The course aims at providing foundational knowledge for understanding
linear and nonlinear dynamical behaviors of structures. It
opens with the formulation of the dynamic model, addressing kinematic
descriptors of motion, rheological models for constitutive behavior,
and external actions. Both linear and nonlinear structural
models are introduced through the corresponding laws of motion.
In the linear framework, the course analyzes harmonic motion and
the free response of the simple harmonic oscillator, including damping
effects. Forced dynamics is explored with emphasis on direct
resonance under harmonic excitation, as well as parametric resonance
in systems possessing geometric stiffness. Multi-degreeof-
freedom systems are studied via modal analysis and the theorem
of modal expansion, including cases with indirect harmonic excitation.
The nonlinear part focuses on paradigmatic systems such as the
Duffing and Van der Pol oscillators. Analytical techniques for nonlinear
equations, particularly the Method of Multiple Scales, are presented
alongside nonlinear normal modes. The effects of damping
and nonlinearities on resonance phenomena, including internal resonances
in multi-degree- of-freedom systems, are discussed. Applications
are developed through case studies supported by symbolic
computation tools.
22, 24, 26 June 2026 and 1, 3, 6, 8 July 2026
Location
Aula Riunioni 329
Dipartimento di Ingegneria Strutturale e Geotecnica
Via Eudossiana 18, Roma