Fundamentals of Fluid dynamics, airfoil properties, standard atmosphere.
Potential flows: 2D and 3D theories; 2nd Green theorem and boundary integral methods; The BEM approach.
Infinite incompressible wings: Glauert theory.
Finite wings: Prandtl theory and lifting surface theory.
Incompressible boundary layer theories: Falkner-Skan and Von Karmann integral equation.
Turbulence: general equations, RANS approach and modelling, Kolmogorov theory.
Fundamentals of Computer Fluid Dynamics.

Notes provided by the teacher

Other suggested tests:
Anderson, Jr. J.D. , Fundamentals of Aerodynamics, 2nd Edition, McGraw Hill, 1991.
Mattioli E. Aerodinamica, Levrotto e Bella, Torino, 1989.

The Aircraft Structures course is part of the activities of the Constructions and aerospace structures (ING-IND/04 SSD).

The teaching program is structured to provide students with knowledge and skills in the structural design of aeronautical components, using methods widely used in the aircraft conceptual and preliminary design phases.

The teaching program is divided into 36 lectures (equal to 9 CFU) divided into the following five main sections:

1) Beam theory: bidirectional bending, torsion, torsion of closed thin-walled beams ( Bredt-Batho theory), torsion of open thin-walled beams, shear of open and closed thin-walled beams (shear center), torsion and shear of multicell thin-walled beams, tapered beams.

2) Introduction to aircraft design and semi-monocoque structures: failure criteria of fragile and ductile materials, loads acting on aircraft, regulations for aircraft design, box-wing concept, fuselage structure, fuselage, and box-wing stress and strain analysis, structural idealization.

3) Thin plates Kirchhoff's theory: in-plane problem, bending problem, eigenfunctions method for simply supported plates.

4) Introduction to structural instability: buckling of the beam (Euler's critical load); buckling of thin plates; buckling on aeronautical structures.

5) Thin shells: shells in the form of a surface of revolution and loaded symmetrically with respect to their axis, pressurized fuselage stress analysis.

- T.H.G. Megson, Aircraft Structures for Engineering Students, Arnold, London, 1999 (for contents 1, 2, 3 and 4 of the syllabus)

- C.T. Sun, Mechanics of Aircraft Structures, John Wiley & Sons, New York, 1998 (for contents 1, 2, 3 and 4 of the syllabus)

- S.P. Timoshenko, Theory of Plates and Shells, McGRAW-hill, 1959 (for contents 3 and 5 of the syllabus)

- Lectures notes by the teacher (for all the contents of the syllabus)

The educational material used by the teacher from time to time is indicated during lectures. The lecture notes are made available on the Moodle platform to facilitate their use for both attending and non-attending students. On the same platform, are also made available the specifications of the project the students have to perform during the year, as well as a collection of written tests of previous exams, to provide students with a valid and realistic test bench for the final exam.

AIRCRAFT:
Trim and static stability
Maneouvrability
Controls effectiveness
General equations of dynamics
Stability derivatives
Flight stability
Response to controls
Flight control systems
ELICOTTERO:
Overview
Controls
Inflow models
Performance
Rotor dynamics

B. Etkin & L.D. Reid "Dynamics of flight - Stability and Control", John Wiley and Sons
D. McLean "Automatic Flight Control Systems", Prentice Hall
G. D. Padfield, "Helicopter Flight Dynamics", Blackwell Science
M. Arra, "L'elicottero", Biblioteca Tecnica Hoepli

Elements ofGasDynamics
Review of fundamental principles. Governing equations of compressible fluid flow.
Steady 1-D isentropic flow with area change, with friction and with heat transfer.
Normal shock waves, oblique shock waves, hodograph shock polar, reflection and interaction of oblique shock waves.
Expansion waves.
Flow with small perturbations.
Introduction to the method of characteristics.

