(Approved September, 2001)

This document describes the rules and regulations of the graduate programs in the Department of Mechanical Engineering and Mechanics. Every graduate student of the Department must comply with these rules and regulations in conjunction with University regulations.

To assist the students during their tenure in the Department, and to aid them adhere to the rules and regulations, the following faculty members will serve as their Advisors unless arranged otherwise.

Welcome aboard. We wish you the best in your graduate studies.

Dr. Alan Lau
Graduate Advisor
(215) 895-2377
September 2001

Table of Contents

I. GENERAL INFORMATION

• 1.1 Core Areas and Subject Areas
• 1.2 Plan of Study

II. REQUIREMENTS FOR THE M.S. DEGREE

• 2.1 M.S. Degree Requirements
  
  • 2.1.1 M.S. Thesis
  • 2.1.2 M.S. Courses
  • 2.1.3 POMEP and Master of Engineering Degree

• 2.2 M.S. Procedural Requirements
  • 2.2.1 M.S. Plan of Study
  • 2.2.2 Clearance of M.S. Candidate for Graduation

III. REQUIREMENTS FOR THE Ph.D. DEGREE

• 3.1 Ph.D. Degree Requirements
  • 3.1.1 Ph.D. Courses
  • 3.1.2 Ph.D. Preliminary and Candidacy Examinations
  • 3.1.3 Ph.D. Dissertation
  • 3.1.4 Technical Writing
  • 3.1.5 Foreign Students with M.S. Degree from Foreign Institutions
  • 3.1.6 Other Requirements

• 3.2 Ph.D. Procedural Requirements
  • 3.2.1 Ph.D. Plan of Study
  • 3.2.2 Faculty Advisors
  • 3.2.3 Ph.D. Preliminary Examination
    • 3.2.3.1 Eligibility for & Timing of the Preliminary Examination
    • 3.2.3.2 Reexamination and Reporting of Results
  • 3.2.4 Ph.D. Candidacy Examination
    • 3.2.4.1 Eligibility & Timing of the Candidacy Examination
    • 3.2.4.2 Procedure of Candidacy Examination
  • 3.2.5 Ph.D. Dissertation
    • 3.2.5.1 Dissertation Advisory Committee
    • 3.2.5.2 Approval of Dissertation Topic
    • 3.2.5.3 Final Oral Examination
  • 3.2.6 Clearance of Ph.D. Candidate for Graduation

IV. TOPICAL COVERAGE IN SUBJECT AREAS

• 4.1 Fundamental Material
  • 4.1.1 Mechanics Area
  • 4.1.2 Thermal Fluid Science Area
  • 4.1.3 Systems and Control Area
• 4.2 Core Course Sequences
  • 4.2.1 Theory of Elasticity
  • 4.2.2 Solid Mechanics
  • 4.2.3 Advanced Dynamics
  • 4.2.4 Advanced Thermodynamics
  • 4.2.5 Heat Transfer
  • 4.2.6 Fluid Mechanics
  • 4.2.7 Robust Control Systems
  • 4.2.8 Nonlinear Control Theory
  • 4.2.9 Real Time Microcomputer Control

V. FORMS REQUIRED FOR M.S. AND Ph.D.

I. GENERAL INFORMATION

The rules and regulations described herein pertain to the Master of Science (M.S.) and Doctor of Philosophy (Ph.D.) programs in the Department of Mechanical Engineering and Mechanics (MEM) as of the Fall Quarter 1997. All students entering either the M.S. program or the Ph.D. program must follow the rules and regulations set forth herein. Students are reminded that in addition to these departmental rules, they will have to meet the requirements of the Graduate School of Drexel University as described in the current Graduate Curricula.

1.1 Core Areas and Subject Areas

The MEM Department offers the following three core areas for specialization: Mechanics, Thermal & Fluid Sciences, and Systems & Control. Each core area consists of three subject areas which are listed below. The subject material in each area is covered by a sequence of two courses listed in the parenthesis, with each course being a three credit course.

To provide sufficient mathematical foundation required for these courses, the MEM Department offers a three-quarter sequence in applied mathematics entitled "Engineering Analysis" (MEM 800/591, 800/592, 800/593 for on-campus; MEM 800/X01, 800/X02, 800/X03 for off-campus). This sequence is equivalent to the sequence "Advanced Engineering Mathematics" (MCS 544, 545, 546) offered by the Mathematics and Computer Science Department.

1.2 Plan of Study

All students entering the MEM Department must file an approved M.S. or Ph.D. Plan of Study. With the consultation of the student's Advisor, the Plan of Study must be filed prior to the third term of study since the requirements for graduation will be those in effect at the time of filing. Any changes or deviations from this Plan of Study that may affect the fulfillment of degree requirements must be approved in writing, in advance, by filing a new Plan of Study. Failure to file a Plan of Study or failure to obtain prior written approval to any changes in a Plan of Study may result in non acceptance of the un-approved courses for fulfilling the degree requirements.

