Seminar course on a topic of current interest in aerospace and mechanical engineering.

Introduction to analytical concepts and examples of dynamic systems and control. Mathematical description and state space formation of dynamic systems; modeling, controllability, and observability. Eigenvector and transform analysis of linear systems including canonical forms. Performance specifications. State feedback: pole placement and the linear quadratic regulator. Introduction to MIMO design and system identification using computer tools and laboratory experiments. Same as SC 501; students may not receive credit for both.

Specific prerequisites vary according to topic but do not extend beyond what is covered in the core courses in the undergraduate curriculum in mechanical engineering. Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in mechanical engineering. Subject matter varies from year to year.

Mathematical methods in aerospace and mechanical engineering; vectors and tensors; partial differential equations of heat and mass transfer, wave motion and potential theory, classification of second order PDEs; eigenfunction expansions, method of characteristics, Fourier and Laplace transforms; complex variable theory, residue integration, conformal mapping; Green's functions, integral equations, variational methods; perturbation methods for non-linear differential equations.

Specific prerequisites vary according to topic, but do not extend beyond what is covered in the core courses in the undergraduate curriculum in mechanical engineering. Elementary introduction to selected fundamental concepts in probability, random processes, signal processing, and statistical mechanics with strong emphasis on their applications to aerospace and mechanical engineering. Examples taken from acoustics, mechanics, thermodynamics, and fluid dynamics.

Aerodynamics and thermodynamics of compressible fluid flow. Laval nozzles, Prandtl-Meyer flow, normal and oblique shock waves. Linearized theory. Application to external and internal flow problems such as airfoils. Cannot be taken for credit in addition to ENGAM423.

Introductory course in mechanical vibrations for graduate students and for undergraduate students with substantial mastery of core undergraduate subjects in mechanics and mathematics. Course includes an elementary introduction to applicable concepts in linear algebra. Potential and kinetic energy functions of single- and multi-degree-of-freedom systems. Matrix formulations of forced vibrations of linear systems. Natural frequencies, resonance, and forced vibration response. Natural modes and mode shapes. Rayleigh's principle. Rayleigh's dissipation function, transient and forced responses of damped vibrations. Random excitation of vibrations. Impedance matrix. O'Hara-Cunniff theorem, modal masses, modal analysis. Vibrations of simple continuous systems such as strings, beams, rods, and torsional shafts. This course cannot be taken for credit in addition to ENG AM 441.

Analytical, numerical, and physical aspects of heat transfer phenomena, with emphasis on nondimensionalization and scaling. Mathematical treatment of steady and unsteady conduction, including finite difference methods. Forced and natural convection in internal and external flows. Thermal radiation and multimode heat transfer. Melting and solidification. Applications to aerospace heat transfer, energy systems, manufacturing, and biological heat transfer.

Introduction to wave propagation and sound. General concepts such as quantitative measures of sound, plane waves, and acoustic energy density and intensity. Derivation of wave equation. Sound radiation from vibrating bodies. Basic ray-acoustic concepts: reflection, refraction, diffraction and scattering of acoustic waves. Other topics may include flow-induced sound, Helmholtz resonators, sound transmission through ducts and mufflers, room acoustics, and absorption and attenuation of sound waves in fluids.

The main goal of this course is to present a unified, mathematically rigorous approach to two classical branches of mechanics: the mechanics of fluids and the mechanics of solids. Topics will include kinematics, stress analysis, balance laws (mass, momentum, and energy), the entropy inequality, and constitutive equations in the framework of Cartesian vectors and tensors. Emphasis will be placed on mechanical principles that apply to all materials by using the unifying mathematical framework of Cartesian vectors and tensors. Illustrative examples from biology and physiology will be used to describe basic concepts in continuum mechanics. The course will end at the point from which specialized courses devoted to problems in fluid mechanics (e.g. biotransport) and solid mechanics (e.g. cellular biomechanics) could logically proceed; students may not receive credit for both. 4 cr.

The ocean environment. Physical processes in deep and shallow water. Time and frequency domain wave equations for homogeneous and inhomogeneous acoustics. Spectral and ray methods for wave propagation in layered fluid and elastic media. Uncoupled and adiabatic normal mode theory. Parabolic equations and computational techniques for fluids and solids. Noise sources and surface effects. Sensors, transducers, and signal processing techniques.