Elements of Propulsion
Theory of propulsion.
Aircraft gas turbine engine, cycle analysis of engines.
Engine performance analysis: gas generator, turbojet engine, turbojet with afterburning, turbofan engine with separate exhaust nozzles, turbofan with afterburning with mixed flow exhaust stream, turboprop engine, ramjet.
Turbomachinery, inlets, nozzles and combustion systems. Propellers. Reciprocating engines.
Chemical rockets: propellants and combustion, thrust chamber and nozzles.

M.J. Zucrow, J.D. Hoffman “Gas Dynamics, vol. I ”John Wiley & Sons, 1976
M.J. Zucrow, J.D. Hoffman “Gas Dynamics, vol. II” Robert E Krieger Publishing Company, 1985
J. D. Mattingly “ Elements of Gas Turbine Propulsion” McGRAW-HILL Int. Edition 1996
A.H. Lefebvre “Gas Turbine Combustion” Taylor & Francis, 1999

1. Fundamentals of matrices and vector spaces
Operations between matrices and between matrices and vectors, properties of matrices. Determinant and its properties (Binet theorem), inverse matrix, rank of a matrix. Vector spaces: bases, base change, similar matrces, orthogonal matrices, Gram-Schmidt orthogonalization.

2. Eigenvalues and eigenvectors of matrices
Definitions; algebraic and geometric molteplicity. Properties of eigenvalues. Diagonalization of a matrix. Properties of symmetric and non-symmmetric matrices. Left eigenvectors, dual basis. Jordan normal form. Generalized eigenvalues and eigenvectors.
3. Solution of linear equation systems
Generalities. Iterative methods. Convergence algorithms. Direct methods: Gauss elimination. Least square solution for oversized systems.
4. Solution of nonlinear equation systems
Root separation. Iterative methods. Method of Newton-Raphson. Convergence criteria.
5. Method of solution for ordinary differential equation systems
Canonical form of ordinary differential equation systems. Methods of solution: (i) spectral representation, (ii) diagonalization, (iii) direct integration through convolution integral.

6. Frequency domain solution of ordinary differential equation systems
Laplace transform. Frequency response function. Impulse, indicial, harmonic responses.
7. Finite-difference methods for solution of ordinary differential equations
Fundamental concepts, first and second order finite differnce formulas. Backwards, forwards, central finite difference formulas. Accuracy order. Arbitrary point finite-difference formulas. Global and truncation errors Methods of Euler (implicit and explicit), and Crank-Nicholson.
8. Numerical integration
Generality; formulas from interpolating polynomials: Newton-Cotes, trapeziodal and Cavalieri-Simpson rules. Degree of precision of integration from interpolating polynomials. Gauss-Legendre quadrature rules and their degree of precision.

9. Calculus of variation
Definition of a functional. Eulero-Lagrange equations. The problem of the brachistocrone. The problem of a beam on elastic soil. Riccati equation for optimal control.

10. Methods for the solution of partial differential equation systems
Eigenfunctions and eigenvalues of a linear operator. Adjoint and self-adjoint operators. Eigenfunction method. Free vibration modes and frequencies. Rayleigh-Ritz and Galërkin methods.

11. Generalized curvilinear coordinates
Covariant and contravariant base vectors. Relations between dual bases. Differential operators on vectors expressed in covarian and contravariant components.

F.B. Hildebrand, “Methods of Applied Mathematics”, Dover Publications, NY, 1992.
A.D. Aleksandrov, A.N. Kolmogorov, M.A. Lavrent'ev, “Mathematics: Its Content, Methods and Meaning”, The MIT Press, Cambridge, Massachusetts, Sixth Edition, 1989.
J.D. Hoffman, ``Numerical Methods for Engineers and Scientists'', McGraw-Hill, Seconf Edition, 1992.

An introduction to the 2 dofs semi-rigid wing model, and derivation of the governing equations through application the Lagrangian formulation. Steady and quasi-steady, 2D, aerodynamic models for the aeroelastic analysis of the semi-rigid wing model. Study of aeroelastic flutter and divergence.