II. REQUIREMENTS FOR THE M.S. DEGREE

2.1 M.S. Degree Requirements

2.1.1 M.S. Thesis

The M.S. Thesis is optional. If the Thesis Option is chosen, the student should register for a total of 9 Thesis credits. The work for an M.S. Thesis will generally be completed under the supervision of a faculty advisor who will direct the research work, assign grades for the Thesis credit, and review the final Thesis document. The Thesis must be approved by the faculty advisor before the student can be cleared for graduation. See Section 2.2.2 for further details.

2.1.2 M.S. Courses

The minimum course requirement for the M.S. Degree is 45 credits, including 9 credits of the optional M.S. Thesis. Students may transfer not more than 15 credits (equivalent to 10 semester-credits) from approved institutions, provided they follow the rules and regulations described in the Drexel University's Graduate Curricula. These 45 credits consist of the required 9 credits of applied mathematics, the required 12 credits of core area courses, and the remaining 24 credits of technical elective courses, as tabulated below.

The 9 credits of applied mathematics may be fulfilled by taking either the applied mathematics course sequences mentioned in Section I, or any other approved equivalent mathematical courses. The 12 credits of core area courses may be fulfilled by taking any two core course sequences, each from a different core area, as listed in Section I.

Of the remaining 24 technical elective credits, at least 12 must be taken from within the MEM Department, while the rest may be taken from the College of Engineering, College of Arts and Sciences, or from other colleges, if consistent with the student's Plan of Study and given advance written approval by his/her Advisor. At least 15 of these 24 elective credits must be exclusive of Independent Study courses or Thesis.

2.1.3 POMEP and Master of Engineering Degree

The MEM Department, in response to industry's needs, offers a Practice-Oriented Manufacturing Engineering Program (POMEP), which awards a certificate in conjunction with a master's degree. The course requirement for POMEP students is 48 credits, which includes the 21 credits (9 for applied mathematics and 12 for MEM core area courses) required for all MEM students, plus 6 credits of required manufacturing core courses, 6 credits of required internship for six months (two terms), and 15 credits of elective courses. Of the 15 elective credits, 9 must be from manufacturing specialization courses, and the remaining 6 must be from business/management core courses. This 48-credit requirement for POMEP students are tabulated below.

For further information and lists of manufacturing and business/management courses in POMEP, please contact Graduate Advisor.

The College of Engineering also offers a Master of Engineering (M.E.) program with the Practice-Oriented Manufacturing Option. This is a multi-disciplinary degree program which can be tailored for students from different engineering departments. Detailed information can be found in Drexel's Graduate Catalog.

2.2 M.S. Procedural Requirements

2.2.1 M.S. Plan of Study

Upon approval by their Advisors, students in the M.S. Program must file a Plan of Study, MEM GR-1 Form (attached) with the Graduate Advisor prior to the third quarter of study. This Plan of Study should clearly indicate how the course requirements cited above are satisfied, whether or not the M.S. Thesis option is chosen, and must also indicate any applicable transfer of credits. Students holding a Bachelor's degree in a Science Department or Engineering Department other than Mechanical Engineering are typically advised to take several undergraduate courses as preparation for graduate studies in MEM Department. Though these courses are not counted toward the required 45 credits for M.S. Degree (or 48 credits for POMEP students), they also must be listed in the Plan of Study.

2.2.2 Clearance of M.S. Candidate for Graduation

At the beginning of the expected quarter of graduation, the M.S. candidate will file the completed MEM GR-2 Form "Clearance for M.S. Degree Applicant" (attached) with the Graduate Advisor. If the M.S. Thesis option has been pursued then the MEM GR-2A Form "Clearance for M.S. Thesis" (attached) must also be filed. When this Form(s) shows that all departmental requirements have been satisfied, the Graduate Advisor will clear the student for graduation.

III. REQUIREMENTS FOR THE Ph.D. DEGREE

A student admitted into the Ph.D. Program is classified as a Ph.D. Applicant. After the successful completion of the Ph.D. Candidacy Examination (described below), the classification of the student changes to Ph.D. Candidate. Each Ph.D. Applicant must obtain, from the Office of Graduate Studies, the Ph.D. Forms Booklet. This booklet contains forms for filing Plan of Study, appointment and approval of supervising professor, appointment of various examination committees, and reporting of the results of these examinations. The rules, regulations, and procedures pertaining to the required credits and the governance of the Ph.D. Candidacy Examinations are described below.

3.1 Ph.D. Degree Requirements

3.1.1 Ph.D. Courses

The Graduate School requires at least 90 credits for the Ph.D. Degree. A Master's degree is not a prerequisite for the Ph.D., but does count as 45 credits toward the 90-credit requirement. Thus, these 90 credits consist of the 45 credits taken normally for the M.S. degree (see Section II) and 45 additional credits for the Ph.D. degree. Of the 45 additional credits for the Ph.D. degree, 18 must be from regular course work (exclusive of Independent Study and Dissertation). The remaining 27 credits may consist of Dissertation, Independent Study, or additional advanced course work consistent with the approved Plan of Study. Thus, beginning with a B.S. degree, the required 90 credits for a Ph.D. degree are tabulated below:

3.1.2 Ph.D. Preliminary and Candidacy Examinations

Every Ph.D. Applicant is required to take the Ph.D. Preliminary and Candidacy Examinations administered by the MEM Department.
The Preliminary Examination is a three-hour examination that covers material from two of the nine core course sequences listed in Section I, as chosen by the student in consultation with his/her Advisor.

