614: Intro Reliability Eng. |
2 |
| Technical Electives |
6 |
|
Credits
|
17
|
| Second Semester |
| ESM 4016: Creative Design II |
3 |
| ESM 4734: Finite Element |
3 |
| Free Elective |
2 |
| University Core (Area 2 or 3, and 7) |
3 |
| Technical Electives |
6 |
|
Credits
|
17
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Undergraduate Course Descriptions (ESM)
1054: INTRODUCTION TO NDE ENGINEERING
Introduction to science and technology of nondestructive evaluation (NDE) engineering. Basic concepts and terminology are presented. Applications in different industries are explored. (1H,1C) II.
1114: SURVEY OF BIOMEDICAL ENGINEERING
Scope and history of BME, engr for diagnosis, therapy, and rehabilitation of living systems, medical electronics and instrumentation, non-invasive diagnostic imaging, life support equipment, automation/quantification of medical data, biological signal analysis, clinical engr, biomechanics, biotechnology, genetic engr, bionics, biodynamics, bioastronautics, environmental engr, biomaterials, space medicine, prosthetics, orthotics, artificial organs, artificial intelligence, studies of engr contributions to health care and physiological research. (2H,1C) I.
2014: PROFESSIONAL DEVELOPMENT SEMINAR FOR ESM STUDENTS
Topics designed to foster the professional development of the ESM student. ESM program objectives and outcomes. Overview of solid mechanics, fluid mechanics, and dynamics. Synergistic applications in biotechnology, adhesion science, and other applied areas. (1H,1L,1C)
2074 (AOE 2074): COMPUTATIONAL METHODS
Solving engineering problems using numerical methods and software, truncation and round-off error, root finding, linear and polynomial regression, interpolation, splines, numerical integration, numerical differentiation, solution of linear simultaneous equations, numerical solutions of ordinary differential equations. A grade of C- or better required in ENGE prerequisite 1114. Pre: ENGE 1114. Co: MATH 2214. (3H,3C)
2104: STATICS
Vector mechanics of forces and moments, free-body diagrams, couples, resultants, equilibrium of particles and rigid bodies in two and three dimensions, forces in trusses, frames, and machines, centroids, centers of mass, distributed forces, internal shear forces and bending moments in beams, shear and moment diagrams, friction, belt friction, area of moments of inertia, parallel axis theorem. Pre: ENGE 1024, MATH 1114. Co: MATH 2224. (3H,3C) I,II,III,IV.
2204: MECHANICS OF DEFORMABLE BODIES
Concepts of stress, strain, and deformation. Factor of safety. Stress-strain relationships and material properties. Stress concentrations. Area moments of inertia. Axially loaded members, torsionally loaded members, bending of beams. Shear and moment diagrams. Stresses due to combined loading. Thin-walled pressure vessels. Transformation of stress including Mohr's circle. Beam deflections and buckling stability. Pre: 2104. (3H,3C) I,II,III,IV.
2214: STATICS AND MECHANICS OF MATERIALS
Forces, moment, resultants, and equilibrium. Stress, strain, and stress-strain relations. Centroids and distributed loads. Analysis of axially loaded bars and beams. Principal stresses and Mohr's circle, combined loading. Pressure vessels and buckling of columns. Partially duplicates 2104 and 2204. Must be ChE major. Co: MATH 2224. (3H,3C) I.
2304: DYNAMICS
Vector treatment of the kinematics and kinetics of particles and rigid bodies, Newton's laws, work and energy, impulse and momentum, impact, mass moments of inertia, rotating axes. Pre: 2104. Co: MATH 2214. (3H,3C) I,II,III,IV.
2974: INDEPENDENT STUDY
Variable credit course.
2984: SPECIAL STUDY
Variable credit course.
2994: UNDERGRADUATE RESEARCH
Variable credit course.
3015-3016: FLUID MECHANICS I, II
Fluid statics. Dimensional analysis. Control volume approach to flow analysis, pipe flows. Introduction to continuum mechanics, differential approach, fluid kinematics, derivation of mass, momentum and energy equations, boundary layers, vorticity dynamics, potential flows, compressible flows, lift and drag. Pre: 2304, MATH 2224 for 3015; MATH 4574 for 3016. Co: ME 3134 for 3015; 3034 for 3016. 3015: (2H,2C) 3016: (3H,3C) 3015: I; 3016: II.
