2 Year

OBJECTIVES

LEARNING OUTCOMES: The goal of this course is to provide the student with basic knowledge of the mechanics of linearly elastic structures and of the strength of materials. By completing this class successfully, the student will be able to compute simple structural elements and reasonably complex structures.

KNOWLEDGE AND UNDERSTANDING: At the end of this course, the student will be able to:

• compute constraint reactions and internal actions in rigid-body systems and beams subjected to point/distributed forces and couples
• compute centroid position and central principal second-order moments of area distributions
• understand the formal structure of the theory of linear elasticity for both discrete and continuous systems (beams and 3D bodies)
• analyze strain and stress states in 3D bodies
• compute the stress state in beams subjected to uniaxial bending, biaxial bending, eccentric axial force
• understand the behavior of beams subjected to shear with bending and torsion
• understand how to compute displacements/rotations in isostatic beam systems, how to solve statically underdetermined systems, how to apply yield criteria, and how to design beams against buckling

APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding skills developed during the course to the analysis of practical problems. This includes the analysis of linearly elastic structures and structural members in terms of strength and stiffness.

MAKING JUDGEMENTS: The student will have to demonstrate his awareness of the modeling assumptions useful to describe and calculate structural elements, as well as his critical judgment on the static response of elastic structures under loads, in terms of stresses, strains, and displacements.

COMMUNICATION SKILLS: The student will demonstrate, mostly during the oral test, his capacity of analyzing and computing the static response of linearly elastic structures, as well as his knowledge of the underlying theoretical models.

LEARNING SKILLS: The student will get familiar with the modeling of structures and structural elements in practical problems, mostly during the development of his skills for the written test. This mainly concerns discrete systems, beams, and three-dimensional bodies.

COURSE SYLLABUS

• Review of basic notions of vector and tensor algebra and calculus.
• Kinematics and statics of rigid-body systems.
• Geometry of area distributions.
• Discrete linearly elastic systems, static-kinematic duality, solution methods.
• Strain and stress in 3D continuous bodies and beam-like bodies.
• Virtual power and virtual work equation for discrete systems, beams, and 3D bodies.
• One-dimensional beam models: Bernoulli-Navier model, Timoshenko model, constitutive equations, governing differential equations.
• Constitutive equation for linearly elastic and isotropic bodies, material moduli.
• Hypothesis in linear elasticity, equilibrium problem for linearly elastic discrete systems, beams, and 3D bodies.
• Three-dimensional beam model: the Saint-Venant problem, uniaxial and biaxial bending, eccentric axial force, shear and bending, torsion.
• Elastic energy of beams and 3D bodies, work-energy theorem, Betti’s reciprocal theorem, Castigliano’s theorem.
• Yield criteria (maximum normal stress, maximum tangential stress, maximum elastic energy, maximum distortion energy).
• Buckling instability, bifurcation diagrams, load and geometry imperfections, Euler buckling load, design against buckling.
• Basic notions on the finite element method and structural analysis software.

OBJECTIVES

COURSE SYLLABUS

• Classification of electrical systems and requirements.
• Analysis of transitory and frequency behavior.
• Distortion in electronic systems and Bode diagrams.
• Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field-Effect Transistors.
• Biasing techniques for Transistors. Amplifiers classification, analysis and circuit design.
• Frequency response of single and cascaded amplifiers.
• Differential amplifiers and Cascode.
• Current mirrors.
• Feedback amplifiers and stability issues. Power amplifiers.
• Operational amplifiers and related applications.
• Oscillator circuits. Integrated circuits and voltage waveform generators.

OBJECTIVES

LEARNING OUTCOMES: Learning the basic elements of Electromagnetism and fundamental physical principles of quantum mechanics.

KNOWLEDGE AND UNDERSTANDING:
Knowledge of the basic principles of electromagnetism and quantum mechanics useful for the own field of study. Understanding of advanced books on the arguments treated during the course.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Capacity to develop autonomously basic conceptual ideas using arguments treated during the course.

MAKING JUDGEMENTS:
Capacity to evaluate autonomously ideas or project using the knowledge acquired in the course.

COMMUNICATION SKILLS:
Capacity to share informations and ideas on the basis of knwoledge acquired in the course.
Comprehension of specific problems and relative solutions proposed.

LEARNING SKILLS:
The knowledge acquired in the course must be of help for the student in future courses, improving the capacity of autonomous learning.