The course is structured around classical topics in mechanics of materials and their application to study of the mechanical behavior of skeletal tissues, whole bones, bone-implant systems, and diarthroidal joints. Topics include: mechanical behavior of tissues, (anisotropy, viscoelasticity, fracture and fatigue) with emphasis on the role of the microstructure of these tissues; structural properties of whole bones and implants (composite and asymmetric bean theories); and mechanical function of joints (contact mechanics, lubrication, and wear). Emphasis is placed n using experimental data to test and to develop theoretical models, as well as on using the knowledge gained to address common health related problems related to aging, disease, and injury. Students may not receive credit for both.

Mechanics and physics of solids at the nanometer scale: introductory graduate level course for students with background in undergraduate engineering mechanics (or solid state physics) and mathematics. Review of continuum solid mechanics fundamentals. Introduction to dislocation theory. Continuum elastic theory of dislocations. Mechanics of thin films. Review of fundamentals of solid state physics. Electron motion in a periodic potential. Derivative of bulk material properties from free-electron and free-atom models. Phonons. Introduction to atomistic computational methods.

Presentation of basic fluid dynamics concepts relevant to understanding the theory of flight. Partial differential and integral equations of incompressible and compressible flow. Discussion of idealized two-dimensional flows using mathematics of complex variables and conformal mapping. Flow around wings and slender bodies. Lifting line theory, numerical panel methods, supersonic flows, unsteady aerodynamics.

Incompressible fluid flow. Review of control-volume approach to fluids engineering problems, with advanced applications. Differential analysis of fluid motion. Derivation of full Navier-Stokes, Euler, and Bernoulli equations. Unsteady Bernoulli equation. Velocity potential and its application to steady two-dimensional flows. Vorticity and vortex motion. Eulerian vs Lagrangian analysis.

Provides an overview of state-of-the-art techniques for robot motion planning. The emphasis is on the algorithms. It covers topology of configuration spaces, potential functions, roadmaps, cell decompositions, sampling-based algorithms, and model checking approaches to robot motion planning and control. 4 cr.

An introduction to the general theory of solid deformation; small deformation emphasized. Topics include: Cartesian tensors, indicial notation. Introduction to continuum mechanics: deformation of continuous media, deformation gradient, strain definitions. Stress, Cauchy's postulate, Cauchy and Piola-Kirchhoff stress tensors. Balance laws. Constitutive equations, strain energy and Green's postulate. Linear Elasticity: Two dimensional problems, Airy stress function, in plane loading of strips, St. Venant's principle, complex variable methods, Goursat-Muskhelishvili representation, stress concentrations around holes and cracks. Three dimensional problems, Kelvin's solution, the Boussinesq problem, Hertzian contact, Eshelby's energy-momentum tensor.

Theory and practice of experimental techniques used in solid mechanics. Topics include ultrasonic NDE, optical strain techniques (e.g., Moire interferometry, spectroscopy), and material strength and stiffness testing (e.g., fracture, fatigue, elastic constants). Also examines the use of computer for data acquisition and control. Some discussion of theory related to filters, sampling theory, uncertainty analysis, and spectra and correlations is incorporated.

Fundamental concepts of modern materials behavior and materials engineering. Emphasis on analytical and numerical methods for predicting material properties and behavior, as well as some discussion of the relationships between solid structure and material properties. Topics include: constitutive relations, fracture, fatigue, plasticity, creep, damping, impact, and deformation. Elastic, plastic, and viscous behavior. Some discussion of the effects of processing--thermodynamics, kinetics--may be addressed. Specific examples from ceramics, metals, polymers, and composites is given, with the emphasis changing for each offering.

Numerical techniques for solving the Navier-Stokes and related equations. Topics are selected from the following list, although the emphasis may shift from year to year: boundary integral methods for potential and Stokes flows; free surface flow computations; panel methods; finite difference, finite element and finite volume methods; spectral and pseudospectral methods; vortex methods; lattice-gas and lattice-Boltzmann techniques; numerical grid generation.

Theoretical foundations of fluid and structural acoustics. Solutions of the wave equation; vibrations of plates and membranes; multiple expansions, influence of source motion; reciprocity; compact Green's functions, radiation from vibrating bodies; matched expansions; acoustics energy equation; aerodynamic sound. 4 class.

An introduction to the finite element method with emphasis on fundamental concepts. Variational equations, Galerkin's method. Finite element applications to linear elliptic boundary value problems in structures, solid and fluid mechanics, and heat transfer. Optimality, convergence, function spaces and energy norms. Isoparametric elements. Mixed methods, penalty methods, selective reduced integration; applications may include Kirchoff plate theory, incompressible elasticity, Stokes flow. Thick and thin beams, plates, and shells. Implementation: element data structures, numerical integration, assembly of equations, element routines, solvers. Advanced topics may include: dynamic analysis, stabilized methods, eigenvalue problems, hybrid analytical methods.