3024: INTRODUCTION TO FLUID MECHANICS
Fluid properties and hydrostatics. Derivation and application of the continuity, momentum, and energy equation (Bernoulli's equation) for ideal and real fluid flow (laminar or turbulent). Dimensional analysis and similtude. Introduction to boundary layers, lift and drag. Pre: 2304, MATH 2224. (2H,2L,3C) I.
3034: FLUID MECHANICS LABORATORY
Introduction to experimental fluid mechanics. Technical writing. Experiments on fluid properties, manometry, hydrostatic forces on submerged surfaces, flow measurements, impulse-momentum principle, velocity measurements, drag forces on cylinders, model testing of ships, flow visualization and hydraulic jumps. Demonstration of modern data acquisition. Pre: 3015. (3L,1C) II.
3054 (MSE 3054): MECHANICAL BEHAVIOR OF MATERIALS
Mechanical properties and behavior of engineering materials subjected to static, dynamic, creep and fatigue loads under environments and stress states typical of service conditions; biaxial theories of failure; behavior of cracked bodies; microstructure-property relationships and design methodologies for homogeneous and composite materials. Pre: 2204. (2H,2C) I,II.
3064 (MSE 3064): MECHANICAL BEHAVIOR OF MATERIALS LABORATORY
Laboratory experiments on mechanical properties and behavior of homogenous and composite engineering materials subjected to static, dynamic, creep, and fatigue loads; behavior of cracked bodies; microstructure-property relationships, and determination of materials properties for use in engineering design. Co: 3054. (3L,1C)
3124: INTERMEDIATE DYNAMICS
Vector analysis, Newton's Laws, rotating coordinate systems, particle dynamics, orbital mechanics, systems of particles, rigid-body dynamics, inertia matrix, Eulerian angles, introduction to gyroscopic motion, Lagrange's equations. Pre: 2304, MATH 2214, MATH 2224. (3H,3C) II.
3154: SOLID MECHANICS
Introduction to elasticity and continuum mechanics, plane stress and plane strain; bending of beams, asymmetrical bending, deflections, shear center; torsion of general cross-section bars; comparison of elasticity solutions with strength of materials; introduction to energy methods; elastic stability of columns. Pre: 2204, 3054. (3H,3C)
3704: BASIC PRINCIPLES OF STRUCTURES
Static equilibrium of forces and moments, concurrent and nonconcurrent force systems, center of gravity, concentrated and distributed loads. Solution of trusses. Stress and strain, elastic behavior of materials, cables and arches, shear, bending, and deformation in beams, indeterminate structures. Not available to students in engineering. (3H,3C) I.
4004 (BSE 4004): INSTRUMENTATION & EXPERIMENTAL MECHANICS
Introduction to instrumentation. Data analysis: uncertainty, error and statistical concepts. Devices: digital multi-meters, oscilloscopes, power supplies, and function generators. Circuits: ballast circuits, wheatstone bridges, operational amplifiers, and transistors. Principles of data acquisition. Fourier analysis. Measurements of velocity, pressure, strain, displacement, forces and accelerations. Laboratory and design projects. Pre: 2204, 2304, 3015 or 3024, ECE 3054. (2H,2L,3C)
4014: APPLIED FLUID MECHANICS
Analysis of flow over practical configurations, panel methods, Reynolds-averaged Navier-Stokes equations, turbulent boundary layers, flow separation and three-dimensional effects. Unsteady flows, fluid-structure interactions. Pre: 2074, 3016. (3H,3C) I.
4015-4016: CREATIVE DESIGN AND PROJECT I, II
Design of engineering systems and projects encompassing the principles and practices of engineering science and of the several engineering fields. Investigation and report on a supervised design project. Requires senior standing. 4015: (2H,3L,3C) 4016: (1H,6L,3C) 4015: I; 4016: II.
4024: ADVANCED MECHANICAL BEHAVIOR OF MATERIALS
Mechanical behavior of materials, emphasizing solid mechanics aspects and methods for predicting strength and life of engineering components. Plasticity, failure criteria, fracture mechanics, crack growth, strain-based fatigue, and creep. Microstructure-property relationships, and laboratory demonstrations. Pre: 3054 or ME 4614. (3H,3C)
4044: MECHANICS OF COMPOSITE MATERIALS
Properties and mechanics of fibrous, laminated composites. Classical lamination theory, micromechanics, stiffness and strength, fabrication and testing. Thermal stresses. Design, analysis, and computerized implementation. Pre: 2204. (3H,3C) I.
