Perturbation methods: theory and applications (River Morphodynamics and Structural Mechanics)

Lecturers: Marco Tubino (DICAM); Francesco Dal Corso (DICAM); Niccolò Ragno (DICAM)

Period: 17 - 21 June 2024 

Timetable: will be posted as soon as available

Programme: 

Part one: Perturbation methods
1. Introduction to perturbation methods: asymptotic expansions, uniform perturbations, singular perturbations
2. Examples of singular perturbations: boundary layer, infinite domain, resonance
3. Matched asymptotic expansion
4. Multiple scale technique

Part two

a. Perturbation methods and river morphodynamics
1. River bars: linear stability theory (temporal and spatial modes)
2. River bars: weakly nonlinear theory and amplitude equation
3. River meandering: linear theory and resonance
4. River meandering: weakly nonlinear theory for resonant meanders
5. Free-forced interactions, curvature and width variations
6. River bifurcations: equilibrium and stability

b. Perturbation methods for dynamics and stability of structures and solids
1. Quasi-static bifurcation of 1 and 2 dof
2. Quasi-static bifurcation of one-dimensional continuous system
3. Dynamic bifurcation under follower load
4. Dynamic bifurcation under parametric resonance
5. Dynamic self-tuning of structures
6. Localization of deformation in solids

Final assessment: solution of a perturbative problem chosen by the student or selected among those proposed (in itinere and at the end of the course).

Duration: 32 hous (4 credits)

Registration: in order to access the course, please send an e-mail to dicamphd [at] unitn.it