As an aid to the applicants, the various topics in each subject area that an applicant is expected to be proficient in are listed in Section IV. It is emphasized that the Ph.D. Preliminary Examination may cover additional basic material, which is not necessarily listed in Section IV.

The Candidacy Examination consists of a research component through which the Ph.D. Applicant must demonstrate his/her ability to conduct independent research. The research topic must be determined in consultation with the student's advisor and it requires the approval of the Department Graduate Advisor. The research topic should be related to the student's research work (e.g. M.S. and Ph.D. work, independent research, etc.). In case the student did not establish yet his/her own independent research, the research topic should consist of a review/summary of a research subject published in the open literature (e.g., a key paper and the accompanying publications relevant to that paper). The review/summary must include a proposed alternative solution and/or a proposed extension of the work reviewed.

The Candidacy Examination consists of: a) A presentation of the research work. This presentation should be publicly announced and open to the public; b) submission of a brief document to the Candidacy Examination Committee. The document should be no longer than 10 pages and submitted to the committee at least two weeks prior to the public presentation; and c) an oral examination conducted by the examining committee, immediately following the public presentation, as outlined in Section 3.2.4 below.

3.1.3 Ph.D. Dissertation

A formal submission of the Ph.D. Dissertation with the Drexel University Library is required for the graduation of the Ph.D. Candidate. Prior to this, the approval of the dissertation topic and the supervision of the candidate's research will be conducted by his/her Dissertation Advisory Committee, followed by a public defense of the dissertation.

3.1.4 Technical Writing

It is required that every Ph.D. student take a formal course in "Technical Writing" for credit. The Drexel University undergraduate course which will satisfy this requirement in technical writing is currently listed as course number TSCOM 310. Students who have taken this course at Drexel as an undergraduate, or its equivalent elsewhere, are exempted from this requirement. If an equivalent course was taken for credit at another institution the student may be permitted by the Graduate Advisor to transfer the course credits to Drexel University. The technical writing requirement may be waived for qualified students at the discretion of his/her faculty Advisor. The waiver must be filed with the Graduate Advisor.

3.1.5 Foreign Students with M.S. Degree from Foreign Institutions

Students under this category may be required to take a special course in an "English as a Second Language" Program before entering Drexel University. Information on this course is provided upon application to the Graduate Program at Drexel University. Once admitted to Drexel University, in order to be appointed as Teaching Assistants, students must enter into Drexel's Incoming Foreign Teaching Assistant Program. The program is recommended for all incoming foreign students for improving their proficiency in the English language and for exposing them to the teaching techniques and campus life at Drexel University.

3.1.6 Other Requirements

All Ph.D. Candidates are expected to teach and participate in other educational activities of the MEM Department, such as the departmental Seminar Series.

3.2 Ph.D. Procedural Requirements

3.2.1 Ph.D. Plan of Study

Upon approval by their Advisors, students in the Ph.D. Program must file a Form D-1 "Ph.D. Plan of Study" (found in the Ph.D. Forms Booklet) with the Office of Graduate Studies through the Graduate Advisor as soon as possible but prior to the third quarter of study. This Plan of Study should clearly indicate how the course requirements cited above are satisfied, and list all required examinations, such as Ph.D. Candidacy Examination, along with the dates taken or expected to be taken.

3.2.2 Faculty Advisors

As detailed in Section I: General Information, upon admittance into the Ph.D. Program, each student is assigned a faculty Advisor.These Advisors will assist the students in interpreting the rules and regulations, and in preparing their Plan of Study. Since these Advisors are only temporary (in conjunction with their Graduate Committee assignment), each student is advised to establish himself/herself with a permanent faculty Advisor, who would then serve as the student's Supervising Professor. The Form D-2 "Ph.D. Supervising Professor Appointment" (found in the Ph.D. Forms Booklet) should be filed with the Office of Graduate Studies through the Graduate Advisor, to notify of this appointment. The Form D-2 should be filed as early as possible, but no later than the successful completion of the Ph.D. Candidacy Examination.