4064: EXPERIMENTAL MECHANICS
Analytical and experimental methods for measuring strain fields in elastic bodies including mechanical, electrical, and optical methods (using electric resistance strain gages, photoelasticity, moire interferometry, and crack extension gages). Pre: 2204. (2H,2L,3C)
4074: VIBRATION AND CONTROL
Single-degree-of-freedom vibration, two- and n-degree-of-freedom systems, continuous systems, introduction to nonlinear systems, system stability,
introduction to the control of dynamic systems. Pre: 3124, MATH 4564. (3H,3C) I.
4084 (AOE 4084): ENGINEERING DESIGN OPTIMIZATION
Use of mathematical programming methods for engineering design optimization including linear programming, penalty function methods, and gradient projection methods. Applications to minimum weight design, open-loop optimum control, machine design, and appropriate design problems from other engineering disciplines. Pre: MATH 2224. (3H,3C)
4105-4106: ENGINEERING ANALYSIS OF PHYSIOLOGIC SYSTEMS
Engineering analysis of human physiology. Physiologic systems are treated as engineering systems with emphasis input-output considerations, system interrelationships and engineering analogs. 4105 - Mass and electrolyte transfer, nerves, muscles, renal system. 4106 - cardiovascular mechanics, respiratory system, digestive systems, senses. Pre: 2304, MATH 2214. (3H,3C) 4105: I,II; 4106: digestive systems, senses.
4114: NONLINEAR DYNAMICS AND CHAOS
Motion of systems governed by first-, second-, and third-order differential and difference equations: stability, geometry, phase planes, bifurcations, Poincare' maps, point attractors, limit cycles, strange attractors, fractal dimensions, Lyapunov exponents. Forced oscillations of one-degree-of-freedom systems: jump phenomena, sub- and superharmonic resonances, Hopf bifurcations, period-multiplying bifurcations, chaos. Pre: 2304, MATH 2214. (3H,3C) II.
4124: MULTI-BODY MECHANICS AND VISUALIZATION
Spatial geometry, vector algebra, three-dimensional rotations, reference frames, generalized coordinates, generalized speeds, configuration constraints, velocity constraints, constraint singularities, kinematic differential equations, force, torque, energy, particle dynamics, rigid-body dynamics, computer algebra, computer animations. Pre: MATH 1114, MATH 2224. (3H,3C)
4154 (MSE 4154): NONDESTRUCTIVE EVALUATION OF MATERIALS
Concepts and methods of nondestructive evaluation of materials. Discussion of techniques and mathematical bases for methods involving mechanical, optical, thermal, and electromagnetic phenomena; design for inspectability; technique selection criteria; information processing and handling; materials response measurement and modeling; signal analysis. Pre: 3054, PHYS 2176 or PHYS 2306. (3H,3C)
4184 (AOE 4184): DESIGN AND OPTIMIZATION OF COMPOSITE STRUCTURES
Design aspects of laminate constitutive relations, coupling and decoupling of in-plane and out-of-plane elastic response. Tailoring of laminated composite materials to meet design requirements on stiffness and strength through the use of graphical and numerical optimization techniques. Introduction to integer programming: branch-and-bound method and genetic algorithms. Stacking sequence design of laminated composite beams and plates via integer programming. Pre: 3054 or AOE 3024 or CEE 3404. (3H,3C)
4204: MUSCULOSKELETAL BIOMECHANICS
Skeletal anatomy and mechanics. Muscle anatomy and mechanics. Theory and application of electromyography. Motion and force measuring equipment and techniques. Inverse dynamics modeling of the human body. Current topics in musculoskeletal biomechanics research. Pre: 2304, (2074 or ME 2004). (3H,3C)
4224: BIODYNAMICS AND CONTROL
Study of human movement dynamics and neuromuscular control of multi-degree-of-freedom systems. Computational simulation of forward-dynamics and state-space linear control of human movement to investigate functional performance and neuromuscular pathology. Pre: 3124, 4204. (3H,3C)
4234: MECHANICS OF BIOLOGICAL MATERIALS AND STRUCTURES
Anatomy and physiology of connective tissue. Techniques for determining the mechanical response of biological soft and hard tissues. Includes static, viscoelastic, creep, fatigue, and fracture. Simplified models of biological structures. Creation of geometric models from medical imaging and computational modeling. Specific topics may include bone, cartilage, ligaments, tendon, teeth, and skin. Pre: 3054, (2074 or ME 2004). (3H,3C)
