Graduate Program in Mechanical and Aerospace Engineering

16-650:500 Experimental Methods.
Prerequisites: Undergraduate fluid mechanics and heat transfer

Survey of current measuring techniques used in Mechanical and Aerospace Engineering research; principles of digital and analog data acquisition and reduction.

16-650:504/5 Mathematical Methods in Engineering.
Prerequisites: Undergraduate calculus and differential equations.

Review of matrix algebra; numerical methods for inversion; ordinary differential equations, functions of a complex variable; calculus of variations; partial differential equations and their classification; Fourier methods; asymptotic and perturbation methods.

16-650:510 Computer-Aided Design.
Prerequisite: Limited enrollment; requires permission of instructor.

A broad introduction to Computer-Aided design and Modeling. Mathematical representations of curves, surfaces and solids. Two-and three-dimensional computer graphics. Programming in required for design projects.

16-650:512 Robotics and Mechatronics.
Prerequisite: Undergraduate courses in dynamics, statics, vibrations and controls.

Introduction to robotics and mechatronics including mechanisms and control theories as well as applications; manipulator models; design considerations; control fundamentals; model and sensor based control algorithm development; walking robots; medical and space robotics; experimental mechatronics.

16-650:514 Design of Mechanisms.
Prerequisite: Undergraduate course in kinematics of mechanisms or equivalent.

Complete mechanism design cycle: synthesis, analysis and redesign; analytical, numerical and visualization techniques applied to mechanism synthesis (type, number and dimensional) and analysis; application of optimization methods in the design cycle; planar and spatial mechanisms.

16-650:518 Biomechanical Systems.
Prerequisites: Undergraduate courses in mechanical design and in solid mechanics.

Selected topics from the study of the human body as a mechanical system, with emphasis on modeling, analysis, and design. The biomechanical systems to be investigated are those that are frequently encountered in orthopedic surgery and physical rehabilitation.

16-650:520 Tissue Mechanics.
Prerequisite: Graduate standing in Mechanical/Aerospace Engineering.

Mechanical properties of living soft and hard tissues as explained from their ultrastructural makeup. Function-property relationships of biological tissues and their pathological implications.

16-650:522 Analytical Dynamics.
Prerequisite: Graduate standing in Mechanical/Aerospace Engineering.

Newtonian mechanics; rotating frames; variational principles; Lagrange's equations, Hamilton's equations, Euler angles, Euler's equations, gyroscopic motion.

16-650:524 Optimal Design in Mechanical Engineering.
Prerequisite: Graduate Standing in Mechanical/Aerospace Engineering

Formulation and solution of engineering optimal design problems in mechanical engineering. Introduction to algorithms for constrained and unconstrained searching. Application to optimal design of mechanical and structural components. Use of discretization techniques; shape optimization problem.

16-650:530 Fluid Mechanics I.
Prerequisite: Undergraduate fluid mechanics.

Physical properties of fluids; basic equations of motion; kinematics; exact solutions of the Navier-Stokes equations; incompressible boundary layer equations and applications; flow past bodies, jets and wakes; introduction to turbulent flows.

16-650:532 Experimental Methods in Fluid Mechanics.
Prerequisite: Undergraduate fluid mechanics.

Experimental and analytical/data tools needed by fluid experimentalists, data acquisition, measurements, model building, optical diagnostics and visualization.

16-650:534 Computational Fluid Dynamics.
Prerequisite: Undergraduate fluid mechanics.

Development and application of computational methods for fluid mechanics based on the incompressible and compressible Navier Stokes equations, boundary layer equations and Euler equations. Selected algorithms including finite difference, finite volume and special techniques. Applications chosen from incompressible and compressible flows.

16-650:550 Mechanics of Materials.
Prerequisites: Undergraduate courses in solid mechanics.

Critical examination and application of the theories and methods for evaluating stresses and deformations of mechanical components and structures under static and dynamic loading.

16-650:554 Mechanics of Continua (Solid Mechanics I).
Prerequisites: Undergraduate mechanics and engineering mathematics.

Introduction to the fundamental concepts of continuum mechanics, including stress and strain, kinematics, balance laws, and material symmetry. Applications to theories of elasticity, plasticity, fracture, viscoelasticity, and classical fluid dynamics.

16-650:556 Theory of Elasticity (Solid Mechanics II).
Prerequisites: 16:642:527 or equivalent.
Corequisite: 16:642:528

The classical theory of linear elasticity. Equations of equilibrium; plane stress; plane strain; Airy stress function; torsion; energy theorems; solutions of selected classical problems.