3.2.3 Ph.D. Preliminary Examination

3.2.3.1 Eligibility for & Timing of the Preliminary Examination:

1. A student holding a B.S. Degree, and currently enrolled in the MEM Graduate Program, can take his/her Ph.D. Preliminary Examination after the completion of at least three academic quarters of graduate study at Drexel University with a minimum Grade Point Average (GPA) of 3.5 in all engineering and science graduate courses.
2. A student holding a M.S. Degree which has not been granted by the MEM Department, can take his/her Ph.D. Preliminary Examination after the completion of at least two quarters of graduate study at Drexel University with a minimum GPA of 3.5 in all engineering and science graduate courses taken while in the MEM Department.
3. Under special circumstances the requirement of a minimum GPA of 3.5 may be waived subject to the unanimous approval by the student's faculty Advisor, the Graduate Advisor, and the Department Head.
4. The Ph.D. Preliminary Examination is given twice each year, during June-July and during January-February. A student who wishes to take the examination must file MEM GR-3 Form "Ph.D. Preliminary Examination Request" (attached) with the Graduate Advisor who coordinates the Ph.D. Preliminary Examination. This form must be filed at least three months before the scheduled Ph.D. Preliminary Examination.

3.2.3.2 Reexamination and Reporting of Results:

1. A student whose performance is unsatisfactory in the Preliminary Examination may take a reexamination subject to the following and if approved by the appropriate examining committee.
   1. The reexamination must be taken during the following Fall or Spring Preliminary Examination period, as determined by the appropriate examining committee.
   2. Students will be permitted to take a reexamination only once.
   3. A student who fails a reexamination may appeal the decision to the Department Graduate Committee. The decision of the Graduate Committee will be forwarded to the Department Head who will notify the student and the entire MEM Faculty of the final decision.
2. The results of the Preliminary Examination, along with any decision(s) pertaining to it will be reported, by the Graduate Advisor, to the student, his/her faculty Advisor, and to the entire MEM Department Faculty within two weeks after the examination was administered.

3.2.4 Ph.D. Candidacy Examination

3.2.4.1 Eligibility & Timing of the Candidacy Examination.

1. A graduate student who successfully completed the Preliminary Examination requirements, as described in section 3.2.3 above, and is currently enrolled in the MEM Graduate Program, can take his/her Ph.D. Candidacy Examination.
2. The Ph.D. Candidacy Examination can be administered any time during the academic year. The student must schedule the examination with his/her advisor and the Department Graduate Advisor.
3. A student who wishes to take the Candidacy Examination must file MEM GR-4 Form "Ph.D. Candidacy Examination Request" (attached) with the Graduate Advisor who coordinates the Ph.D. Candidacy Examination. This form must be filed at least three months before the scheduled Ph.D. Candidacy Examinations.

3.2.4.2 Procedure of Candidacy Examination

1. Chairman of the Committee:
   If the student has a Supervising Professor, that Professor will serve as the Chairman of the Candidacy Examination Committee. If a student does not have a Supervising Professor, the Chairman of the Candidacy Examination Committee will be appointed by the MEM Department Head. Normally, the Advisor who approves the MEM GR-4 Form "Ph.D. Candidacy Examination Request" will be the Chairman of the Candidacy Examination Committee and the student's Supervising Professor.
2. Constituency of the Committee:
   The Candidacy Examination Committee will consist of at least five members with (a) at least two members from the core area of the student, (b) at least two members from outside the core area of which one must be from outside the MEM Department.
3. Notification of Committee appointment with the Office of Graduate Studies: The constituency of the Candidacy Examination Committee and the schedule of the examination must be reported to the Office of Graduate Studies by filing the Form D-3 "Ph.D. Candidacy Committee Appointment and Examination Schedule" (found in the Ph.D. Forms Booklet) with the Office of Graduate Studies by the Supervising Professor or Department Graduate Advisor. This should be done at least four weeks prior to the scheduled date of the examination.
4. Upon satisfactory performance in the Candidacy Examination the student becomes a Ph.D. Candidate, and his/her registration changes to that status. In the event of unsatisfactory performance, the Candidacy Examination committee will decide whether the student will be permitted to take a reexamination, and its timing.
5. The results of the Candidacy Examination will be reported by the Department Graduate Advisor to the entire MEM Faculty in a timely fashion.
6. Reporting of the Results to the Office of Graduate Studies:
   The results of the Candidacy Examination should be reported to the Office of Graduate Studies, through the Graduate Advisor, on Form D-4 "Report of Ph.D. Candidacy Examination Committee" (found in the Ph.D. Forms Booklet) within 48 hours of the examination. The Office of Graduate Studies requires that all relevant information (e.g., recommendations for additional course work, etc.) appear on Form D-4 and/or its attachments. The same procedure applies in the event of unsatisfactory performance in the oral examination.

3.2.5 Ph.D. Dissertation

3.2.5.1 Dissertation Advisory Committee :

Upon successful completion of the Ph.D. Candidacy Examination, the student's Supervising Professor will form a Dissertation Advisory Committee for the student. This committee, chaired by the Supervising Professor, will consist of at least five members with at least one member from outside the MEM Department. The composition of the committee should be consistent with the research program of the student. The composition of the committee will be reported to the Office of Graduate Studies, through the Graduate Advisor, on Form D-5 "Ph.D. Thesis Advisory Committee" (found in the Ph.D. Forms Booklet).

