# Graduate courses

The following courses, numbered 5000-9999, are offered for graduate credit. Courses numbered 5000-6999, which are offered for undergraduate credit only, may be found in the undergraduate bulletin, as well as all other undergraduate courses (numbered 0900-4999). Courses in the following list numbered 5000-6999 may be taken for undergraduate credit unless specifically restricted to graduate students as indicated by individual course limitations. For interpretation of numbering system, signs and abbreviations, see theĀ Wayne State Graduate Bulletin.

The Mechanical Engineering Department has three research thrust areas, namely, the "*Advanced Materials and Manufacturing"*, the "*Advanced Propulsion and Energy Systems"*, and the "*Noise and Vibration Control"*. The graduate ME curriculum is structured accordingly as reflected in the *Curriculum Map of the ME Graduate Programs*. Graduate students have to select their fields of study in one of the three thrust areas of the ME Department.

**5000 Engineering Analysis I. Cr. 4**

Prereq: MAT 2150 and senior standing. Applications of ordinary differential equations. The method of Frobenius, Bessel functions, Legendre polynomials. Orthogonality of characteristic functions. Fourier series and Fourier integrals. Characteristics and solutions of partial differential equations. Method of separation or variations. Applications to initial and boundary value problems in engineering. Material Fee as indicated in the Schedule of Classes (F)

##### 5010 Engineering Analysis II. Cr. 4

Prereq: MAT 2150 and senior standing. Basic operations of complex numbers. Analytic functions and Cauchy-Riemann conditions. Cauchy and Goursat theorem. Residue theorem. Conformal mapping and its applications. Schwarz-Christoffel transformation. Basic properties of the Laplace transformation. Convolution integral. Applications to mechanical and electrical engineering problems. Material Fee as indicated in the Schedule of Classes (W)

##### 5040 Finite Element Methods I. Cr. 4

Prereq: M E 2400; MAT 2150 or MAT 2350. Introduction to finite element methods. Review of equations from solid mechanics, variational methods, potential energy principles. Displacement-based formulation of bar, beam, plane strain and plane stress elements. Isoparametric element formulation. Assembly of elements and solution of global stiffness equations. Detailed examples of problems from structural analysis and solid mechanics. Computer laboratory sessions using the MSC/Nastran and Altair Hypermesh computer codes. (F,W)

##### 5100 (BME 5010) Engineering Physiology. (CHE 5100) (ECE 5100) (I E 5100) Cr. 4

Prereq: BME 5005 or consent of instructor. The basic principles of human physiology presented from the engineering viewpoint. Bodily functions, their regulation and control discussed in quantitative terms and illustrated by simple mathematical models when feasible. (F,W)

##### 5120 Fundamentals of Alternative Energy Technology. (AET 5120) Cr. 4

Prereq: senior standing in science or engineering discipline. Input-output analysis, thermodynamic efficiency and availability, energy balances, economics and environmental considerations. Fuel cell examined from energy efficiency perspective. Photovoltaics, wind power, biomass conversion technologies. (W)

##### 5160 (BME 5210) Musculoskeletal Biomechanics. Cr. 4

Prereq: BME 5010 or BMS 5550; M E 2400. Structure and properties of the major tissue components of the musculoskeletal system and evaluation of how tissues combine to provide support and motion to the body. (W)

##### 5170 (BME 5570) Design of Human Rehabilitation Systems. (ECE 5170) (I E 5170) Cr. 4

Prereq: senior standing. Design, fabrication and testing of customized hardware to aid handicapped patients. (F)

##### 5180 (BME 5370) Introduction to Biomaterials. (MSE 5180) Cr. 4

Prereq: B E 1300, BME 5010 or BMS 5550. Introduction to study of both biological materials (bone, muscle, etc.) and materials for medical applications. Topics include tissue properties and effects of pathology, biocompatability, and design considerations. (Y)

##### 5210 Convective and Radiative Heat Transfer. Cr. 4

Prereq: M E 4210. Radiative processes and properties of solids. Radiative heat transfer among surfaces in an enclosure. Introduction to gas radiation. Derivation of the energy equation for laminar flows. Application of semi-empirical correlation for forced and free convection of laminar and turbulent flows. Some analytical methods for convective heat transfer. Heat exchange analysis. (F)

