The course aims to provide students with the knowledge and basic methodological tools necessary to analyze the dynamic behavior of structures. These tools will allow students to understand the causal connections between the physical-mechanical phenomenon and the general criteria relative to sturctural dynamics for discrete and continous systems.
Course Prerequisites
Calculus I and II. General phisics. Statistics.
Teaching Methods
a. Blackboard lectures and applications (blackboard-based and/or numerical); b. Laboratory sessions; c. Individual assignments; d. Midterm assessments (optional).
Assessment Methods
Written exam followed by an oral exam, subject to successful completion of the written exam.
Texts
Iervolino I. (2021), Dinamica delle Strutture e Ingegneria Sismica. Hoepli, Milano.
Contents
1. Single-degree-of-freedom systems a. Equations of motion for linear elastic systems with viscous damping; b. Free vibrations; c. Harmonic and periodic excitation; d. Active and passive vibration isolation; e. Step, rectangular pulse, and impulse excitations; f. Convolution integral; g. Numerical integration of the equations of motion: the Newmark method; h. Seismic base excitation and elastic response spectra; i. Introduction to the dynamics of nonlinear inelastic systems.
2. Multi-degree-of-freedom systems a. Mass, stiffness, flexibility, and viscous damping matrices; b. Equations of motion for damped and undamped systems, in absolute and relative coordinates; equations of motion in flexibility form; c. Mode shapes and decoupling of the equations of motion for classically damped systems; d. Computation of mode shapes; e. Response analysis of linear systems by modal superposition; f. In-phase and out-of-phase harmonic excitations, and arbitrary excitations; g. Modal response spectrum analysis of structures; h. Static condensation of the stiffness matrix.
3. Distributed-mass systems (continuous systems) a. The beam in free longitudinal vibrations (P-wave equation); b. The shear-deformable beam in free transverse vibrations (S-wave equation); c. The Euler–Bernoulli beam undergoing free flexural vibrations.