16-650:570 Conduction Heat Transfer.
Prerequisite: Undergraduate course in heat transfer.

Analytical methods in steady and transient heat conduction in solids; finite difference and finite volume methods in heat conduction.

16-650:574 Thermodynamic Theory.
Prerequisite: Undergraduate thermodynamics.

Principles and methods of thermodynamics, including classical, statistical and irreversible thermodynamics.

16-650:578 Convection Heat Transfer.
Prerequisites: Undergraduate course in heat transfer and 16-650:530 or equivalent.

Forced and free convection in internal and external laminar and turbulent flows; mass transfer; applications.

16-650:582 Computational Heat Transfer.
Prerequisites: Undergraduate fluid mechanics and heat transfer.

Development and application of computational methods for conduction, natural, forced and mixed convection, radiation, traditional and recent conjugate heat transfer and mass transfer. Selected algorithms include finite difference, finite volume, finite element and spectral techniques. Applications chosen from thermal energy systems, environmental heat transfer, microelectronics packaging, materials processing and other areas.

16-650:601/2 Independent Study.
Prerequisite: Consent of instructor and graduate director.

Independent studies or investigations in a selected area of mechanical and aerospace engineering. The instructor must prepare a syllabus on the subject being studied for the students file.

16-650:604 Advanced Engineering Analysis.
Prerequisites: 16-642:527, 16-650:522 or 16-650:530

Behavior of linear and nonlinear systems; phase-plane analysis; bifurcation; stability criteria; perturbation methods. Examples from fluid mechanics, heat transfer, and dynamics.

16-650:606 Advanced Mechanical Engineering Topics.

Topics of current interest in Mechanical and Aerospace Engineering, such as applications of computer-aided intelligence, computer-aided manufacturing, and waves in fluids.

16-650:608/9 Seminar in Mechanical Engineering.
Prerequisite: Ph.D. Candidacy in Mechanical and Aerospace Engineering, or consent of the Graduate Director.

Lectures by invited speakers, faculty, and graduate students on current research topics in mechanical and aerospace engineering.

16-650:618 Special Applications in Control.
Prerequisites: Graduate background in Mechanical Control Systems and Vibration.

Control analysis and design with applications to industry.

16-650:622 Advanced Optimization.
Prerequisite: 16-650:614

Focusing on the mathematical framework of optimization, the course will provide students with in-depth coverage of mathematical programming, probabilistic optimization methods, global optimization, multi-objective optimization and their objectives.

16-650:626 Advanced Design and Fabrication.
Prerequisites: 16-650:514, 614 or equivalent.

Synthesis of design methodologies with application to industrial problems.

16-650:630 Fluid Mechanics II.
Prerequisite: 16-650:530 or equivalent, or permission from instructor

Vortex dynamics of incompressible, inviscid and low viscosity fluids. One, two, and three -dimensional compressible flows. Linear, nonlinear acoustic and gravity waves, etc. and shock waves using shock polars. Stability of viscous and inviscid vortex, wave and boundary layer flows. Special Topics: 1) Accelerated Flows: Rayleigh-Taylor and Richtmeyer-Meshkov for supersonic combustion and inertial confinement fusion. 2) Visualization and quantification of evolving flows. 3) turbulent scaling laws.

16-650:631 Fluid Mechanics III.
Prerequisite: 19-650:530 or equivalent, or permission from instructor.

Waves, low reynolds number flows, stratified and inviscid flows.

16-650:634 Compressible Flows.
Prerequisite: 16-650:630 or equivalent.

Linear and nonlinear theory of one-dimensional inviscid unsteady motion, compression and expansion waves, shock tube and wave interactions; two-dimensional inviscid steady motions, including linearized subsonic and supersonic flows; boundary layer theory of compressible fluids.

16-650:636 Turbulence.
Prerequisite: 16:650:530

Physical aspects and methods of analysis of turbulent flows; scaling laws, modeling techniques, and statistical description of turbulence; application to problems in engineering science and geophysical fluid dynamics.

16-650:638 Hydrodynamic Stability.
Prerequisite: 16-650:530 or equivalent.

Thermal, centrifugal and shear instabilities; linear, nonlinear and energy methods.

16-650:640 Acoustics.
Prerequisites: Undergraduate fluid mechanics and 16-642:530 (or concurrent registration in it).

Sound wave propagation in gases and liquids. Reflection and transmission phenomena. Emission and absorption of sound.

16-650:642 Suspensions.
Prerequisites: 16-650:530 or equivalent and one graduate level course in applied mathematics or consent of instructor.