##### 5250 Alternative Energy Technology System and Design. (AET 5250) Cr. 4

Prereq: senior standing in science or engineering discipline. Topics such as: batteries, flywheels, capacitors, motors, controllers, power management, heat dissipation, systems containment, manufacturing processes, systems dynamics. Lectures and design projects. (F)

##### 5300 Intermediate Fluid Mechanics. Cr. 4

Prereq: M E 3300. Introduction to continua. Integral and differential equations of motion. Ideal flow theory. Flow over blunt bodies. Introduction to boundary layer. Sound waves. Compressible flows.

(F)

##### 5330 Advanced Thermal Fluid System Design. Cr. 4

Prereq: M E 4210, ENG 3060, and senior standing in AGRADE program. Design of thermal fluid systems to meet system performance requirements, system simulation, design optimization and economics limitations. Material Fee as indicated in the Schedule of Classes. (F,W)

##### 5360 Introduction to Computational Biofluidics and Heat Transfer. Cr. 4

Prereq: M E 3300, M E 4210. Basic numerical techniques for biofluidics and its applications. Use of techniques to improve surgical procedures; analysis of biofluidics applied to understanding disease. (F)

##### 5400 Dynamics II. Cr. 4

Prereq: M E 3400. Kinematics and rigid bodies in space. Classical particle solutions: central force, motion on a surface of revolution, spherical pendulum. Energy and momentum integrals. Equations of motion in general rotating coordinate frames. Euler angles, angular momentum and kinetic energy of rigid bodies. Fixed point motion, steady solutions. Applications to spatial motions of rigid bodies. Hamilton's Principle and Lagrange's equations of motion. Material Fee as indicated in the Schedule of Classes (F)

##### 5410 Vibrations II. Cr. 4

Prereq: M E 4410. Multidegree-of-freedom systems. Eigenvectors and eigenvalues and orthogonality of normal modes. Mode-summation method. Solution to forced vibrations by Laplace transforms, numerical methods and Continuous Systems Modeling Program (CSMP). Rayleigh's principle and Dunkerley formula for approximate frequencies. Torsional geared and branched systems. Lagrange's equations. Vibration of continuous systems: longitudinal and transverse vibrations of beams; torsional vibrations, vibrating string and membranes. (F)

##### 5425 Analysis of Vibration Movements and Instrumentation. Cr. 4

Prereq: M E 4410. Basic tools and instrumentation, such as spectral analyzers to measure and analyze vibration time histories of excitation and response signals (stationary or non-stationary) in the time and frequency domains. Fast Fourier transform, frequency time analyses. Material Fee as indicated in the Schedule of Classes (B)

##### 5440 Industrial Noise Control. Cr. 4

Prereq: senior standing or consent of instructor. Nature and origin of noise in mechanical systems and design for their control. Measurement of sound pressure levels, sound power levels, sound intensity levels, reverberation time, absorption coefficients of materials. (B:W)

##### 5460 Fundamentals in Acoustics and Noise Control. Cr. 4

Prereq: senior or graduate standing. Videotapes and multimedia materials on sound generation, propagation and interaction with solid boundaries. Fundamental theories of sound radiation and control; solving practical engineering noise and vibration problems. (B:F)

##### 5470 Creative Problem Solving in Design and Manufacturing. Cr. 4

Coreq: M E 4250 or equiv. Concepts of laws of natural development of engineering systems. Algorithm for inventive (creative) problem-solving (AIPS-85). Creative use of physical and geometrical effects in design of mechanical and manufacturing systems. Concepts of strength, stiffness, vibratory effects, reliability in mechanical design. (W)

##### 5490 Computational Multibody Dynamics. Cr. 4

Prereq: M E 3400 and M E 3480 or equiv. Modeling and time simulation of mechanical and dynamic systems using computational software. Applied kinematics and kinetics; constraints, elasticity, ODE and DAE solvers, eigenvalue analysis, control, reliability, system design, optimization, GD&T, vehicle dynamics. (F,W)