Theodorsen theory for 2D unsteady aerodynamics. V-g method for flutter analysis. Padè approximants of the `lift deficiency function' and related finite-state aeroelastic model. Correlation between Theodorsen theory and Wagner theory.

Aeroelastic modelling of 3D wings: bending-torsion structural dynamics model, `strip theory' aerodynamic model and application of the Galerkin method. Extension to swept wing analysis. Aeroelastic stability analysis.

Unsteady, 3D aerodynamics: incompressibe, inviscid flows; diffferential formulation for quasi-potential incompressible flows; boundary integral formulation for quasi-potential flows and panel method for its numerical solution. Definition of the aerodynamic matrix for aeroelastic stability analysis. Rational matrix approximation of the aerodynamic matrix, corresponding finite-state aeroelastic model and flutter analysis.

Aeroelastic model of wing section with trailing-edge flap. Actuation of flap for flutter suppression, as derived from application of optimal control theory with inclusion of an observer.

Bisplinghoff, R.L., Ashley H., Halfman, R., Aeroelasticity. Dover Publications, 1996.
Fung, Y.C., An Introduction to the Theory of Aeroelasticity. Dover Publications, 1994.
Wright, J.R. and Cooper, J.E., Introduction to Aircraft Aeroelasticity and Loads. Wiley and Sons, 2007.
Dowell, E.H., A modern course in aeroelasticity. Kluwer Academic Publishers, 2004.
Hodges, D.H. and Pierce, A., Introduction to Structural Dynamics and Aeroelasticity. Cambridge Aerospace Series, 2002.

Fundamentals:
Mechanics of fluids: Incompressible and compressible conservation laws, dimensional analysis, asymptotic solutions. Sound Field; Wave equation for fluids, speed of sound and acoustic energy; Diffraction; Geometrical acoustics; waves in solids; Sound frequency analysis; Decibel and Sound Pressure Level; Acoustic Filters; Sound fields summation; Interference and frequency contents.

Waves equation
Wave equation in a field without sources; Simple and harmonic solutions; Sound Intensity; Energy and specific energy; waves reflection and transmission; Sound generation and transmission mechanisms. Sound sources: Monopole; Dipole; Quadrupole.

Digital signal processing and probability fundamentals.

Acoustic measurement facilities
Anechoic chambers; reverberant chambers.

Quantitative measures of sound
Mathematics fundamentals; Fourier analysis; Measurements systems; acoustic sources characterization by means of microphone measurements.

Experimental techniques for turbulent flows measurements
Hot wire anemometry. Single and multi components; Laser Doppler Anemometry; Particle Image Velocimetry; Laser Induced Fluorescence.

Optical methods for the analysis of density fields
Interferometry, Schlieren, Shadowgraph.

Measurements in aerodynamic wind tunnels
Pitot tube, pressure transducers, mass flow rate meters, thermal measurements with thermocouples; force measurements with dynamometric balances, acoustic measurements.

P.K. Kundu. Fluid Mechanics. Academic Press, San Diego, USA, 1990.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics 2ed., Course of Theoretical Physics vol. 6, Butterworth-Heinemann (1987)

H.H. Hubbard, editor. Aeroacoustics of Flight Vehicles: Theory and Practice. Volume 1 Noise
Sources; Volume 2 Noise Control (Nasa Reference Publication 1258). Acoustical Society of
America, 1995.

M.S. Howe. Acoustics of Fluid-Structure Interactions. Cambridge University Press, Cambridge,
UK, 1998.

W.K. Blake. Mechanics of Flow-induced Sound and Vibration, Volume I. Academic Press,
Orlando, 1986

Thomas J. Mueller, Aeroacoustic Measurements, Springer; 1 edition (2002)

Stavros Tavoularis, Measurement in Fluid Mechanics, Cambridge University Press (2005).

Lecture notes.

Preliminary sizing: weights estimate, mission profile, aero-structural preliminary sizing, propulsion, lofting.

Multidisciplinary conceptual design optimization: Local and global methods. multi-objective opt., matamodels and surrogates, DOE, KBE, robust optimization.

