# Subjects

**Mechanical Sciences and Dynamic Systems**

**MATERIALS SCIENCE FUNDAMENTALS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Introduction to Materials Science. Chemical bonds. Atomic arrangements. Crystallography and X-ray Diffraction. Structural Imperfections. Microstructure. Diffusion. Phase Diagrams. Crystal Growth. Structure and Properties of Polymeric Materials. Structure and Properties of Ceramic Materials. Structure and Properties of Composite Materials. Electronic Properties of Materials. Thermal Properties of Materials. Optical Properties of Materials.

**PROPERTIES AND STRUCTURE OF MATERIALS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Introduction to Materials: Types of Materials; Structure-Properties Relationship Processing; Environmental Effect on Materials Behavior; Selection of Materials. Atomic Structure. Atom Composition; Electronic Structure; Periodic Table; Atomic Bond; Binding Energy and Interatomic Spacing. Atomic Arrangement: Short Range x Long Range Order; Unit cells; Miller Indexes (Points, Directions and Plans); Interstices; Ionic crystals; Covalent structures. Crystal Network Imperfections: Point Defects; Line Defects; Surface Defects; Influence of Crystalline Structure; Control of the Sliding Process. Types of Materials, Their Structures and Applications: Metallic Materials; Ceramic Materials; Polymeric Materials; Composite Materials; Semiconductor Materials.

**EXPERIMENTAL TENSION ANALYSIS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Stress and strain analysis; stress-strain ratio; equilibrium equations; fundamental concepts in stress and strain measurements; basic equations of elasticity theory. Experimental techniques: simulations, photoelasticity, extensometry, residual stress, moiré and shadow moiré. Software applications in practical problems.

**MECHANICAL BEHAVIOR OF MATERIALS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Elastic behavior of materials, Principles of plasticity theory, Plastic deformation in single crystals, Disagreement theory, hardening mechanisms, mechanical testing of materials, Fluency and relaxation, plastic conformation of metals.

**MATERIAL TECHNOLOGY**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Classification and selection of materials and their applications. Relationships between microstructure and material properties. Material processing. Economic, social and environmental aspects in the use of materials. Specification of materials against industrial processes.

**FINITE ELEMENTS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Initial and boundary value problems: Laplace and Poisson differential equations and plane elasticity problems. Weak and strong formulation of the weighted residue method. Variational methods. Finite element methods.

**COMPUTATIONAL METHODS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Numerical systems and errors. Resolution of systems of linear equations. Eigenvalues and eigenvectors. Finite element method and finite difference method applied. Function optimization. Gradient based methods. Evolutionary methods. Formulation of structural optimization problems. Application of numerical methods to solve engineering problems.

**EXPERIMENTAL TECHNIQUES IN MECHANICAL ENGINEERING**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Basic principles of model analysis. Uncertainty analysis. Statistical treatment. Statistical and dynamic characteristics of the instruments. Transducer operating principles. Signal conditioning. Measurement of force, torque and deformation. Pressure and temperature measurement. Fluid flow measurement. Static and dynamic data acquisition and signal processing systems.

**CONTROL OF MULTIVARIABLE SYSTEMS**

**Mandatory**: Yes

**Workload**: 60

**Credits**: 4

**Syllabus**: Systems Representation: Block diagrams; Determination of Global Transfer Function; Simulation diagrams; Signal Flow Charts; Dynamic Matrix A Diagonalization; Transformation of a Dynamic Matrix A into the AssociatedPartner Form. Control System Features: Routh Stability Criterion; Nyquist Stability Criteria; Gain and Phase Margins; System Types; Frequency Response Analysis; Goat Diagrams; Nichols Chart; Root Location Theory. Structural Properties of Multivariable Linear Control Systems. Synthesis of Multivariable Linear Regulators, Observers, and Followers Using Full Assignment of the Autostructure.

**RESEARCH METHODOLOGY AND SCIENTIFIC WRITING**

**Mandatory**: Yes

**Concentration Area(s)**: Common Core

Mechanical Sciences and Dynamic Systems

**Workload:**30

**Credits**: 2

**Syllabus**: Thesis preparation: theme, bibliographic review, file, preliminary project. Dissertation structure: introduction, development, conclusion. Editorial uniformity: Tables, figures, abbreviations, bibliographic references. Graphic uniformity: graphic forms and layouts. Complementary elements: summary, cover page, participation in seminars of notable invited professionals and presentation of an individual seminar chosen by the student and his advisor related to the future thesis.