4304: HEMODYNAMICS
Study of the human cardiovascular system and blood flow. Anatomy and physiology of the human heart, vascular system, and its organization. Blood physiology and rheology. Non-Newtonian blood flow models. Steady and pulsatile blood flow in rigid and elastic arteries. Pressure waves in elastic arteries. Three-dimensional blood flow in the aortic arch and flow around heart valves. Pre: 3016 or ME 3404. (3H,3C)
4404: FUNDAMENTALS OF PROFESSIONAL ENGINEERING
A refresher of basic principles and problem solving techniques involving twelve subject areas most common to all engineering curricula. The topics include those tested by the National Council of Engineering Examiners on the EIT (Engineer in Training) examination, the first requirement, in all fifty states, toward P.E. (Professional Engineer) licensing. Duplicates material of other engineering courses and impracticable for nonengineers, hence not usable for credit toward any degree. Pre: Junior and senior standing in Engineering or in Building Construction or Graduate students in Engineering. Pass/Fail only. (2H,2C) II.
4444 (AOE 4054) (CEE 4444): STABILITY OF STRUCTURES
Introduction to the methods of static structural stability analysis and their applications. Buckling of columns and frames. Energy method and approximate solutions. Elastic and inelastic behavior. Torsional and lateral buckling. Use of stability as a structural design criterion. Pre: AOE 3024, CEE 3404. (3H,3C) II.
4524: INTRODUCTION TO WAVE MOTION
Introduction to fundamentals of wave propagation. Topics include wave speed and dispersion relations, group velocity, wavepackets, waveguides, wave reflections, effects of nonuniformity and nonlinearity. General phenomena will be illustrated through use of specific physical applications and well-known model equations. Examples will be drawn from all areas of the physical sciences including solid and fluid dynamics, acoustics, geophysics, and electromagnetic field theory. Pre: MATH 4564. (3H,3C)
4574 (MSE 4574): BIOMATERIALS
Lectures and problems dealing with materials used to mimic/ replace body functions. Topics include basic material types and possible functions, tissue response mechanisms, and considerations for long term usage. Integrated design issues of multicomponent materials design in prosthetic devices for hard and soft tissues are discussed. Must meet prerequisite or have graduate standing in the College of Veterinary Medicine. Pre: MSE 3054. (3H,3C)
4614: INTRODUCTION TO RELIABILITY-BASED ENGINEERING DESIGN
Basic concepts of reliability, useful probability distributions, probabilistic design, safety factors and safety index, system reliability, failure rate, service life calculations. Pre: 2204, 3064. (2H,2C)
4714: SCIENTIFIC VISUAL DATA ANALYSIS AND MULTIMEDIA
Classical and advanced methods of visual data analysis within scientific applications context; emphasis on examples of scientific investigation with visual tools, and new visual methods with computer graphics; visual data analysis of numerical experimental and analytical results including: gradients, function-extraction, chaos, nth-order tensor glyph representations, molecular synthesis. Pre: (MATH 1015, MATH 1016) or (MATH 1205, MATH 1206). (3H,3C) II.
4734 (AOE 4024): AN INTRODUCTION TO THE FINITE ELEMENT METHOD
The finite element method is introduced as a numerical method of solving the ordinary and partial differential equations arising in fluid flow, heat transfer, and solid and structural mechanics. The classes of problems considered include those described by the second-order and fourth-order ordinary differential equations and second-order partial differential equations. Both theory and applications of the method to problems in various fields of engineering and applied sciences will be studied. Pre: 2074, MATH 2224. (3H,3C)
4904: PROJECT AND REPORT
Variable credit course. X-grade allowed.
4974: INDEPENDENT STUDY
Variable credit course.
4984: SPECIAL STUDY
Variable credit course.
4994: UNDERGRADUATE RESEARCH
Variable credit course.
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