The MAE department offers graduate study leading to the Master of Science and Doctor of Philosophy degrees in:

• Aerospace Engineering
• Mechanical Engineering

Graduate Admissions Information

Incoming students are encouraged to apply for Departmental Reasearch positions, which offer full tuition and support to qualified students. In addition, research funds are used to provide assistantships that support the thesis research of graduate students. A limited number of fellowships providing partial support is also available for students enrolled in the B.S./M.S. program.

The department believes that the success of its graduates at all levels is due to emphasis on project and problem-oriented course material coupled with the broad-based curricular requirements.

Each M.S. student may select either Plan A which requires a research thesis or Plan B which does not require a thesis. Doctoral dissertations in all programs must be original contributions to the existing body of knowledge in engineering and science.

Academic requirements for graduate degrees in engineering are as specified by The Case School of Engineering. A more detailed set of rules and regulations for each degree program contained here is available from the department, and may also be found on the department Web page. More general information may be found at the Graduate Studies website, specifically, in the Case General Bulletin under the heading “School of Graduate Studies” as well as in the Graduate Student Handbook.

Design & Technical Eclectives

Vector and tensor calculus; finite deformation and strain analysis; kinematics of continuous media; stress tensor and traction; conservation and balance laws; observer transformation and material symmetry; constitutive theory.

Quantitative and qualitative descriptions of the action of muscles in relation to human movement. Introduction to rigid body dynamics and dynamics of multi-link systems using Newtonian and Lagrangian approaches. Muscle models, receptors and reflexes with application to control of multi-joint movement. Forward and inverse dynamics of multi-joint, muscle driven systems. Dissection, observation and recitation in the anatomy laboratory with supplemental lectures concentrating on kinesiology and muscle function. Prerequisite: Consent of instructors. XLIST:EBME402

The physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics and combustion sciences: statistical calculations of thermodynamic properties of gases; quantum mechanical analysis of atomic and molecular structure; transport phenomena; propagation, emission and absorption of radiation; chemical and physical equilibria; adiabatic flame temperatures of complex reacting systems; reaction kinetics. Consent of instructor.

Structural behavior of the musculo-skeletal system. Function of joints, joint loading, and lubrication. Stress-strain properties of bone and connective tissue. Analysis of fracture and repair mechanisms. Viscoplastic modeling of skeletal membranes. Prerequisite: EMAE 181, ECIV310

Derivation and discussion of the general equations for conservation of mass, momentum, and energy using tensors. Several exact solutions of the incompressible Newtonian viscous equations. Kinematics and dynamics of inviscid, incompressible flow including free streamline theory developed using vector, complex variable, and numerical techniques.

Continuation of EMAE 453. Low Reynolds number approximations. Matching techniques: inner and outer expressions. High Reynolds number approximations: boundary layer theory. Elements of gas dynamics: quasi one-dimensional flow, shock waves, supersonic expansion, potential equation, linearized theory, and similarity rules. Prerequisite: EMAE 453

Basic ideas of thermodynamics and dominant methods of their development: operational, postulational, and statistical. Entropy and information theory. Irreversible thermodynamics. Applications.

Chemical kinetics and thermodynamics; governing conservation equations for chemically reacting flows; laminar premixed and diffusion flames; turbulent flames; ignition; extinction and flame stabilization; detonation; liquid droplet and solid particle combustion; flame spread, combustion-generated air pollution; applications of combustion processes to engines, rockets, and fire research.

Energy sources of propulsion. Momentum theorems and performance criteria. Air breathing systems and their components; chemical rockets - liquid and solid propellant - nuclear rockets - solid, liquid, and gaseous core; rocket heat transfer and heat protection; electric propulsion – electrothermal, electrostatic, and plasma thrusters; thermonuclear propulsion. Consent of instructor.

Analysis of engineering heat transfer from first principles including conduction, convection, radiation, and combined heat and mass transfer. Examples of significance and role of analytic solutions, approximate methods (including integral methods) and numerical methods in the solution of heat transfer problems. Prerequisite: EMAE 453

Fluid mechanic and thermodynamic aspects of the design of fluid power machinery such as axial and radial flow turbomachinery and their component characterizations. Consent of instructor required.

An advanced course on design methodologies. Conceptualization, preliminary design, detail design, and manufacturing. Failure analysis, materials selection, methods of design optimization, and current approaches in computer-aided design. Prerequisite: EMAE 360

Application of computer methods to engineering design. Optimization and automated design methods. The use of linear and non-linear programming methods for engineering design and related problems. Unconstrained minimization, penalty function s, feasible directions. Consent of instructor required.

Mechanical properties, static and dynamic characteristics, stress analysis methods, design properties, manufacturing methods, mechanical testing and design considerations. Prerequisite: ECIV310

A comprehensive treatment of design analysis methods of machine components. Emphasis is on solid mechanics.

A comprehensive treatment of design analysis methods and computational tools for machine components. Emphasis on vibration and machinery dynamics.

Fundamental and applied aspects of metals, polymers and ceramics. Behavior of materials in stress and strain cycling, methods of computing cyclic stress and strain, cumulative fatigue damage under complex loading. Application of linear elastic fracture mechanics to fatigue crack propagation. Mechanisms of fatigue crack initiation and propagation. Case histories and practical approaches to mitigate fatigue and prolong life.

