Twin Cities campus
 
Twin Cities Campus

Mechanical Engineering Ph.D.

Mechanical Engineering
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Mechanical Engineering and Industrial Engineering Graduate Programs, University of Minnesota, 1120 Mechanical Engineering, 111 Church Street S.E., Minneapolis, MN 55455 (612-625-2009; fax: 612-624-2010)
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2017
  • Length of program in credits: 62
  • 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.
Coursework and research for all graduate degrees are offered in bioengineering; biomechanics; combustion; computer-aided design; computer-aided manufacturing; computer graphics; control systems; design; energy conservation; environmental control; environmental engineering; fluid mechanics; heat and mass transfer; history of science and technology; human factors engineering; industrial engineering; innovative methodologies; integration of structural and environmental systems; lubrication; manufacturing engineering; particle technology; plasma chemistry; plasma heat transfer; power, propulsion, and applied thermodynamics; socioeconomic systems; solar energy; solar processing and thermochemistry; statistics; structures; systems dynamics; technology assessment; thermal energy storage; thermal environmental engineering; thermodynamics; transportation; tribology; vibration; and interdisciplinary finite element methodology. Additional instructional and research programs can be formulated.
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 3.00.
A four-year B.S. degree in engineering, science, or mathematics.
Special Application Requirements:
Applications are accepted for fall semester only. The application deadline is December 15. Additional information is available at http://www.me.umn.edu/education/graduate/prospective/admissions.shtml
Applicants must submit their test score(s) from the following:
  • GRE
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
Key to test abbreviations (GRE, TOEFL, IELTS).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
18 credits are required in the major.
20 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. requires a minimum of 38 course credits, consisting of 18 credits in the major and 20 additional graduate level credits. Courses must be taken on an A/F basis, with the exception of seminars and the ethics course. A minimum of 12 course credits at the 8000-level are required (seminars and ethics courses may not be included). Students must complete 2-3 graduate seminar credits, and one research and professional ethics course. 24 thesis credits are also required.
Major Course Credits
Take 18 credits in any 5xxx or 8xxx level mechanical engineering courses. Independent research courses do not count toward the credit requirement. The following courses also meet the requirement for ME graduate course credits.
AEM 5401 - Intermediate Dynamics (3.0 cr)
AEM 5501 - Continuum Mechanics (3.0 cr)
AEM 8201 - Fluid Mechanics I (3.0 cr)
AEM 8202 - Fluid Mechanics II (3.0 cr)
EE 5231 - Linear Systems and Optimal Control (3.0 cr)
EE 8215 - Nonlinear Systems (3.0 cr)
Ethics Course
Take one research and professional ethics course. The following may be used or consult with advisor for further options.
ME 8001 - Research Ethics and Professional Practice (0.0 cr)
Seminar
Take 2-3 seminar credits. The following may be used or consult with advisor for further options
ME 8773 - Graduate Seminar (1.0 cr)
ME 8774 - Graduate Seminar (1.0 cr)
Supporting Program
The remaining course credits may be taken in the major or in any supporting field with significant scientific or engineering content, and may include 12 credits in a minor.
Thesis Credits
Take 24 thesis credits after passing the preliminary oral exam
ME 8888 - Thesis Credit: Doctoral (1.0-24.0 cr)
Use of 4xxx-level Courses
No more than six 4xxx-level course credits may be used for graduate-level credit. Only the following courses are acceptable.
AEM 4511 - Mechanics of Composite Materials (3.0 cr)
AEM 4581 - Mechanics of Solids (3.0 cr)
CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy (3.0 cr)
EE 4541 - Digital Signal Processing (3.0 cr)
MATH 4512 - Differential Equations with Applications (3.0 cr)
PHYS 4051 - Methods of Experimental Physics I (5.0 cr)
PHYS 4101 - Quantum Mechanics (4.0 cr)
PHYS 4201 - Statistical and Thermal Physics (3.0 cr)
PHYS 4211 - Introduction to Solid-State Physics (3.0 cr)
 