Analytical methods are developed for studying the propagation and diffraction of waves in uniform and inhomogeneous fluid media. Illustrative applications are made to sound waves, gravity waves, waves in random media, evanescent waves. 4 class.

Introduction to turbulence. Deterministic versus statistical descriptions of fluids; kinematics; correlations and spectra; closure of the fluid equations of turbulence. Reynolds stresses; spectral evolution; analysis of scales. Analysis of isotropic turbulence and modeling of turbulent flows. Current topics.

This course will cover the state-of-the-art in analytical and (especially) computational techniques for solving problems with multiple spatial and temporal scales. Such problems are now at the forefront of computational mechanics with applications ranging from turbulence and its modeling to the coupling of atomistic and continuum scales in solid mechanics. We will begin with the more traditional methods including multi-scale perturbation techniques and renormalization group theory. Thereafter we will focus on more recent developments with distinct computational focus including: the Optimal Prediction Method of Chorin et al., the Equation Free Method of Kevrekidis et al, the Variational Multi-scale Method of Hughes et al. and the Heterogeneous Multi-scale Method of Weinan et al. We will also cover an approach to determine unknown parameters in the models derived from these methods. The differences and similarities between these methods will also be discussed and highlighted.

Brief review of the fundamental conservation and constitutive equations, exact solutions of the viscous Navier-Stokes equations, similarity solutions, boundary layer theory; creeping flows, flow in Hele-Shaw cells, lubrication theory, thin shear layer approximations, jets and wakes, hydrodynamic instability and transition to turbulence, Reynolds-averaged Navier-Stokes equations.

Nanotechnology is emerging as the technology of the 21st century. There is an ever growing effort by scientists and engineers across disciplines to envision, fabricate and integrate nanoscale devices for countless applications. This course will give a rigorous introduction to the basic concepts and experimental techniques in nanoscience and nanotechnology. The course will review relevant quantum mechanics and solid state physics as a basis for understanding the physical phenomena at the nanoscale. Then, basic issues in nanofabrication, Scanning Probe Microscopy (SPM), nanoelectronics and nanomechanics will be discussed.

Wave equation in cylindrical and spherical co-ordinate systems. Propagation in waveguides. Diffraction: the Rayleigh integral and the Helmholtz-Kirchhoff integral. Green's function and angular spectrum methods. Diffraction of sound beams: Guassian beams, unfocused and focused sources, and arrays. Diffraction by apertures, discs and wedges. Scattering of sound; Rayleigh scattering, scattering cross-section, elastic scatters. Propagation in inhomogeneous media: rays, the eikonal equation, the Blokhintzev invariant and the acoustic field near caustics. Absorption and dispersion of acoustic waves. Transmission and reflection at a fluid-solid interface.

Systematic development of wave phenomena in weakly inhomogeneous and moving media. Emphasis is on acoustic waves, with selected examples from other branches of wave physics. Both ray-tracing and full-wave methods are discussed. Introduction to the statistical description of random media and of turbulent media. Formulations for relating statistical properties of wave phenomena to the statistical properties of the medium.

Propagation of finite amplitude sound, principles of one-dimensional unsteady compressible flow. Discussion of non-linear distortion, generation of harmonics, weak shocks, N-waves, and of shock profiles. Supersonic aerodynamics, flow around bodies in supersonic flight, generation of sonic booms, non-linear acoustics theory of boom propagation through the atmosphere. Selected additional topics in non-linear acoustics.

Bubbles and acoustic cavitation play an important role in many aspects of application of sonic and ultrasonic energy in fluids and biological tissue. This course will introduce the study of bubble phenomena in sound fields. The fundamental physical acoustics of bubbles and the fundamental physics which can be illustrated by the study of bubble dynamics will be stressed. The family of Rayleigh-Plesset equations for time-dependent bubble behavior will be derived from the Navier-Stokes equations. Analytical approximations to the Rayleigh-Plesset equations in various limiting cases will be derived and studied. Approximations to the thermodynamic behavior of oscillating bubbles will be considered in detail. Thermal, acoustic, and viscous contributions to dissipation will be treated. Numerical solutions will also be studied, specifically in the context of highly nonlinear behavior during acoustically forced oscillations. Other topics covered will include scattering of sound and acoustic radiation, acoustics of bubbly liquids, bubble-mediated bioeffects, shape instabilities, acoustic levitation, sonoluminescence, heat and mass transfer during bubble oscillations, sonochemistry and cavitation detection and monitoring.

Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in wave propagation. Subject matter varies from year to year.

Methodologies required for constructing and operating intelligent mechanisms. Comprehensive introduction to robot kinematics for motion planning. Dynamics and control of mechanical systems. Formal treatment of differential relationships for understanding the control of forces and torques at the end effector. Discussion of robot vision and sensing and advanced topics in robot mechanics, including elastic effects and kinematic redundancy. Meets with ENG MN 740; students may not take both for credit.

Discussion of basic phenomena occurring when the response of a solid structure immersed in or bounding a flow has a significant influence on the flow. Methods are developed and applied to a general range of vibration problems that arise in diverse situations involving the interaction of laminar and turbulent flows with rigid and elastic structures.

Mechanics of biological systems, with emphasis on biological application of fluid mechanics. Topics will be chosen from the following: cardiovascular dynamics--pulsatile flow, vessel elasticity, non-Newtonian behavior, flow in bifurcations, thermodilution; pulmonary dynamics--oscillatory flow, convection-diffusion interactions, surface tension effects, high frequency ventilation, turbulence; clinical applications--urodynamics, bone fracture, dental mechanics, male impotency; mechanics of propulsion--microorganisms in viscous liquids, swimming, flying.

Physical principles and multivariable control techniques involved in the active control of sound and vibration. Topics in sound control include reduction of noise in ducts, structural control to reduce acoustic radiation, and sound field control in enclosures. Vibration control for both lumped and distributed parameter systems, with examples from space structure control and active vibration isolation. Control techniques include feedback and feedforward approaches, LMS adaptive algorithms, linear quadratic regulators, and modern robust control techniques. Effects of system modeling errors and simplifications (i.e., modal truncation) are studied. Laboratory experience implementing a vibration-control scheme for a cantilever beam.

Fundamental concepts of modal testing; analysis of multi-degree-of-freedom systems; viscous and hysteretic damping models; proportional and non-proportional damping; receptance, mobility and inertance frequency response functions; random and transient vibrations; practical issues concerning mobility measurement techniques; modal parameter extraction in frequency domain and time domain; structural modification; effects of non-linearities on modal analysis; engineering applications.

Introduction to the theory and design methods of non-linear control systems. Application to robotics, vibration and noise control, fluid control, manufacturing processes, and biomedical systems. Mathematical methods based on the theory of differentiable manifolds; non-linear control techniques include feedback linearization, backstepping, forwarding, and sliding mode control. Additional course topics will include controllability and observability, Lyapunov stability and its applications, limit cycles, input-output stability, zero dynamics, center manifold theory, perturbation theory, and averaging.

Fundamentals of multivariable control analysis and synthesis. Control objectives include achieving robust stability and performance (robust control) and minimization of cost functions (optimal control). Topics include modeling (state space, transfer function matrix), MIMO poles and zeroes, controllability and observability, stability and robustness, structured and unstructured perturbations, the small gain theorem, optimization theory, and the Maximum Principle. Estimation and control techniques include Linear Quadratic (H2), full-state LQR, LQG, (H), and Kalman filtering. Applications and numerical examples taken from robotics, aircraft control, and vibration control. Meets with ENG SC 701; students may not take both for credit.

Regular and singular perturbation theory. Topics taught through examples related to solid mechanics, fluid mechanics, and dynamics, and include: matched asymptotic expansions, method of multiple scales, WKB, strained coordinates, asymptotic expansion of integrals, method of averaging, exponential asymptotics, asymptotic summation, perturbation of dimension.

First time graduate teaching fellows are required to register for special training which will be organized and facilitated by their assigned professor in cooperation with their department.

Participation in a research project under the direction of a faculty advisor. If not leading to an MS thesis or PhD dissertation, a final report is normally required.

Participation in a research project under the direction of a faculty advisor. If not leading to an MS thesis or PhD dissertation, a final report is normally required.

Preparation of an original thesis under the guidance of a faculty member. 8 pract.

Preparation of an original thesis under the guidance of a faculty member. 8 pract.

Graduate students may study, under a faculty member's supervision, subjects not covered in a regularly offered course. Final report and/or written examination normally required.

Graduate students may study, under a faculty member's supervision, subjects not covered in a regularly offered course. Final report and/or written examination normally required.

Advisor and hours arranged.

Advisor and hours arranged.