Particle and rigid-body kinematics and dynamics. Inertia tensor, coordinate transformations and rotating reference frames. Application to rotors and gyroscopes. Theory of orbital motion with application to earth satellites. Impact dynamics. Lagrange equations with applications to multi-degree of freedom systems. Theory of small vibrations. Prerequisite: EMAE 181

Vector methods in planar and three-dimensional mechanisms. Matrix methods and relative spatial motion. Mobility analysis of mechanisms. Body guidance, function, and path generation. Optimal synthesis of mechanisms. Prerequisite: EMAE 271

Stress waves in one-dimension, problem formulation for 3-D waves. Reflection and refraction at a plane boundary stress pulses and Raleigh surface waves. Wave guides and dispersion relationships. Solutions of mixed initial and boundary value problems for isotropic linear elastic materials. Scattering of elastic waves. Elastic plastic waves.

Free and forced-vibration problems in single and multi-degree of freedom damped and undamped linear systems. Vibration isolation and absorbers. Modal analysis and approximate solutions. Introduction to vibration of continuous media. Noise problems. Laboratory projects to illustrate theoretical concepts and applications. Prerequisite: MATH224 and EMAE 181.

Orientation and configuration coordinate transformations, forward and inverse kinematics and Newton-Euler and Lagrange-Euler dynamic analysis. Planning of manipulator trajectories. Force, position, and hybrid control of robot manipulators. Analytical techniques applied to select industrial robots. Prerequisite: EMAE 181 XLIST:EEAP489

Modern computer controlled manufacturing technology and processes. Design for manufacture using feature based solid modeling software. Computerized inspection techniques using coordinate measuring machine (CMM), rapid prototyping, manufacturing integration, control and quality assurance. Hands-on laboratory sessions in CAD/CAM studio. Prerequisite: EMAE 290.

Using variational approach, comprehensive development of principle of virtual work, Hamilton’s principle and Lagrange equations for holonomic and non-holonomic systems. Modern dynamic system formulations. Hamilton’s equations of motion, canonical transformations, Hamilton-Jacobi theory.

Nonlinear oscillations; including equations of Duffings, van der Pol, Hill, and Mathieu; and perturbation solution approaches. Bifurcation theory and jump phenomena. Strange attractors, chaos, poincare maps, and related engineering applications.

Compressible boundary layer theory. Blowing and suction effects. Three-dimensional flows; unsteady flows. Introduction to real gas effects. Prerequisite: EMAE 454

Mathematics and physics of turbulence. Statistical (isotropic, homogeneous turbulence) theories; success and limitations. Experimental and observational (films) evidence. Macrostructures and microturbulence. Other theoretical approaches. Prerequisite: EMAE 454

Variational and energy principles in dynamics, structures and mechanics of continua. Calculus of variations, principle of virtual work, energy principles and generalization, statics of deformable bodies, dynamics, development of variational principles in fluid mechanics, direct solution methods. Consent of instructor required.

Energy equation of viscous fluids. Dimensional analysis. Forced convection; heat transfer from non-isothermal and unsteady boundaries, free convection and combined free and forced convection; stability of free convection flow; thermal instabilities. Real gas effects, combined heat and mass transfer; ablation, condensation, boiling. Prerequisite: EMAE 453 and EMAE 454

Fundamental law, initial and boundary conditions, basic equations for isotropic and anisotropic media, related physical problems, steady and transient temperature distributions in solid structures. Analytical, graphical, numerical, and experimental methods for constant and variable material properties. Consent of instructor required.

Development of the basic kinetic theory model of a gas, including essential physical ideas and some important fundamental results (equilibrium state, entropy, transport coefficients). Numerical methods of analysis, with special emphasis on computer simulation techniques, especially molecular dynamics and Monte-Carlo methods. Applications to basic fluid flows and low earth orbit flight. Consent of instructor required.

Finite difference, finite element, and spectral techniques for numerical solutions of partial differential equations. Explicit and implicit methods for elliptic, parabolic, hyperbolic, and mixed equations. Unsteady incompressible flow equations in primitive and vorticity/ stream function formulations. Steady and unsteady transport (passive scalar) equations. Consent of instructor required.

Mathematical foundations and advanced principles of dynamics. Multi-degree of freedom discrete systems. Modal analysis, steady-state and transient response. Non-linear systems and random vibrations.

Prerequisite: EMAE 401 or ECIV 411

Prerequisite: ECIV410

Prerequisite: EMAE 401 or ECIV 411

Prerequisite: EMAE 401 or ECIV411

Prerequisite: EMAE 401 or ECIV411

Mathematical description of light; Maxwell’s equations; diffraction of light; design of critical optical elements; amplitude and phase based optical methods for displacement and stress measurements – photoelasticity, method of caustics, image shearing technique, coherent gradient technique, holography, geometric and optical methods of moiré interfermotry, image correlation techniques; optical methods for temporal measurements – normal displacement interferometer, normal velocity interferometer, transverse displacement interferometer. Time-resolved non-contact methods for temperature measurement; electric resistance strain gages; loading devices for investigating high strain rate deformation of engineering materials – split Hopkinson compression bar, split Hopkinson tension bar, torsional Kolsky bar, plate impact experiments. Prerequisite: EMAE 401 or ECIV411.

Stability of parallel flows: general development with application to channel flows and boundary layer flows; magnetohydrodynamic parallel flows; rotating Couette flow; superposed fluids; thermal instability of fluids heated from below; non-linear considerations. Prerequisite: EMAE 454

Exposure to experimental problems and techniques provided by the planning, design, execution, and evaluation of an original project. Lectures: review of the measuring techniques for flow, pressure, temperature, etc.; statistical analysis of data: information theory concepts of instrumentation; electrical measurements and sensing devices; and the use of digital computer for data acquisition and reduction. Graduate standing or consent of instructor required.