**BIOMATERIALS**

**Mandatory**: No

**Workload**: 60

**Credits**: 4

**Syllabus**: Definition of biomaterials. Biocompatibility essays, surface chemistry of implant materials. Ceramic Materials. Polymers. Metals and composites. Important applications of these materials.

**CORROSION ASSOCIATED WITH MECHANICAL EFFORTS**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**: Metallurgical and mechanical factors in corrosion. Corrosion under tension: intergranular and transgranular. Fatigue corrosion. Embrittlement under hydrogen. Corrosion with erosion, cavitation. Corrosion under friction. Liquid metal embrittlement.

**POLYMER SCIENCE**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**:

Chemical structure. Ways to express molar mass. Degree of polymerization. Thermoplastics and thermosets. Polymers in solution. Solubility parameters. Thermodynamics of polymers in solution. Phase balance. Methods to determine molar mass of polymers in solution. Solid state polymer. Degree of crystallinity and crystallization kinetics of polymers.

**FOUNDATIONS OF MATHEMATICAL METHODS**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**:

Fundamentals of Set Theory. Metric spaces. Fixed point theorem; compact sets. Linear spaces, Banach space. Linear functions; dual spaces. Measurement theory: Jordan and Lebesgue measures, measurable functions. Lebesgue Integral; Fubini's theorem. Hilbert space, linear operating equations. Inverse function and implicit function theorems. Distributions: generalized Green formula. Sobolev's space; Sobolev's identity; decomposition theorem. Hilbert spaces and their duals. Trace theorem. Intermediate spaces; interpolation of spaces.

**STATISTICAL METHODS**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**:

Error theory. Errors in Experimental Activity. Statistical Modeling of Measurement Error. Linear Regression and Correlation. The Least Squares Method. Analysis of Variance. Significance Tests. Special Topics in Data Analysis in Engineering.

**CHARACTERIZATION OF MATERIALS AND SEMICONDUCTORS**

**Mandatory**: No

**Workload**: 30

**Credits**: 2**Syllabus**: Infrared Spectroscopy, Raman, Ultraviolet-Visible, Nuclear Magnetic Resonance, Atomic Spectroscopy, Chromatography, Mass Spectroscopy, Thermal Analysis. Basic concepts of solid state electronics. Physical Properties of Materials. Crystalline semiconductor materials. PN diode junction. Bipolar transistor (NPN and PNP). Metal-Oxide-Semiconductor (MOSFET) Field Effect Transistor. Junction Field Effect Transistor (J-FET). Diacs, Thyristors and Triacs. Amorphous semiconductor materials.

**MECHANICAL VIBRATIONS**

**Mandatory**: No

**Workload**: 60

**Credits**: 4

**Syllabus**: Free and forced response of dynamic systems with one degree of freedom. Systems analysis with two degrees of freedom. Systems analysis with multiple degrees of freedom. Exact and approximate solution of continuous systems. Computational methods in vibration analysis.

**DYNAMIC SYSTEMS**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**: Mathematical description of mechanical models: kinetics and kinematics of continuous and hybrid mechanical systems. Point system kinematics, coordinate transformation, relative motion, rigid body kinematics. Dynamics Fundamentals: Newton, D'Alembert, Lagrange and Hamilton equations of motion. Introduction to variational principles. Flexible multibody system dynamics: hybrid generalized coordinates and generalized Lagrange equation. Applications of symbolic computing in the modeling of multibody systems and application of the finite element method.

**SPECIAL TOPICS IN MECHANICAL ENGINEERING**

**Mandatory**: No

**Workload**: 30

**Credits:**2

**Syllable**: To be defined, covering advanced topics of interest in the area of Mechanical Engineering.

**Bibliography**: To be defined.

**TRIBOLOGY**

**Mandatory**: No

**Workload**: 30

**Credits**: 2

**Syllabus**: Tribology is the science and technology concerned with the interaction of surfaces with relative motion, including friction, wear and lubrication. Friction, wear and lubrication is a triad that an engineer will always encounter at every stage of a project's development. Understanding the nature of these phenomena, their consequences, and ways to control their effects are fundamental to modern engineers.

**DYNAMIC STRUCTURE ANALYSIS METHODS**

**Mandatory**: No

**Workload**: 60

**Credits**: 4

**Syllabus**: Principles of Newtonian Dynamics. Analytical Dynamics: methods based on energy. Systems of varying degrees of freedom - matrix formulation and modal analysis. Congruous Systems. Approximate Methods. Introduction to the Finite Element Method for Vibration Analysis.