1. Dynamics and vibration of single, two and multi-degree-of-freedom systems
1.1 Free and forced vibrations of single-degree-of-freedom linear systems. Natural frequency and damping factor. The Frequency Response Function. The superposition principle and the response to different kinds of input (step, harmonic, periodic, non-periodic).
1.2 Non-linear vibration of single-degree-of-freedom systems. Non-linear motion equation and linearization about a certain equilibrium position. Free non-linear vibration: dependency of the natural frequency on the oscillation amplitude. Forced non-linear vibration: jump phenomenon, subharmonics and combination harmonics.
1.3 Two and multi-degree-of-freedom systems. Non-linear motion equations and linearization about a certain equilibrium position. Free and forced vibrations of two and multi-degree-of-freedom linear systems. Natural frequencies, vibration modes, Frequency Response Function.
1.4 Principal coordinates and modal superposition approach. Modal parameters identification.
2. Vibrations in continuous systems
2.1 Transversal vibrations in stretched strings. Wave equation. Wave propagation solution and standing wave solution. Natural frequencies, vibration modes, forced response.
2.2 Introduction to simple elastic beam models. Euler-Bernoulli beam theory.
2.3 Axial vibrations in beams. Natural frequencies, vibration modes, forced response.
2.4 Torsional vibrations in circular shafts. Natural frequencies, vibration modes, forced response.
2.5 Bending vibrations in slender beams. Natural frequencies, vibration modes, forced response.
2.6 Principal coordinates and modal superposition approach.
3. Introduction to finite element method
3.1 Discretization of the continuous domain into a set of sub-domains: mesh and degrees-of-freedom.
3.2 Euler-Bernoulli beam element: reference systems, degrees-of-freedom, shape functions, inertia and stiffness matrices.
3.3 Modelling of planar beam structures. Coordinate transformation from the local to the global reference system. Assemblage procedure to obtain the matrices of a complete structure. Expression of the nodal forces corresponding to concentrated and distributed loads. Structural damping model.
3.4 Natural frequencies, vibration modes, forced response, motion imposed to the supports.
3.5 Examples and applications.
4. Stability of mechanical systems subjected to non-linear force fields
4.1 Definition of force field. Conservative and non-conservative force fields. Mathematical models of aerodynamic forces and contact forces.
4.2 Stability analysis of single-degree-of-freedom systems, about a certain equilibrium position. Static and dynamic instability.
4.3 Stability analysis of two-degrees-of-freedom systems, about a certain equilibrium position. Flutter instability.
4.4 Examples and applications.
Lecture handouts, training material and proposed exercises will be made available on the course web page.