- Lecture Notes
- Sobieszczanski-Sobieski, Alan Morris, Michel van Tooren, "MULTIDISCIPLINARY DESIGN OPTIMIZATION SUPPORTED BY KNOWLEDGE BASED ENGINEERING", Wiley, 2015

The Analysis of Aeronautical Structures course is part of the activities of the Constructions and aerospace structures (ING-IND/04 SSD).

The teaching program is structured to provide students with knowledge and skills in the structural design of aeronautical components, using methods widely used in the aircraft detailed design phase.

The teaching program is divided into 36 lectures (equal to 9 CFU) divided into the following eight main sections:

1) Tensor Calculus Fundamentals: N-th order tensors. Tensor operations. Curvilinear coordinates. Covariant and contravariant base vectors. Vectors and tensors in curvilinear coordinates. Differential operators in curvilinear coordinates.

2) Kinematics of Deformable Continua: Lagrangian and Eulerian descriptions of motion. Finite strain theory. Displacement and deformation gradient tensors. Polar decomposition theorem. Lagrangian and Eulerian finite strain tensors (Cauchy-Green and Eulero-Almansi). Rates of deformation tensors. Linearization of the finite strain theory (infinitesimal strain theory). Material and spatial descriptions of the continuity equation.

3) Dynamics of Deformable Continua: Material and spatial forms of linear momentum balance, Cauchy's theorem. Cauchy and Piola-Kirchhoff stress tensors. Material and spatial forms of the angular momentum balance. Material and spatial forms of the mechanical energy balance.

4) Thermodynamics of Deformable Continua: Material and spatial forms of the energy balance. Stokes' heat flux theorem. Material and spatial forms of the thermodynamic energy balance. The second law of thermodynamics.

5) Constitutive relations theory: Noll's axioms. Limitations on the constitutive relations due to the second law of thermodynamics. Constitutive relations for thermoelastic materials: definition of isothermal elastic tensor, thermal stress tensor, and thermal conductivity tensor. Constitutive equation for linear isotropic thermoelastic materials.

6) Thermoelastic problems in aeronautical structures: Uncoupled thermoelastic formulation. Initial boundary value problem of the heat conduction equation. Thermal stress analysis for elastic bodies subjected to external and thermal loads: Euler-Bernoulli beam and Kirchhoff plate.

7) Finite Element method: Strong and weak forms of the uncoupled thermoelastic problem. The relation between strong and weak forms and boundary conditions. Virtual work principle. Discretization and definition of shape functions. Shape function choice criteria. Evaluation of element mass, stiffness and damping matrices. Evaluation of equivalent nodal loads vector. Assembly procedure. The imposition of displacement constraints. Conformal elements. Non-conformal elements – patch test. Isoparametric elements. Standard methods for shape functions construction. Applications in aeronautical problems: truss, beam, plate, and shell.

8) Introduction to the code Autodesk Inventor: Geometric preprocessor. Material properties definition. Constraints and external loads imposition. Solution methods. Post-processing. Structural analysis of a wing and/or a fuselage.

- M.E., Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981 (for contents 1, 2, 3 and 5 of the syllabus)

- Boley, B.A, Weiner. J.H., Theory of Thermal Stresses, John Wiley & Sons, New York, 1960 (for contents 4, 5 and 6 of the syllabus)

- Thomas J.R., Hughes, ‘The Finite Element Method – Linear Static and Dynamic Finite Element Analysis,’ Dover, 2000 (for content 7 of the syllabus)

- T.H.G., Megson, Aircraft Structures for Engineering Students, Arnold, London, 1999 (for content 7 of the syllabus)

- Lectures notes by the teacher (for all the contents of the syllabus)

The educational material used by the teacher from time to time is indicated during lectures. The lecture notes are made available on the Moodle platform to facilitate their use for both attending and non-attending students. On the same platform, are also made available the specifications of the project the students have to perform during the year, as well as a collection of written tests of previous exams, to provide students with a valid and realistic test bench for the final exam.