Fluid mechanics of small bubbles, droplets, and rigid particles in fluids. Fluid forces and heat transfer rate. Two-phase fluid dynamics. Applications to aerosols, bubbly liquids, emulsions, and hydrosols.

16-650:651 Mechanics of Inelastic Behavior (Solid Mechanics III).
Prerequisite: 16-650:550 or 16-650:650

Mechanics of inelastic behavior, including Plasticity, Viscoelasticity and Micromechanics. Yield Criteria, flow hardening rules, Drucker’s postulates, multi-axial theories, and boundary value problems. Rheological models, creep compliances and relaxation moduli, complex moduli, rheologically simple materials. Dislocation theories, crystal plasticity, Eshelby’s solution for an inclusion, mechanics of phase transformation.

16-650:652 Composite Materials, Fracture Mechanics, and Thermoelasticity (Solid Mechanics IV).
Prerequisite: 16-650:554, 16-650:650

Composite materials; anisotropy, elastic constants, stress-strain averages, energy principles, bounds, and micromechanics models. Basics principles of fracture mechanics: mechanisms of fracture and crack growth, energy release rates, complex stress functions, stress intensity, fracture criteria, mixed-mode fracture, dynamic fracture. Thermoelasticity: linear coupled theory, uncoupled theory, solution of selected applied problems involving heat and deformation, application to composite and advanced materials.

16-650:653 Structural Mechanics (Solid Mechanics V).
Prerequisites: 16-650:550, 16-650:554 and 16-650:650 or permission of instructor.

Review of plate theory. Foundations of shell theory. Variational calculus and energy theorems, stability and buckling. Composite structures: anisotropic structures, laminated beams, plates and shells, failure mechanisms.

16-650:654 Dynamics of Solids and Structures (Solid Mechanics VI).
Prerequisites: Undergraduate course in mechanical vibration, and 16-650:550, 16-650:554, and 16-650:650.

Review of multi-degree of freedom vibration. Vibration of continuous systems: strings, beams, membranes and plates. Vibration and waves. Waves in beams and plates. Bulk elastic waves. Reflection and Transmission, Rayleigh surface waves, ultrasonics. Additional topics such as random vibration as time permits.

16-650:660 Finite Element Methods in Solid Mechanics.
Prerequisites: 16-650:554.

General theory, application of finite element methods to the solution of the equations of elasticity viscoelasticity and plasticity. Two-and three-dimensional linear and nonlinear, static and dynamic problems. Computer programs for such problems.

16-650:661 Advanced Mechanical and Random Vibration.
Prerequisite: 16-650:654

Continuous systems, exact and approximate solutions; integral formulation, vibration under combined effects, inclusion principle qualitative and quantitative behavior of the eigensolution, computational techniques. Random vibration of nonlinear oscillators, Markov processes.

16-650:662 Advanced Stress Waves in Solids.
Prerequisite: 16-642:654

Propagation of elastic waves in solids, reflection and transmission, Rayleigh waves, waves in plates, dispersion, radiation from a point load, Fourier transforms methods; scattering; waves in anisotropic materials; propagation of discontinuities; shocks.

16-650:663 Advanced Plasticity.
Prerequisite: 16-650:651

Advanced theories and computational models in plasticity. Crystal plasticity for metallic systems based on dislocation theory and statistical mechanics. Sources of hardening for single and multiple glide conditions. Nucleation and growth of defects induced by plastic deformation. Large-strain constitutive relations for crystalline materials. Numerical implementation into Finite Element formulations.

16-650:664 Advanced Fracture Mechanics.
Prerequisite: 16-650:652

Fracture mechanics; linear elastic, dynamic, elastic-plastic materials and structures. Time dependent; fracture and fatigue crack growth for metals, ceramics, polymers, and composites. Mathematical methods in fracture mechanics; weight functions (3D), Green's functions (dislocation and point force), complex variable methods (2D), integral transforms, and applications of the FEM and BEM.

16-650:665 Advanced Composite Materials.
Prerequisite: 16-650:650

Classification of anisotropy; and elastic constants; particulate, fiber, and disc reinforcements; stress-strain average and energy principles; mean-field theory, self-consistent and generalized self-consistent models method; differential scheme; Hashin-Shtrikman's variational principles, bounding techniques; viscoelastic, plastic, and viscoplastic composites.

