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Twin Cities Campus

Aerospace Engineering and Mechanics Ph.D.

Aerospace Engineering & Mechanics
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Director of Graduate Studies, Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street S.E., Minneapolis, MN 55455 (612-625-8000; fax: 612-626-1558)
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2017
  • Length of program in credits: 66
  • This program does not require summer semesters for timely completion.
  • Degree: Doctor of Philosophy
Along with the program-specific requirements listed below, please read the General Information section of this website for requirements that apply to all major fields.
The Department of Aerospace Engineering and Mechanics offers a Ph.D. degree in aerospace engineering and mechanics. The Ph.D. program emphasizes engineering sciences that are basic to fluid mechanics, aerospace systems, and solid mechanics. Theoretical, analytical, experimental, and computational aspects of these fields are covered by the courses and research opportunities offered by the department.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
The preferred undergraduate GPA for admittance to the program is 3.20.
A four-year B.S. degree in an engineering, basic science, or mathematics program is required.
Other requirements to be completed before admission:
Admission depends primarily on the applicant's undergraduate record, personal statement, and letters of recommendation.
Special Application Requirements:
GRE scores are not required but are strongly recommended for students applying for graduate fellowships. In all cases, these test scores are taken into account if provided. Students are admitted fall semester only. Only under unusual circumstances are students allowed to begin their studies at another time during the academic year. The application deadline is December 15. Additional information is available at http://www.aem.umn.edu/teaching/graduate/Application_procedures.shtml
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 79
    • Internet Based - Writing Score: 21
    • Internet Based - Reading Score: 19
    • Paper Based - Total Score: 550
  • IELTS
    • Total Score: 6.5
  • MELAB
    • Final score: 80
Key to test abbreviations (TOEFL, IELTS, MELAB).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
12 to 30 credits are required in the major.
12 to 30 credits are required outside the major.
24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
A minimum GPA of 3.00 is required for students to remain in good standing.
The Ph.D. program emphasizes coursework and research in engineering sciences that are basic to this field. Options include coursework and research in aerodynamics and aerospace systems, dynamical systems, material properties, and fluid and solid behavior. The Ph.D. requires about two years of coursework, but the heart of the program is the student's thesis research. The first year of the Ph.D. program is similar to the master's program and most Ph.D. students receive the master's degree. The second year is devoted to more advanced courses and beginning research. Subsequent years include some coursework with increased focus on research. The time required to complete a research project varies, but most students finish the Ph.D. within five years after the bachelor's degree. The program must include a minimum of 42 credits of approved courses; of these, a minimum of 12 credits must be in AEM courses at the 5xxx or 8xxx level and a minimum of 12 credits outside the major are required. Four semesters of seminar attendance are required (AEM 8000), but only one credit may be used towards the course credit requirements. The remaining 18 course credits may be taken in the major or in any supporting field. No more than 8 credits of 4xxx level courses and no more than 13 credits taken as S/N are allowed.
Required Courses
Take one 2-course sequence in fluids, solids or dynamics
Fluids
AEM 8201 - Fluid Mechanics I (3.0 cr)
AEM 8202 - Fluid Mechanics II (3.0 cr)
Solids
AEM 5501 - Continuum Mechanics (3.0 cr)
AEM 5503 - Theory of Elasticity (3.0 cr)
Dynamics
AEM 5401 - Intermediate Dynamics (3.0 cr)
AEM 8411 - Advanced Dynamics (3.0 cr)
Additional Major Credits
Take an additional 6 credits in AEM at the 5xxx or 8xxx level. The following sequences in controls or computational fluid mechanics may be used, or any other AEM courses chosen in consultation with adviser.
Controls
AEM 5321 - Modern Feedback Control (3.0 cr)
AEM 5451 - Optimal Estimation (3.0 cr)
AEM 8421 - Robust Multivariable Control Design (3.0 cr)
Computational Fluid Dynamics
AEM 5253 - Computational Fluid Mechanics (3.0 cr)
AEM 8253 - Computational Methods in Fluid Mechanics (3.0 cr)
Minor or Supporting Program
Take 12 credits in a minor or supporting program outside AEM
Seminar
1 credit of AEM 8000 may be used towards program credit requirements.
AEM 8000 - Seminar: Aerospace Engineering and Mechanics (1.0 cr)
Thesis Credits
Take 24 credits after passing preliminary oral exam
AEM 8888 - Thesis Credit: Doctoral (1.0-24.0 cr)
 