##### 5500 (WI) Advanced Engineering Design. Cr. 4

Prereq: B E 2550, M E 4250, ENG 3060. Open only to AGRADE students. Team work on semester-long project, design concepts to be developed using various design theories, students perform patent literature search, design, fabricate and test prototypes. Final written report and public presentation required. Satisfies Writing Intensive course requirement. Material Fee as indicated in the Schedule of Classes (F,W)

##### 5580 Computer-Aided Mechanical Design. Cr. 4

Prereq: M E 3480 or graduate standing in mechanical engineering. Aspects of constraint-based solid modeling and parametric modeling using software such as Unigraphics, Solid Edge, I-DEAS, Pro-E. Building intelligent solid models, application to data management and sheet metal design. Introduction to computer-aided simulation and manufacturing. (S)

##### 5600 Advanced Mechanics of Materials. Cr. 4

Prereq: M E 2400. Statically indeterminate problems. Force method. Displacement methods. The three-moment equation. Euler formulas for columns. Column formulas for concentric and eccentric loadings. Energy methods and applications. Unsymmetrical bending of beams. Shear center. Bending of curved bars. Thick-walled cylinders. Torsion of non-cylinders. Rotating discs. Torsion of non-circular shafts. Membrane analogy. (W)

##### 5610 Experimental Mechanics of Materials. Cr. 4

Prereq: M E 2400. Experimental characterization of mechanical behavior. Instrumentation and measurement of load, strain, deflection, etc., characterization of creep, fracture toughness, dynamic-mechanical response (damping and vibration). Statistical analysis of data. (W)

##### 5620 Fracture Mechanics in Engineering Design. Cr. 4

Prereq: M E 2400. Linear and nonlinear fracture mechanics principles and their applications to structural design. Stress-intensity factors, J-integral, CTOD concepts to develop fracture control plans. (Y)

##### 5700 Fundamentals of Mechanics. Cr. 4

Prereq: MAT 5070. Classical mechanics (Lagrangian and Hamiltonian applications); thermodynamics (derivation of thermodynamic laws from mechanics); continuum kinematics and basics of tensor analysis; continuum mechanics (basic laws; thermodynamics of continuum media; classical continuum models). Material Fee as indicated in the Schedule of Classes (F)

##### 5720 Mechanics of Composite Materials. Cr. 4

Prereq: M E 2400, senior standing. Analytical modeling of micromechanical and macromechanical behavior of composite materials. Stiffness, strength, hydrothermal effects, laminate analysis, viscoelastic and dynamic behavior. Experimental characterization of mechanical behavior. (F)

##### 5730 Tribology and Lubrication Technology. Cr. 4

Prereq: M E 2400. Friction, wear, and lubrication fundamentals: wear mechanisms, application of coatings, surface engineering fundamentals. (Y)

##### 5800 Combustion Engines. Cr. 4

Prereq: M E 2210 or equiv. Thermodynamics and cycle analysis of spark ignition, compression ignition, and gas turbine engines. Combustion processes in actual systems, performance characteristics, combustion abnormalities. Analysis of intake, fuel and exhaust systems. (F)

##### 5810 Combustion and Emissions. Cr. 4

Prereq: M E 5800; or consent of instructor. Fundamentals of emission formation in combustion systems, wall quenching and imperfect combustion, unburned hydrocarbons, carbon monoxide, aldehydes, nitrogen oxides, species stratification in the combustion chamber, particulates. Effect of design parameters and engine operating variables on emission formation. Emission controls and instrumentation.

(W)

##### 5820 Thermal Environmental Engineering. Cr. 4

Prereq: M E 4210. Design and analysis of heating, ventilating and air-conditioning systems. Moist air properties calculations, heat transfer and transmission coefficients, heating load, cooling load, heating equipment and cooling equipment, duct design, fans, air distribution, systems design and analysis, refrigeration principles. (S)

##### 5900 National Design Competition Projects. Cr. 1-4 (Max. 6)

Prereq: written consent of director of undergraduate studies or graduate students' adviser. (T)

##### 5990 Directed Study. Cr. 1-4 (Max. 6)

Prereq: senior or graduate standing; seniors: written consent of adviser and chairperson; graduates: written consent of adviser, chairperson, and Engineering Graduate Office for Master's students. Open only to seniors and graduate students. (T)