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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 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 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
EE 5231 - Linear Systems and Optimal Control
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Properties and modeling of linear systems. Linear quadratic and linear-quadratic-Gaussian regulators. Maximum principle. prereq: [3015, CSE grad student] or instr consent
EE 8215 - Nonlinear Systems
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Current topics in stability analysis of nonlinear systems, design of controllers for nonlinear systems, discrete-time and stochastic nonlinear systems. prereq: instr consent
ME 8001 - Research Ethics and Professional Practice
Credits: 0.0 [max 0.0]
Grading Basis: No Grade
Typically offered: Every Fall, Spring & Summer
Intellectual property, data management, social responsibility, authorship, and plagiarism, conflict of interest, and reporting misconduct. Case studies. Recent newspaper articles.
ME 8773 - Graduate Seminar
Credits: 1.0 [max 1.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Recent developments. prereq: CSE grad student
ME 8774 - Graduate Seminar
Credits: 1.0 [max 1.0]
Grading Basis: S-N or Aud
Typically offered: Every Fall & Spring
Recent developments. prereq: 8773
ME 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
AEM 4511 - Mechanics of Composite Materials
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Analysis, design, and applications of laminated and chopped fiber reinforced composites. Micro-/macro-mechanical analysis of elastic constants, failure, and environmental degradation. Design project. prereq: 3031, [CSE upper div or grad student]
AEM 4581 - Mechanics of Solids
Credits: 3.0 [max 3.0]
Course Equivalencies: 02289 - AEM 4581/AEM 5581
Prerequisites: 3031, [Math 2373 or equiv], [Math 2374 or equiv], CSE upper div
Typically offered: Fall Even Year
Continuum mechanics in one dimension: kinematics; mass, momentum/energy, constitutive theory. Wave propagation, heat conduction. Strings. Euler-Bernoulli theory. 3-D deformations/stress. Topics from fracture mechanics, structural stability, vibrations, thin films, layered media, smart materials, phase transformations, 3-D elastic wave propagation. Elasticity, viscoelasticity, plasticity. prereq: 3031, [Math 2373 or equiv], [Math 2374 or equiv], CSE upper div
CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy
Credits: 3.0 [max 3.0]
Course Equivalencies: 00119 - Chem 3502/4502
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Microscopic descriptions of chemical systems. Quantum theory. Applications to atomic/molecular structure. Molecular spectroscopy. Quantum statistical mechanics. Discussion of solutions to several differential equations. prereq: [1062/1066 or 1072H/1076H], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374 or MATH 2243 or concurrent registration is required (or allowed) in MATH 2243 or MATH 2373 or concurrent registration is required (or allowed) in MATH 2373], [PHYS 1302 or PHYS 1402V or PHYS 1502V]
EE 4541 - Digital Signal Processing
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Summer
Review of linear discrete time systems and sampled/digital signals. Fourier analysis, discrete/fast Fourier transforms. Interpolation/decimation. Design of analog, infinite-impulse response, and finite impulse response filters. Quantization effects. prereq: [3015, 3025] or instr consent
MATH 4512 - Differential Equations with Applications
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Laplace transforms, series solutions, systems, numerical methods, plane autonomous systems, stability. prereq: 2243 or 2373 or 2573
PHYS 4051 - Methods of Experimental Physics I
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Contemporary experimental techniques. Introduction to modern analog and digital electronics from an experimental viewpoint. Use of computers for data acquisition and experimental control. Statistics of data analysis. prereq: concurrent registration is required (or allowed) in 2605 or equiv lab experience or instr consent
PHYS 4101 - Quantum Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical techniques of quantum mechanics. Schrodinger Equation and simple applications. General structure of wave mechanics. Operator methods, perturbation theory, radiation from atoms. prereq: [2303 or 2601 or Chem 3502], two sems soph math
PHYS 4201 - Statistical and Thermal Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Principles of thermodynamics and statistical mechanics. Selected applications such as kinetic theory, transport theory, and phase transitions. prereq: 2601
PHYS 4211 - Introduction to Solid-State Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
A modern presentation of the properties of solids. Topics include vibrational and electronic properties of solids; diffraction of waves in solids and electron band structure. Other possible topics include optical properties, magnetic phenomena, and superconductivity. prereq: 4101, 4201