3.2.5.2 Approval of Dissertation Topic :

At the discretion of the Ph.D. advisor, the Ph.D. Candidate will give a presentation of his/her Dissertation topic to his/her Dissertation Advisory Committee. This presentation should be publicly announced and open to public. The student will submit a comprehensive Ph.D. Dissertation Proposal, which normally will include abstract, introduction, detailed literature review, research progress, proposed research, timetable, etc.. The committee will approve/reject the general methodology and approach and the scope of work so that it can be completed in a manageable time. The result of the presentation will be reported to the Graduate Advisor on MEM GR-4 Form "Approval of the Ph.D. Dissertation Topic" (attached).

3.2.5.3 Final Oral Examination :

Upon completion of the Dissertation, there will be a final public presentation and defense of the Dissertation. A final oral examination committee will examine the Dissertation and the presentation. This committee, chaired by the student's Supervising Professor, will consist of at least five members, with at least one member from outside the MEM Department. The composition of this committee is reported to the Office of Graduate Studies, through the Graduate Advisor, on Form D-6 "Ph.D. Final Oral Examination Committee" (found in the Ph.D. Forms Booklet), at least four weeks prior to the scheduled date of examination. Within 48 hours of the examination, its results must be reported to the Office of the Graduate Studies by the Graduate Advisor or by the Supervising Professor, on Form D-7 "Report of Ph.D. Final Oral Examining Committee" (found in the Ph.D. Forms Booklet).

3.2.6 Clearance of Ph.D. Candidate for Graduation

The Ph.D. Candidate will be cleared for graduation by the Graduate Advisor after filling out the MEM GR-5 Form "Clearance for Ph.D. Degree Applicant" (attached) to ascertain that all departmental requirements have been satisfied. This form must be filed 30 days prior to and not later than 10 days before the end of the quarter in which the student is expected to complete the requirements.

Finally, following the approval of MEM GR-5 Form, the Ph.D. Candidate must complete Form D-8 "Application for Doctoral Degree" (found in the Ph.D. Forms Booklet) with the Office of Graduate Studies. Submission of the Dissertation with the Drexel University Library is a prerequisite for completing this form. The Form D-8 should be filed as soon as possible but no later than two days before the day of Commencement.

IV. TOPICAL COVERAGE IN SUBJECT AREAS

4.1 Fundamental Material

The material listed in this Section (Section 4.1) is undergraduate material that helps to build the foundation for graduate-level core courses described in Section 4.2 below. In the Preliminary Examination, students are examined on material from two graduate-level core course sequences (Section 4.2).

4.1.1 Mechanics Area

Major Topics

Statics (MEM202): Concurrent force systems; statics of particles; equivalent force/moment systems; distributed forces; centroids; equilibrium of rigid bodies; trusses, frames and machines; internal forces in structural members; friction; moments of inertia.

Dynamics (MEM238): Kinematics of particles (Newton's Second Law, energy and momentum methods); kinematics of rigid bodies; plane motion of rigid bodies.

Mechanics Of Materials (MEM230, MEM330): Tension, compression and shear; axially loaded members; torsion; shear forces and bending moments; stress in beams; analysis of stress and strain; deflections of beams; statically indeterminate beams; columns; energy principles.

Further Information: By request from Dr. H. Sosa

4.1.2 Thermal Fluid Sciences Area

Major Topics

Fluid Mechanics (MEM220, MEM320): Fluid statics, conservation equations for fluid motion, applications of the Bernoulli equation, pipe flow, basic inviscid and potential flow, basic compressible flow, one-dimensional isentropic, normal shock, two-dimensional supersonic flow, oblique shocks and Prandtl-Meyer expansion, supersonic nozzles, diffusers

Heat Transfer (MEM345, MEM440): Fundamentals of heat transfer by conduction, convection, and radiation; steady and unsteady

heat conduction, forced and free convection. Combined heat transfer problems in engineering systems.

Thermodynamics (MEM310, MEM410): Fluid properties, First and Second Law applications, thermal efficiencies, properties of real fluids, analysis of ideal and real gas mixtures; gas-phase reacting systems.

Further Information: By request from Dr. Y. Cho

4.1.3 Systems and Control Area

Major Topics

Introduction to Control (MEM255): Modeling of linear & nonlinear systems, linearization, transfer functions, poles and zeros, state-space models, eigenvalues, eigenvectors and transition matrices, block diagrams and signal flow graphs, frequency and time-domain analysis.

Control System Design (MEM355): Root-locus and Nyquist techniques, Compensator design, Stability, controllability, and observability, regulator, observer, and set-point controllers.

Microcomputer Based Control Systems (MEM458, MEM459): Discrete-time systems, z-transform, sampling theorem, the pulse transfer function, discrete state equations, stability, time-domain analysis, frequency-domain analysis, design of discrete-time controllers, digital simulation, microcomputer and microprocessor implementation of digital controllers.

Further Information: By request from Dr. B.C. Chang.

4.2 Core Course Sequences

The Preliminary Examination covers material from two of the nine core course sequences listed in Section I. The material covered in each of the core course sequence include but not limited to those topics listed below.