##### 5995 Special Topics in Mechanical Engineering I. Cr. 1-4 (Max. 8)

Prereq: consent of chairperson. Maximum of eight credits in special topics may be elected in any one degree program. Topics to be announced in Schedule of Classes. (I)

##### 6180 (BME 6480) Biomedical Instrumentation. (ECE 6180) (I E 6180) Cr. 4

Prereq: ECE 3300, BME 5010 or BMS 5550, and BME 5020. Engineering principles of physiological measurements. Signal conditioning equipment, amplifiers, recorders and transducers. Recent advances. (F)

##### 6450 Advanced Manufacturing Processes and Methods. (I E 6450) Cr. 4

Prereq: M E 3450, B E 2550, or consent of instructor. Review of novel manufacturing processes, methods and systems; emphasis on optimum design for manufacturability, technical, economic, and industrial limitations. Elements of computer-aided manufacturing, and numerical methods application. (W)

##### 6550 Modeling and Control of Dynamic Systems. Cr. 4

Prereq: M E 5540. Modeling and analysis of physical systems comprised of interconnected mechanical, electrical, hydraulic and thermal devices; bond graphs; introduction to state-space equations and closed loop system dynamics. Material Fee as indicated in the Schedule of Classes (W)

##### 6991 Internship in Industry. Cr. 1-4 (Max. 4)

Offered for S and U grades only. Written report describing internship experience. (T)

##### 7020 Finite Element Methods II. Cr. 4

Prereq: M E 5040. Continuation of M E 5040. Isoparametric elements, plate and shell elements. Dynamic analysis of structures. Hybrid variational techniques. Applications to solid mechanics, incompressible materials, heat transfer and fluid mechanics. Pre- and post-processing, use of computer graphics in analysis. (W)

##### 7100 (BME 7100) Mathematical Modeling in Impact Biomechanics. (ECE 7100) (I E 7100) Cr. 3-4

Prereq: M E 3400, and BME 5010 or BMS 5550; consent of instructor. Review of models created for impact simulations. Regional impact simulation models. Human and dummy models subject to various restraint systems. (W)

##### 7160 (BME 7160) Impact Biomechanics. (ECE 7160) (I E 7160) Cr. 4

Prereq: M E 2400, and BME 5010 or BMS 5550. Biomechanical response of the body regions and the whole body to impact. Mechanisms of injury in blunt impact. Effects of restraints on injury reduction. Development of test surrogates such as dummies. Material Fee as indicated in the Schedule of Classes (I)

##### 7180 (BME 7300) Advanced Topics in Biomaterials and Tissue Mechanics. (MSE 7180) Cr. 4

Prereq: BME 5210 or 5370. Seminar format: advanced topics presented to the class; lectures by the instructor and by the participants based on literature reviews. Topics determined by student interest.

(B)

##### 7195 (BME 7210) Tissue Biomechanics. Cr. 4

Prereq: BME 5010 or BMS 5550; BME 5020, BME 5210. Tissue-level mechanical properties. Analytical models of hard and soft tissue mechanics. Soft tissue viscoelasticity, quasilinear viscoelasticity and biphasic theory. Wolff's law and bone remodeling, bone fatigue and microfracture. Form and function relationships from microstructure to macrostructure. Application of theoretical models to experimental data sets. (B:F)

##### 7200 Advanced Thermodynamics and Combustion. Cr. 4

Prereq: M E 4210 or consent of instructor. Postulational basis of thermodynamics; potentials and transformation theory; method of calculating properties from basic data. Introduction to statistical thermodynamics; calculation of properties of gases and plasmas; equilibrium mixture calculations. Advanced energy analysis of systems. (F)

##### 7260 Heat and Mass Transfer. Cr. 4

Prereq: M E 4200. Formulation of heat and mass transfer problems; lumped, differential and integral formulations. Solution of problems using the method of separation of variables, partial solutions, variation of parameters, superposition and Laplace transformation. Applications in different thermal and combustion systems. (F)

##### 7290 Advanced Combustion and Emissions I. Cr. 4

Prereq: M E 3200 and 4200 or consent of instructor. Flame propagation theories, structure or pre-mixed hydrocarbon flames, mathematical formulations for flame propagation and emission formation in homogenous mixtures in engines. Material Fee as indicated in the Schedule of Classes (W)

