Ishwar K. Puri, Professor and Head Scott W. Case, Professor and Associate Head University Distinguished Professor: A. H. Nayfeh Reynolds Metals Professor: H. Aref Clifton C. Garvin Professor: R. C. Batra Adhesive and Sealant Science Professor: D. A. Dillard Frank Maher Professor: N. E. Dowling N. Waldo Harrison Professor: M. W. Hyer Preston Wade Professor: M. P. Singh Paul and Dorothea Torgersen Dean's Chair in Engineering Professor: R. Benson Tucker Professor: R. L. Mahajan Professors: M. S. Cramer; J. C. Duke; J. W. Grant; M. R. Hajj;
L. G. Kraige; J. J. Lesko; S. A. Ragab Associate Professors: S. L. Hendricks; R. D. Kriz; M. L. Madigan;
M. A. Stremler; S. Thangjitham Assistant Professors: R. De Vita; D. M. Dudek; S. Jung; S. D. Ross;
J. J. Socha; A. E. Staples Adjunct Professors: F. dell'Isola; J. S. Wayne Professors Emeritus: D. Frederick; R. A. Heller; R. M. Jones;
L. Meirovitch; D. H. Morris; D. Post; K.L. Reifsnider; D. J. Schneck; C. W. Smith; D. P. Telionis; H. W. Tielman
Affiliate Faculty: D. Gao; C. Hall; D. Inman;
R. Kapania; M. Paul; R. Plaut; P. Vlachos; R. Yoon Career Advisor: S. Griffin ESM Engineering Communications Program Director: M. C. Paretti
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 has a rich tradition for providing an interdisciplinary engineering education. We strive to prepare our graduates to succeed in advanced graduate or professional study, industry, and government. In these activities, our alumni will:
Apply fundamentals of engineering mechanics and related areas of applied science to define, model, and solve a wide range of engineering problems.
Apply fundamental mathematical and scientific principles, as well as computational and experimental techniques, to the demands of engineering and scientific practice.
Function on and lead teams that engage in new areas of research and development in engineering, particularly those that cross the boundaries of traditional disciplines.
Maintain high productivity and high ethical standards.
Continually enhance their knowledge throughout their careers.
Communicate effectively to a broad range of audiences.
These educational objectives are supported by a curriculum that provides its graduates with:
an ability to apply fundamental knowledge of mathematics, science, and engineering
an ability to design and conduct mechanics experiments
an ability to analyze and interpret experimental and computational mechanics data
an ability to design a system, component, or process to meet desired needs by synergistically combining mechanics of materials, fluid mechanics, and dynamics, when necessary
an ability to effectively function as the leader, or member, of a multi-disciplinary team
an ability to identify, formulate, and solve engineering problems involving mechanics of materials, fluid mechanics, and/or dynamics
an understanding of professional and ethical responsibility
an ability to communicate effectively – orally, graphically, and in writing
the broad education necessary to understand the impact of engineering solutions on society and the environment
a recognition of the need for, and an ability to engage in, life-long learning and accomplishment
a knowledge of contemporary issues (e.g., social, political, technical, economic, etc.)
a fundamental understanding that will enable the appropriate use and development of the techniques, skills, and modern engineering tools necessary for engineering practice
a recognition of the importance of safety in phases of engineering design and practice
A total of 12 credit hours of technical electives and 6 credit hours of senior design give the student freedom to develop individually tailored programs of concentrated study. The department has emphasis areas in Biomechanics, Engineering physics, Fluid mechanics, Motions, or Solid mechanics. Exposure to the design process exists throughout the curriculum, culminating in a senior level capstone design course. The department offers official university degree options in Biomechanics and Engineering Physics. The graduation checksheets for all degree options are available at http://www.esm.vt.edu/curriculum_checksheet.php.
The Cooperative Education Program is available to qualified candidates at undergraduate and graduate levels.
Undergraduate courses in engineering science and mechanics are taught on a service basis for all engineering curricula. A minor in engineering science & 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. Students with an interest in this program should contact the department for additional information.
The Engineering Science and Mechanics program at Virginia Tech is accredited by the Engineering Accreditation Commission of ABET, Inc., 111 Market Place, Suite 1050, Baltimore, MD 20120-4012 – telephone (410) 347-7700.
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.
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, (MATH 2224 or MATH 2224H). Co: MATH 2224. (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: (MATH 1114 or MATH 1114H). 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, (MATH 2224 or MATH 2224H). (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. I Co: MATH 2224. (3H,3C)
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, (MATH 2224 or MATH 2224H). 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
3015: Fluid statics. Dimensional analysis. Control volume approach to flow analysis, pipe flow, boundary layers, compressible flow, open channel flow. 3016: Introduction to continuum mechanics. Fluid kinematics. Differential approach to flow analysis: derivation of mass, momentum and energy equations, vorticity dynamics, potential flows, compressible flows, viscous flows. Pre: 2304, (MATH 2224 or MATH 2224H) for 3015; MATH 4574, ESM 3015 for 3016. Co: ME 3134 for 3015; 3034 for 3016. (3H,3C)
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. I Pre: 2304, MATH 2224. (2H,2L,3C)
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. Pre: 2204.
Co: 3054.
(3L,1C)
3114: PROB DEFINITION ENGR DESIGN
Define open-ended engineering design projects, identify relevant broad social, global, economic, cultural and technical needs and constraints, determine ways in which technical skills contribute to addressing complex engineering design challenges. Identify a capstone project for ESM 4015-4016. Pre-requisite: Junior standing in ESM. (2L,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 or MATH 2214H), (MATH 2224 or MATH 2224H). (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. (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. I (3H,3C)
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. I Pre: 2074, 3016. (3H,3C)
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. Senior standing required. Instructor consent. I 4015: (2H,3L,3C) 4016: (1H,6L,3C)
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. (3H,3C)
4044: MECHANICS OF COMPOSITE MATERIALS
Introduction to the deformation, stress, and strength analysis of continuous-fiber-polymer-matrix laminated composites. Fabrication, micromechanics of stiffness and expansional coefficients, classical lamination theory (CLT). Environmentally induced stresses. Computerized implementation and design. Pre: 2204. (3H,3C) I.
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. I Pre: 3124, MATH 4564. (3H,3C)
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:
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 or MATH 2214H). (3H,3C) II.
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 2206 or PHYS 2306). (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 or 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 or ESM 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 or MATH 1205H), (MATH 1206 or MATH 1206H). (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 or MATH 2224H). (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.