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AEM 8201 - Fluid Mechanics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Mathematical and physical principles governing the motion of fluids. Kinematic, dynamic, and thermodynamic properties of fluids; stress and deformation; equations of motion; analysis of rotational and irrotational inviscid incompressible flow; two-dimensional and three-dimensional potential flow. prereq: 4201 or equiv, Math 2263 or equiv
AEM 8202 - Fluid Mechanics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Analysis of incompressible viscous flow; creeping flows; boundary layer flow. prereq: 8201
AEM 5501 - Continuum Mechanics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Concepts common to all continuous media; elements of tensor analysis; motion, deformation, vorticity; material derivatives; mass, continuity equation; balance of linear, angular momentum; geometric characterization of stress; constitutive equations. prereq: CSE upper div or grad, 3031, Math 2243 or equiv or instr consent
AEM 5503 - Theory of Elasticity
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Introduction to the theory of elasticity, with emphasis on linear elasticity. Linear and nonlinear strain measures, boundary-value problem for linear elasticity, plane problems in linear elasticity, three dimensional problems in linear elasticity. Topics from nonlinear elasticity, micromechanics, contact problems, fracture mechanics. prereq: 4501 or equiv, Math 2263 or equiv or instr consent
AEM 5401 - Intermediate Dynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Three-dimensional Newtonian mechanics, kinematics of rigid bodies, dynamics of rigid bodies, generalized coordinates, holonomic constraints, Lagrange equations, applications. prereq: CSE upper div or grad, 2012, Math 2243
AEM 8411 - Advanced Dynamics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Advanced analytical mechanics and non-linear dynamical systems. Review of Lagrangian mechanics. Hamilton's equations of motion. Canonical transformations and Hamilton-Jacobi theory. Kane's equations. Analysis of differential equations and numerical methods. Phase plane, averaging, and perturbation methods. Stability/bifurcations of equilibria. prereq: 5401 or equiv
AEM 5321 - Modern Feedback Control
Credits: 3.0 [max 3.0]
Course Equivalencies: 01565
Typically offered: Every Fall
State space theory for multiple-input-multiple-output aerospace systems. Singular value decomposition technique, applications to performance/robustness. Linear quadratic gaussian and eigenstructure assignment design methods. Topics in H[infinity symbol]. Applications. prereq: 4321 or EE 4231 or ME 5281 or equiv
AEM 5451 - Optimal Estimation
Credits: 3.0 [max 3.0]
Course Equivalencies: 01703
Typically offered: Fall Even Year
Basic probability theory. Batch/recursive least squares estimation. Filtering of linear/non-linear systems using Kalman and extended Kalman filters. Applications to sensor fusion, fault detection, and system identification. prereq: [[MATH 2243 or STAT 3021 or equiv], [4321 or EE 4231 or ME 5281 or equiv]] or instr consent
AEM 8421 - Robust Multivariable Control Design
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Application of robust control theory to aerospace systems. Role of model uncertainty/modeling errors in design process. Control analysis and synthesis, including H[sub2] and H[infinity symbol] optimal control design and structural singular value [Greek letter mu] techniques. prereq: 5321 or equiv
AEM 5253 - Computational Fluid Mechanics
Credits: 3.0 [max 3.0]
Course Equivalencies: 02288
Prerequisites: [4201 or equiv], [CSci 1113 or equiv], CSE grad student
Grading Basis: A-F or Aud
Typically offered: Every Fall
Introductory concepts in finite difference and finite volume methods as applied to various ordinary/partial differential model equations in fluid mechanics. Fundamentals of spatial discretization and numerical integration. Numerical linear algebra. Introduction to engineering and scientific computing environment. Advanced topics may include finite element methods, spectral methods, grid generation, turbulence modeling. prereq: [4201 or equiv], [CSci 1113 or equiv], CSE grad student
AEM 8253 - Computational Methods in Fluid Mechanics
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Spatial discretization. Spectral methods. Temporal discretization. Nonlinear sources of error. Incompressible Navier-Stokes equations. Compressible Navier-Stokes equations. prereq: 4201
AEM 8000 - Seminar: Aerospace Engineering and Mechanics
Credits: 1.0 [max 4.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
To be determined prereq: DGS consent
AEM 8888 - Thesis Credit: Doctoral
Credits: 1.0 -24.0 [max 100.0]
Grading Basis: No Grade
Typically offered: Every Fall, Spring & Summer
(No description) prereq: Max 18 cr per semester or summer; 24 cr required