##### 7300 Advanced Fluid Mechanics. Cr. 4

Prereq: M E 5300 or consent of instructor. Tensor derivation of conservation laws, transport theorem. Thermodynamics of continuous media and constitutive equations. Kinematics of vorticity, dynamics of flows; perfect fluids, compressibility effects. (F)

##### 7310 Computational Fluid Mechanics and Heat Transfer. Cr. 4

Prereq: M E 5300 or consent of instructor. Introduction to numerical techniques for the solution of inviscid and viscous compressible and incompressible flows and the use of existing algorithms and mathematics libraries. (W)

##### 7400 Advanced Dynamics. Cr. 4

Prereq: M E 5400. Modeling and development of governing equations of motion for discrete and continuous systems. Generalized coordinates. Principle of virtual work and Hamilton's theorems; Jacobi's integral and Routhian functions. Hamilton's canonical equations and Gibbs-Appell equations. Kinematics of deformable bodies and strains. Stress components and constitutive equations. Formulation of equations of motion for deformable bodies by Hamilton's Principle. Introduction to the stability of dynamic systems. Material Fee as indicated in the Schedule of Classes (W)

##### 7410 Vibrations of Continuous Systems. Cr. 4

Prereq: M E 5400, 5410, 5600. Various exact and approximate solution methods for analyzing the vibrations of continuous systems. (B)

##### 7420 Random Vibrations. Cr. 4

Prereq: M E 5410. Mathematical description of stochastic processes. Response analysis of mechanical systems. Frequency response, spectral density, filters. (I)

##### 7451 Advanced Manufacturing II: Material Forming. Cr. 4

Prereq: M E 3450, 5700, or consent of instructor. Fundamental plasticity and mechanics of forming, various forming processes; classical theory and recent progress in the field; focus on autobody manufacturing. (B:F)

##### 7452 Laser Technology in Engineering. Cr. 4

Prereq: graduate standing in engineering. Principles of lasers; various types, applications in material processing such as cutting, joining, surface treatment; laser system operations, maintenance and safety practice. (F)

##### 7460 Advanced Acoustics and Noise Control. Cr. 4

Prereq: M E 5000 or equiv., 5460 or consent of instructor. State of the art technologies in acoustic radiation, numerical algorithms, and software packages used in manufacturing industries, and their application to noise, vibration and harshness (NVH) related problems.

(B:W)

##### 7480 Nonlinear Vibration. Cr. 4

Prereq: M E 5410, 7400. Classification of nonlinearities in mechanical systems and their qualitative effect on their dynamic response. Phase portrait, concept of limit cycle, Duffing's and Van der Pol oscillators, and parametric vibration. Harmonic balance, averaging methods, and multiple scales methods. Nonlinear modal interaction and chaotic dynamics. (B:W)

##### 7550 Control of Dynamic Systems. Cr. 4

Prereq: M E 6550 or consent of instructor. Analysis and control of linear dynamic systems using state-space equations; stability, controllability, observability, modal control. Analysis and synthesis of nonlinear systems; describing functions, limit cycles, stability, introduction to adaptive control. Material Fee as indicated in the Schedule of Classes (W)

##### 7590 Nonlinear Control Systems. (ECE 7420) Cr. 4

Prereq: M E 5550 or ECE 5470. Review of nonlinear control problems in industries, analysis of nonlinear systems using phase plane, Lyapunov describing function methods, design of nonlinear controllers, applications to the control of robots, aircrafts and automotives. (W)

##### 7610 Theory of Elasticity. Cr. 4

Prereq: M E 5700 or consent of instructor. Boundary value problems of linear elasticity. Variational principles in linear elasticity. Theory of beams, plates and shells. Homogenized description of composite materials. Material Fee as indicated in the Schedule of Classes (F)

##### 7680 Manufacturing Processing Mechanics. Cr. 4

Prereq: M E 5040. Electric packaging, composite curing, metal forming; modeling and verification by laser based techniques. (Y)