4.2.1 Theory of Elasticity

Major Topics

Review of Mechanics of Materials; vector and tensor analysis; indexical notation; integral theorem; analysis of stress; equilibrium equations; principal stresses and stress invariants; analysis of strain; displacements and small strains; principal strains and strain invariants; compatibility; generalized Hooke's law; engineering elastic constants; governing equations in linear elasticity; strain energy; uniqueness of solution; Saint-Venant's principle; elementary problems in three dimensions.

Two dimensional problems in Cartesian and polar coordinates; solution by polynomials and Fourier series; Airy's stress function; solution by means of complex variables; torsion problem; bending of bars.

Three-dimensional problems, elastic contact; energy principles and applications; Rayleigh-Ritz methods; advanced topics.

Reference Material

Timoshenko, S.P. and Goodier, J.M., Theory of Elasticity, McGraw-Hill, 3rd ed., 1970.

Chou, P.C. and Pagano, N.J., Elasticity, Dover, 1992.

Recommended Courses

Theory of Elasticity I & II (MEM 660, MEM 661)

Further Information: By request from Dr. T. Tan

4.2.2 Solid Mechanics

Major Topics

The student is expected to have knowledge on the foundations of continuum mechanics. Major subjects include: Algebra and analysis of tensors. Kinematics of deformable bodies: material and spatial descriptions; material time derivative; measures of strain; rate of deformation and spin tensors. Balance principles: conservation of mass, linear and angular momentum, balance of energy; Cauchy and Piola-Kirchhoff stress tensors.

Constitutive equations: Introduction to phenomenological plasticity; strain-stress curves; ideal plastic models; crystal plasticity; fundamental one-dimensional problems; stress and strain deviatoric tensors; Von Mises and Tresca yield criteria; flow laws; isotropic and kinematic strain hardening. Nonlinear behavior of materials; kinematics of large deformations; Cauchy and Green elasticity; exact solutions for compressible and incompressible nonlinear elastic materials.

Reference Material

Chandrasekharaiah, D.S. and Debnath, L., Continuum Mechanics, Academic Press, 1994.

Fung, Y.C., Foundations of Solid Mechanics, Prentice Hall, 1965.

Gurtin, M., An Introduction to Continuum Mechanics, Academic Press, 1981.

Lublimer, J., Plasticity Theory, Mac Millan, 1990.

Malvern, L.E., Introduction to the Mechanics of a Continuous Medium, Prentice- Hall, 1969.

Recommended Courses

Continuum Mechanics (MEM 663)
Introduction to Plasticity (MEM 664)
Time– Dependent Solid Mechanics (MEM 665)

Further Information: By request from Dr. H. Sosa.

4.2.3 Advanced Dynamics

Major Topics

The student will be expected to show competence in Analytical Dynamics (Lagrangian) as well as Vector Dynamics in three dimensions (Eulerian). As a prerequisite, the student must have an undergraduate background in Statics and Dynamics at the level of the text by Beer & Johnston, as well as working knowledge of Vector Analysis and Matrix Algebra.

The topical coverage the student should be conversant with includes, but is not limited to: analytical statics, principle of virtual work, Lagrange's equations, generalized coordinates and forces, stability about dynamic equilibrium, conservation of generalized momentum constraints, Lagrange multipliers, generalized impulse and momentum, nonholonomic constraints, central forces, effect of rotation of the earth, three-dimensional vector dynamics applied to systems of particles and rigid bodies, linear vibration theory for systems with multiple degrees of freedom, normal coordinates, small oscillations about steady state.

Reference Material

Beer, F.P. and Johnston, E.R., Vector Mechanics for Engineers, 3rd ed., McGraw-Hill, 1977 (Elementary level).

Greenwood, D.T., Classical Dynamics, Prentice Hall, Inc., 1977 (Advanced level).

Recommended Courses

Advanced Dynamics I & II (MEM 666, MEM 667).

Further Information: By request from Dr. S. Siegler.

4.2.4 Advanced Thermodynamics

Major Topics

The student will be tested for competence in classical and statistical thermodynamics. The student is also expected to be able to demonstrate a reasonable background in undergraduate thermodynamics topics at the level of the texts by Van Wylen and Sonntag, Wark, or Black and Hartley.

The topical coverage includes, but is not limited to: first and second laws and properties of real and ideal substances, basic kinetic theory of gases, velocity and speed distributions, transport properties, elementary quantum mechanics, including energy level and degeneracy concepts, classical and quantum statistics, calculation of thermodynamic properties of ideal gases and gas mixtures, chemical equilibrium and thermochemistry, and real gas equations of state.

Reference Material

Wark, Thermodynamics, 5th ed., McGraw-Hill, 1988.

Van Wylen and Sonntag, Fundamentals of Classical Thermodynamics, 3rd ed., Wiley, 1986.

Callen, Thermodynamics and an Introduction to Thermostatics, 2nd ed., Wiley, 1985.

Incorpera, Introduction to Molecular Structure & Thermodynamics, Wiley, 1984.

Tien and Lienhard, Statistical Thermodynamics, Hemisphere, 1979.