16-650:666 Advanced Micromechanics.
Prerequisite: 16-650:650 or 16-650:651

Origins of internal stress, Green's tensor function. Eshelby's solutions of ellipsoidal inclusions; crystal plasticity; continuous distribution of dislocations; single crystal versus polycrystalline; Martensitic transformation in shape-memory alloys, ferroelectric ceramics.

16-650:667 Advanced Stability of Elastic Systems.
Prerequisites: 16-650:554, 16-650:650

Hamilton's principle; discrete and continuous systems; dynamical theories of beams and plates; nonlinear vibrations; Liapunov stability; limit cycles; chaotic motion. Applications include the static and dynamic stability of thin-walled structures.

16-650:668 Advanced Viscoelasticity.
Prerequisite: 16-650:651

Basic rheological models and differential constitutive equations; Boltzman's superposition principle and hereditary integrals, Laplace transform; creep, relaxation, and complex moduli; discrete and continuous spectra; thermorheologically simple materials; glass transition temperature; William-Landel-Ferry (WLF) equation; chronorheologically simple and rheological complex materials; physical aging.

16-650:669 Advanced Thermoelasticity.
Prerequisite: 16:650:652

Formulation and solution of problems involving the effects of temperature on the elastic and inelastic behavior of materials and structures. Thermodynamics of deformation; heat transfer; thermo-elasticity/thermoviscoelasticity.

16-650:670 Combustion.
Prerequisites: Undergraduate courses in thermodynamics and fluid mechanics.

Fundamentals of combustion processes; premixed flames, diffusion flames, one dimensional gas dynamics, thermal explosion theory.

16-650:674 Radiation Heat Transfer.
Prerequisite: Undergraduate course in heat transfer.

Theory of radiant heat transfer; characteristics of ideal and real systems; radiant energy exchange with and without participating media; analytical numerical and experimental techniques; gray and nongray system analysis; secular radiation.

16-650:678 Boiling and Condensation Heat Transfer.
Prerequisites: Undergraduate courses in heat transfer and in fluid mechanics.

A detailed presentation of boiling and condensation heat transfer; nucleate boiling, transitional boiling, film boiling, film condensation, and dropwise condensation.

16-650:682 Thermal Transport in Materials Processing.
Prerequisites: Undergraduate courses in heat transfer and fluid mechanics.

Transport phenomena in processes such as heat treatment, bonding, extrusion, casting, injection molding, crystal growing, metal forming and plastic processing; analysis, mathematical modeling and numerical simulation of such processes for design and optimization of the relevant systems.

16-650:699 Nonthesis Study. (N1,N1). Staff.
16-650:701/2 Research in Mechanical and Aerospace Engineering. (With Advisor)


DESCRIPTIONS OF RECOMMENDED COURSES TAUGHT BY OTHER DEPARTMENTS

16-198:510 Numerical Analysis.
Prerequisites: Ability to use high-level language such as: FORTRAN IV; a minimum of four terms of undergraduate mathematics including calculus and linear algebra.

Derivation, analysis, and application of methods used to solve numerical problems with computers; solution of equations by iteration, approximation of functions, differentiation and quadrature, differential equations, linear equations and matrices, least squares.

16-332:505 Control System Theory I.
Prerequisite: 16-332:501

Transform theory and transfer function concepts; Nyquist and Bode plots; Nyquist and Hurwitz criterion of stability and design techniques involving Hall and Nichols charts; design of compensating networks via root locus technique; state space formulation of control systems; definition of stability in time domain for general systems; methods of finding stability constraints; discrete systems; z-transforms; difference equations; stability criterion.

16-332:506 Control System Theory II.
Prerequisite: 16-332:505

Review of state space techniques; transfer function matrices, concepts of controllability, observability, and identifiability; identification algorithms for multivariable systems, minimal realization of a system and its construction from experimental data; state space theory of digital systems; design of a three mode controller via spectral factorization.

16-640:509 Topics in Analysis.: Techniques of Asymptotic Analysis.
Prerequisites: Ordinary & Partial Differential Equations & Complex Analogies.

General boundary--layer theory; matched asymptotic expansions, WKB and turning point theory; multiscale expansions; PLK method; maximal balance and other principles of asymptotology; asymptotics beyond all orders

16-642:527, 528 Methods of Applied Mathematics.
Prerequisites: Advanced calculus and ordinary differential equations.

Appropriate topics from linear algebra, linear operators in Hilbert space, linear integral equations, boundary value problems, calculus of variations, numerical solution of ordinary and partial differential equations. One or both of these courses are required of MAE graduate students.

Rutgers Mechanical and Aerospace Engineering Graduate Program Home Page