COURSE SYLLABUS

1) Electric Charge and Electric Field : Conductors, Insulators, and Induced Charges.
Coulomb’s Law. Electric Field and Electric Forces. Electric Field Lines. Charge and Electric Flux, Gauss’’ s Law. Charges on Conductors.
2) Electric Potential: Electric Potential Energy, Electric Potential, Equipotential Surfaces, Potential Gradient. Definition of electric dipole. Approximated formula for the electric potential of a dipole at large distances.
3) Capacitors and Capacitance. Capacitors in series and parallel configuration. Electrostatic Potential Energy of a Capacitor. Polarization in Dielectrics. Induced Dipoles. Alignment of Polar Molecules. Electric Field inside a dielectric material. Relative dielectric constant. Capacitors with dielectric materials.
4) Electric current, Vector current density J, Resistivity (ρ) and conductivity ( σ) of materials, Ohm’s law in vector and scalar form, Resistors and resistance, Microscopic theory of electric transport in metals (Drude model). Differences between thermal velocity and drift velocity of charge carriers. Thermal coefficient of resistivity for metal and semiconductors. Resistors in parallel. Kirchhoff current law and the conservation of charge. Resistors in series. Kirchhoff voltage law ( KVL) and the conservative nature of electric field. Resistor and capacitor in series. Charging a capacitor. Solving the equation for current and voltage in RC circuits, time constant.
5) Introduction to magnetism, historical notes. Magnetic Force on a moving charged particle in a Magnetic Field. Definition of the vector ( cross ) product. Vector product expressed by the formal determinant and calculated by Sarrus Rule. Thomson’s q/m experiment and the discovery of the electron. Magnetic force on a current carrying conductor. Local equation for the magnetic force, the second formula of Laplace. Introduction to current loops, the torque. Force and Torque on a current loop in presence of a constant magnetic field. The magnetic dipole moment. Torque in vector form. Stable and unstable equilibrium states. Equivalence between a magnetic dipole of a current loop and the dipole of a magnet. Potential energy of a dipole moment in a magnetic field. Force exerted on a magnetic dipole in a non-uniform magnetic field. Working principle of a dc motor. Generalization of a magnetic dipole to current loops with irregular area. Magnetic dipole of a coil consisting of n loops in series. The Hall effect.
6) Historical introduction to the Biot Savart Laplace equation. Electric current as sources of magnetic field, the current element. The Biot Savat Laplace (BSL) equation. BSL equation for an infinitely long wire with an electric current flow. The flux of the magnetic field B. The Gauss Law for the magnetic field. Forces acting on wires with electric current flow. Magnetic field on the axis of a current loop and a coil. Ampere Circuital Law. Definition of a Solenoid. Magnetic field from a long cylindrical conductor. Magnetic field from a toroidal coil. The Bohr magneton. Magnetic materials. Paramagnetism, Diamagnetism, Ferromagnetism.
7) Magnetic induction experiments. Faraday Law. Lenz Law. Flux swept by a coil and Motional Electromotive Force. Induced Electric Field. Displacement current. The four Maxwell equations in integral form. Symmetry of the Maxwell equation. Self induction. Inductors. Inductor as circuit element.Self inductance of a coil. Magnetic Field Energy. The R-L circuit. The LC circuit. The RLC series circuit.
8) The electromagnetic waves. Derivation of EM waves from Maxwell Equation. The electromagnetic spectrum. Electromagnetic energy flow and the Poynting vector. Energy in a sinusoidal wave. Electromagnetic momentum flow. Standing Electromagnetic waves.
9) Light waves behaving as particles. The photocurrent experiment. Threshold frequency and Stopping Potential. Einstein’s explanation of Light absorbed as “Photons”. Light Emitted as Photons: X-Ray Production. Light Scattered as Photons: Compton Scattering.
10) Interference and diffraction of waves. The Wave Particle Duality. De Broglie wavelength. The x-ray diffraction from a crystal lattice, the Bragg’s Law. The electron diffraction experiment of Davisson and Germer. The double slit experiment with electrons. Waves in one dimension: Particle Waves, the one-dimensional Schrödinger equation. Physical interpretation of the Wave Function. Wave Packets. Uncertainty principle. Particle in a box. Energy-levels and wave functions for a particle in a box. The tunneling effect.