##### 7720 Advanced Mechanics of Composite Materials. Cr. 4

Prereq: M E 5720. Review of tensor notation with application to stress strain and constitutive equations. Analytical models for viscoelastic and dynamic behavior of anisotropic composite materials and structures. Experimental characterization of viscoelastic and dynamic behavior. (Y)

##### 7820 Engineering Non-Destructive Evaluation (NDE) Methods and Industrial Applications. Cr. 4

Prereq: M E 4500. Basic and state-of-the-art methods utilized in NDE work at various engineering industries, enriched by hands-on laboratory work, audio visual and research projects as well as interaction with local industry. (Y)

##### 7850 Dynamics and Vibration of Automotive Engines. Cr. 4

Prereq: M E 3410 and 5800. Kinematics, dynamics and balance of reciprocating engines, engine mounts and torsional vibrations of powertrains. (Y)

##### 7990 Directed Study. Cr. 1-4 (Max. 4)

Prereq: written consent of adviser, chairperson and engineering graduate officer for master's students; written consent of adviser, chairperson and Dean of Graduate Studies for Ph.D. students. Student selects some field of engineering for advanced study and instruction. (T)

##### 7995 Special Topics in Mechanical Engineering II. Cr. 1-4

Prereq: consent of chairperson. Maximum of six credits in Special Topics in any one degree program. A consideration of special subject matter in engineering. Topics to be announced in Schedule of Classes. (I)

##### 7996 Research. Cr. 1-4 (Max. 4)

Prereq: consent of chairperson and adviser. A combined experimental and analytic study of a problem in a special field of engineering.

(T)

##### 7997 Mechanical Engineering Graduate Seminar. Cr. 0

Prereq: graduate standing. Offered for S and U grades only. Advanced concepts in mechanical engineering; presentation of research results and current developments. Written reports required. (F,W)

##### 8020 Crashworthiness and Occupant Protection in Transportation Systems. Cr. 4

Prereq: M E 5160, 7100, 7020. Crashworthiness and occupant safety facts, computational environment influences, review of federal motor vehicle safety regulations, windshield impact response, modeling and simulation of restraint system, occupants, energy management, and barrier crash tests. (B)

##### 8290 Advanced Combustion and Emissions II. Cr. 4

Prereq: M E 7290 or consent of instructor. Heterogeneous combustion theories, diffusion flames, droplet combustion, spray combustion, mechanisms of emission formation in compression ignition, stratified charge and gas turbine engines. (I:F)

##### 8300 Advanced Topics in Fluid Mechanics. Cr. 4

Prereq: M E 5300. Advanced topics in fluid flow with heat and mass transfer. Review of analytical methods and conservation laws. Linear and nonlinear hydrodynamic instability. Dynamical systems and chaos in fluid flow. (B:F)

##### 8999 Master's Thesis Research and Direction. Cr. 1-8 (8 req.)

Prereq: consent of adviser. (T)

##### 9990 Pre-Doctoral Candidacy Research. Cr. 1-8 (Max. 10)

Prereq: consent of department. For Ph.D. program applicants. Offered for S and U grades only. Research in preparation for doctoral dissertation. (T)

##### 9991 Doctoral Candidate Status I: Dissertation Research and Direction. Cr. 7.5

Prereq: consent of dissertation adviser; Ph.D. candidate in department. Required in academic-year semester following advancement to Ph.D. candidacy. Offered for S and U grades only. (T)

##### 9992 Doctoral Candidate Status II: Dissertation Research and Direction. Cr. 7.5

Prereq: consent of dissertation adviser; M E 9991. Required in academic-year semester following 9991. Offered for S and U grades only. (T)

##### 9993 Doctoral Candidate Status III: Dissertation Research and Direction. Cr. 7.5

Prereq: consent of dissertation adviser; M E 9992. Required in academic-year semester following 9992. Offered for S and U grades only. (T)

##### 9994 Doctoral Candidate Status IV: Dissertation Research and Direction. Cr. 7.5

Prereq: consent of dissertation adviser; M E 9993. Required in academic-year semester following 9993. Offered for S and U grades only. (T)

##### 9995 Candidate Maintenance Status: Doctoral Dissertation Research and Direction. Cr. 0

Prereq: consent of dissertation adviser; completion of 30 credits in

M E 9991-9994. Offered for S and U grades only. (T)