Smith, Elementary Statistical Thermodynamics, Plenum, 1982.

Herzberg, Spectra of Diatomic Molecules, Van Nostrand & Reinhold, 2nd ed., 1950.

Sonntag and Van Wylen, Fundamentals of Statistical Thermodynamics, Krieger, 1985.

Bejan, Advanced Engineering Thermodynamics, Wiley, Interscience, 1988.

Lay, Statistical Mechanics and Thermodynamics of Matter: An Introductory Survey, Harper & Row, 1990.

Black and Hartley, Thermodynamics, Harper Collins, 1991.

Recommended Courses

Statistical Thermodynamics I & II (MEM 601, MEM 602).

Further Information: By request from Drs. N. Cernansky and D. Miller.

4.2.5 Heat Transfer

Major Topics

Basic concepts in heat transfer and fundamental mechanisms, the heat conduction equation and its boundary conditions, analytical solutions of steady state and transient heat conduction equation with and without heat generation, application of transform techniques, heat conduction with moving boundaries.

Heat transfer in free and forced convection, the equations of motion and energy, boundary layer analysis, determination of friction factor and heat transfer coefficients, fundamentals of boiling and condensation, basic thermal analysis of heat exchangers.

The concept of blackbody radiation, radiation heat transfer among surfaces separated by a nonparticipating medium, problems involving radiation combined with conduction and convection.

Reference Material

Eckert and Drake, Analysis of Heat and Mass Transfer, McGraw-Hill.

Arpaci, Conduction Heat Transfer, Addison-Wesley, 1966.

Kays and Crawford, Convective Heat and Mass Transfer, McGraw-Hill, 1993.

Siegel and Howell, Thermal Radiation Heat Transfer, McGraw-Hill, 1993.

Incorpera and Dewitt, Fundamentals of Heat and Mass Transfer, Wiley, 3rd ed., 1990.

Kakac and Yener, Heat Conduction, Hemisphere Publishing Co., 1985.

Bejan, Convection Heat Transfer, Wiley, 2nd edition, 1995.

In addition, it is recommended that the student be familiar with the materials covered in a typical undergraduate heat transfer text.

Recommended Courses

Conduction Heat Transfer (MEM 611).

Convection Heat Transfer (MEM 612).

Radiation Heat Transfer (MEM 613).

Further Information: By request from Drs. B. Farouk and Y. Cho.

4.2.6 Fluid Mechanics

Major Topics

The student is expected to have a basic understanding of the principles of fluid mechanics and the methods for the analysis of 2-D ideal and viscous fluids. It is assumed that the student has the analytical background in vector and tensor analysis, complex variables and differential equations.

The topical coverage may include, but is not limited to: concept of fluid as a continuum, kinematics, conservation laws for fluids, vorticity and circulation, ideal inviscid 2-D flows, momentum integral equations, Navier-Stokes equations, exact solutions of the Navier-Stokes equations, viscous flows, laminar boundary layers including non-steady flows, similarity methods, asymptotic methods, introduction to stability, turbulence, shock waves, and compressible flows.

Reference Material

Schlichting, H., Boundary Layer Theory, 7th Ed., McGraw-Hill, 1979.

Currie, I.G., Fundamental Mechanics of Fluids, McGraw-Hill, 1974.

White, F., Fluid Mechanics, McGraw-Hill, 1986.

White, F., Viscous Fluid Flow, McGraw-Hill, 2nd Ed., 1991.

Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, 1973.

Recommended Courses

Foundation of Fluid Mechanics (MEM 621)

Boundary Layer Theory (MEM 622)

Further Information: By request from Dr. D. Wootton.

4.2.7 Robust Control Systems

Major Topics

Linear spaces and linear operators; internal stability, coprime factorization, matrix fraction description, irreducible MFD's, Smith-McMillan form; poles and zeros; canonical realizations of multivariable systems, minimal realizations; structure of stabilizing controllers; algebraic Riccati equation, state-space computation of coprime factorizations; YJB controller parametrization; linear fractional transformation; state-space structure of the proper stabilizing controllers; formulation of control problems; optimization problem, optimization problem, model matching problem, tracking problem, robust stabilization problem; inner-outer factorizations, spectral factorizations; Sarason's interpolation theory; Hankel-norm approximations, balanced realizations.

Reference Material

Francis, B. A., A Course in Control Theory, Springer-Verlag, 1987.

Vidyasagar, M., Control System Synthesis - A Factorization Approach, The MIT Press, 1985.

Chen, C-T, Linear Systems Theory and Design, CBS College Publishing, HRW, 1984.

Kailath, T., Linear Systems, Prentice-Hall, Inc., 1980.

Kwakernaak, H., and Sivan, R., Linear Optimal Control Systems, John Wiley & Sons, Inc., 1972.

Zhou, K., Doyle, J. C. and Glover, K., Robust and Optimal Control, Prentice Hall, 1996.

Recommended Courses

Robust Control Systems I & II (MEM 633, MEM 634)

Further Information: By request from Dr. A. Yousuff.

