stochastic differential equations for structural engineering

Department of Civil and Environmental Engineering
Ph.D. programme in Structural, Seismic and Geotechnical Engineering
ACADEMIC YEAR 2016 – 2017
STOCHASTIC DIFFERENTIAL EQUATIONS FOR STRUCTURAL
ENGINEERING
Held by Prof. Claudio Floris
COURSE DESCRIPTION
- Theory of the stochastic processes with emphasis to the process calculus.
Itô's and Stratonovich's integrals, Wong-Zakai's corrective terms. Classic
stochastic differential equations (SDE): Brownian motion, scalar SDE's
(generalized Langevin equations), multidimensional SDE's. Fokker-PlanckKolmogorov's differential equation and Kolmogorov backward differential
equation, solutions in the transient regime and at the equilibrium.
- Examples relevant for the Structural Engineering: the stochastic second
order oscillator with external or parametric excitation, the seismic and wind
excitation; the continuous beam modelled as a s.d.o.f. system; the Duffing
oscillator as model of a beam or a plate with second order effects.
- Approximate methods for the statistical characterization of the solution X(t)
or X(t) of an SDE: equivalent linearization, moment equation approach,
stochastic averaging.
Bibliography:
- Arnold L., Stochastic Differential Equations: Theory and Applications, Wiley
Interscience
- Di Paola M., Stochastic Differential Calculus. In: F. Casciati (Editor) Dynamic
Motion: Chaotic and Stochastic Behaviour, Springer Verlag, Wien, 1993, pp.
29-92
Politecnico di Milano
Department of Civil and Environmental Engineering
Piazza Leonardo da Vinci, 32
20133 Milano
Tel. 02 2399 4322
Fax 02 2399 4300
[email protected]
Partita Iva: 04376620151
Codice fiscale: 80057930150
- Lin Y.K., Cai G.Q. Probabilistic Structural Dynamics: Advanced Theory and
Applications, McGraw-Hill
- Muscolino G., Dinamica delle Strutture, Pitagora
- Papoulis A., Probability, Random Variables, and Stochastic Processes,
McGraw-Hill.
- Soong T.T., Grigoriu M., Random Vibration of Mechanical and Structural
Systems, Prentice Hall
- Wong E., Stochastic Processes in Information and Dynamical Systems,
McGraw-Hill
Teaching activities:
- 25 hours (laboratory and classes)
- From November to December 2016