AIMS AND LEARNING OUTCOMES

The course provides basic theoretical foundations and technical references for the dynamic analysis of structures subject to forcing considered as deterministic actions. Students will be able to study the dynamic response of simple structural systems in relation to the main environmental dynamic actions (wind and earthquake). The approach through discrete systems is privileged, not forgetting to provide the basis for the dynamic analysis of simple structures (strings and beams) treated as continuous systems.

The course also intends to provide a first approach to experimental dynamic analysis with a Didactic Laboratory of "Experimental Modal Analysis", introduced starting from 2016. In this way it is possible to have an impact on student learning in terms of: (a) experience with physical models of structures for a deeper understanding of structural schemes; (b) comparison between numerical prediction and experimental evaluation with awareness of the limits of the idealizations introduced in the modeling; (c) introduction to the world of electrical transduction measurements, increasingly widespread due to the growing need for monitoring structures and infrastructures.

All the examples and the elaborations will be carried out in Matlab environment, with the possibility of a direct application of all the formulations described during the course.

TEACHING METHODS

Lectures are held both using the blackboard (traditional or on multimedia support in the case of online learning) and with the aid of a video projector. The teaching material and the outline of the lectures are available on Aulaweb, also indicating possible books to complement the lectures. The theory lectures are accompanied by the development of application examples representative of real cases. A significant part of the final part of the course (about 10 hours) is dedicated to the Experimental Modal Analysis Laboratory in which the students, divided into small groups,  instrument a simple structure by carrying out the practical exercise in first person (not only by attending it). In this way it is possible to put into practice most of the notions learned during the course, at the same time experiencing the difficulties inherent in an experimental practical test.

SYLLABUS/CONTENT

Discrete systems with one degree of freedom
Free vibrations, Forced vibrations, Notes on "Damping in Buildings", Numerical integration, Frequency analysis (simple harmonic force, periodic and aperiodic force), notes on rheological models, discrete Fourier transform,
Response spectrum and seismic response spectrum
Discrete systems with N degrees of freedom
Equations of motion, Real examples, Free undamped vibrations, Static condensation of the degrees of freedom, Matlab code for the modal analysis of plane structures (matrix formulation of the displacement method),
Forced undamped vibrations, Forced damped vibrations, Classically damped structures - Frequency analysis, Modal truncation, Seismic analysis, Introduction to control systems, Hints on complex modal analysis
Experimental Modal Analysis Laboratory
Construction of a frame and its numerical modeling, test design, vibration measurement, experimental modal analysis and comparison with model predictions.
Introduction to the Dynamics of Continuous Systems
Equations of Motion, Properties of Operators (Differential Approach), Free Undamped Vibrations, Forced Vibrations, Application Examples

RECOMMENDED READING/BIBLIOGRAPHY

Notes of the course (AulaWeb)

Video of the lectures (Teams)

Muscolino, G. (2012). Dinamica delle strutture con fondamenti ed applicazioni di ingegneria sismica e dinamica aleatoria, Pitagora 

Inman, D.J. (2014). Engineering Vibrations, 4th Ed., Pearson