4.2.8 Nonlinear Control Theory

Major Topics

The student will be expected to demonstrate a broad knowledge in the qualitative behavior of nonlinear dynamical systems as well a facility in methods of nonlinear systems analysis and control system design. As a prerequisite to study in this field, the student should have a solid background in linear systems analysis and control systems design and background first year graduate mathematics including linear algebra and ordinary differential equations. The student should also be comfortable with the use of the computer in engineering analysis.

The topical coverage will include, but is not limited to: geometric theory of nonlinear dynamics; stability, controllability and observability of nonlinear systems; exact linearization, decoupling and stabilization by smooth feedback; systems with parameters: bifurcation and stability; regulator design; tracking and regulation; discontinuous feedback control.

Reference Material

Isidori, A., Nonlinear Control Systems: An Introduction, Springer-Verlag, 1989.

Beltrami, E., Mathematics for Dynamic Modeling, Academic Press, 1987.

Gelb, A. and Vander Velde, W. E., Multiple-Input Describing Functions and Nonlinear System Design, McGraw-Hill: New York, 1968.

Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag: New York, 1983.

Hagedorn, P., Non-Linear Oscillations, Oxford University Press: New York, 1981.

La Salle, J. and Lefschetz, S., Stability by Liapunov's Direct Method, Academic Press, New York, 1961.

Utkin, V. I., Sliding Modes and Their Application in Variable Structure Systems, MIR: Moscow, 1978.

Recommended Courses

Nonlinear Control Theory I & II (MEM 636, MEM 637)

Further Information: By request from Dr. H.G. Kwatny.

4.2.9 Real Time Microcomputer Control

Major Topics

Discrete-time systems and the z-transform; sampling and data reconstruction; the pulse transfer function; discrete state equations; time-domain analysis; digital simulation; stability; frequency-domain analysis; introduction to LabVIEW programming; data acquisition and processing.

Design of discrete-time controllers; sampled-data transformation of analog filter; digital filters; microcomputer implementation of digital filters; LabVIEW programming techniques; using the DAQ library; writing a data acquisition program; LabVIEW implementation of PID controllers.

Reference Material

Phillips, C. L. and Nagle, H. T., Digital Control System Analysis and Design, 3rd Edition, Prentice-Hall, 1995.

National Instruments, LabVIEW Student Edition, Prentice-Hall, 1995.

The MATH Works Inc., The Student Edition of MATLAB for Macintosh Computers, Version 4, Prentice Hall, 1995. (1992 Edition is also acceptable.)

Johnson, G.W., LabVIEW Graphical Programming: Practical Applications in Instrumentation and Control, McGraw-Hill, 1994.

Franklin, G. F., Powell, J. D., and Workman, M. L., Digital Control of Dynamic Systems, Addison-Wesley, 1990.

Astrom, K. J., Wittenmark, B., Computer Control Systems, Prentice-Hall, 1984.

Recommended Courses

Real Time Microcomputer Control I & II (MEM 639, MEM 640)

Further Information: By request from Dr. B.C. Chang.

V. FORMS REQUIRED FOR M.S. AND PH.D.

FORMS REQUIRED FOR MASTER OF SCIENCE (M.S.)

FORMS REQUIRED FOR DOCTOR OF PHILOSOPHY (Ph.D.)

Notes: D-forms are in the Ph.D. FORMS Website , available from the Office of Graduate Studies (OGS).

Grad Adv. & OGS means that the form needs signatures from both parties.

FORMS	PURPOSE	SUBMIT TO	WHEN
	Re-admission Form (.pdf)	Grad Adv. & OGS	(2)
D-1	Plan of study	Grad Adv. & OGS	Before the 3rd term of studies
D-2	Supervising Professor Appointment	Grad Adv. & OGS	Before the candidacy examination
GR-3	Preliminary Examination Request (.pdf)	Grad Adv.	One term before the examination
GR-4	Candidacy Examination Request (.pdf)	Grad Adv.	One term before the examination
D-3	Candidacy Committee	Grad Adv. & OGS	After passing written examination
D-4	Report of Candidacy Committee	Grad Adv. & OGS	Within 48 hours of the oral examination
D-4a	Individual Reports	OGS	Along with form D-4
D-5	Thesis Advisory Committee	Grad Adv. & OGS	After passing the candidacy examination
GR-5	Approval of These Topic (.pdf)	Grad Adv.	After approval of proposal
D-6	Final Oral Examination Committee	Grad Adv. & OGS	4 weeks before final oral examination
D-7	Report of Final Oral Examination	Grad Adv. & OGS	Within 48 hours of the examination
GR-6	Clearance (.pdf)	Grad Adv.	During term of graduation
	Completion Form (.pdf)	OGS	Before commencement

Ph.D. students are encouraged to follow instructions available from the Office of Graduate Studies Website regarding graduation and thesis requirements.

(1) For students taking Thesis option.

(2) This form is used by Drexel M.S. students to apply for enrolling into the Ph.D. Programs.